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Time Scale for Cold-Air Pool Breakup by Turbulent Erosion

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Time Scale for Cold-Air Pool Breakup by Turbulent Erosion MeteorologischeZeitschrift, V ol. 12,No.4, 229-233(August 2003) c by Gebruder¨ Borntraeger 2003 Article Time scale for cold-air pool breakupby turbulenterosion SHIYUAN ZHONG1, XINDI BIAN2, and CHARLES DAVID WHITEMAN 3 1Departmentof Geosciences,University ofHouston, Houston, TX 2 USDAForest Service,East Central Research Station, East Lansing,MI 3Pacic NorthwestNational Laboratory,Richland, W A (Manuscriptreceived November 15, 2002; in revisedform March 27, 2003; accepted May 2, 2003) Abstract Turbulent erosion has been proposed asamajor mechanismfor removing wintertime cold-air pools (CAPs) from basins and valleys. The timescales involved in this erosion process, which areof great interest for winter weatherforecasting, have not been studied systematicallyin the past. In this short contribution, a semi-analyticalmodel is developed to estimatethe timerequired for the dissipation of cold airpools from above by downward micro-scaleturbulent erosion for different wind speeds aloft, different staticstabilities inside the cold pool, and for different basin crosssections. The calculations show that micro-scaleturbulent erosion is arather slow process and that the erosion ratedecreases rapidly with timeas staticstability increases in the capping inversion atthe top of the cold pool. The rateof erosion is determined mainly by wind speed above the CAP and the temperatureinversion strength inside the CAP; it is lesssensitive to the shape of the topography.Shallow CAPs of afewtens of metersin depth with aweakinversion maybe removed in a matterof hours if winds aloft aresuf ciently strong to initiate and maintain turbulent mixing. It is unlikely, however, that deeper CAPs with amoderateto strong inversion canbe destroyed by micro-scaleturbulent erosion unless combined with other regional and synoptic-scale processesthat produce larger-scaleturbulent mixing. Zusammenfassung Erosion durch Turbulenz ist schon lange alswesentlicher Prozess bei der Zerstorung¨ von winterlichen Kaltluftseen in Becken und T¨alern betrachtet worden. DerZeitraum diesesErosionsprozesses, der beson- ders wichtig fur¨ Vorhersagen imWinter ist, ist bis jetztjedoch noch nicht systematischuntersucht worden. In diesemBeitrag wird ein semi-analytischesModell beschrieben, das die benotigte¨ Zeit fur¨ die Au osung¨ einesKaltluftsees durch mikroskalige turbulente Erosion von oben absch¨atzt. DiesesModell berucksichtigt¨ die Windgeschwindigkeit oberhalb und die Stabilit¨atinnerhalb des Kaltluftseessowie den Querschnitt des Beckensbzw. Tales.Die Berechnungen zeigen, dassmikroskalige turbulente Erosion ein langsamerProzess ist und dasssich die Erosionsrate imLaufe der Zeit stark verlangsamt, wenn die statischeStabilit¨ at in der abgrenzenden Inversion oberhalb des Kaltluftseeszunimmt. DieErosionsrate wird vor allemvon der Windgeschwindigkeit oberhalb des Kaltluftseesund vom Temperaturgradienten innerhalb des Seesbestimmt. DerQuerschnitt des Beckensbzw. Talesspielt dabei eine weniger wichtige Rolle. Ein acherKaltluftsee von einigen Metern ( 50 m)mit einemschwachen T emperaturgradienten kann durch mikroskalige turbulente Erosion in einigen Stunden zerstort¨ werden, wenn die Windgeschwindigkeit oberhalb des Seesausreichend ist, um turbulente Durchmischung zu initiieren bzw. aufrechtzuhalten. Es ist unwahrscheinlich, dassein tiefer Kaltluftseemit einemm¨ aßigen bis starken Temperaturgradienten allein durch mikroskalige turbulente Ero- sion zerstort¨ werden kann, außer dass regionale oder synoptische Prozessevorhanden sind, die groߨ ere Wirbel verursachen. 1 Introduction ceptablyhigh levels in CAPs that last formany days (REDDY et al., 1995).CAPs canalso affect the valley Acoldair pool(CAP) is anaccumulation of cold air in a orbasin populationby producing hazardous episodes of basin orvalley (relative to the air abovethe valley) that persistent freezingrain, drizzle orfog,interfering with is characterized bya persistent temperature inversion. air andground transportation (S MITH et al., 1997).Un- CAPs are especially prevalentin the winter in basins or derstandingthe mechanisms leadingto CAPformation valleys havingpoorly developed along-valley wind sys- anddestruction is aproblemof practical as well as scien- tems. Highstatic stability in CAPs cantrap air overnight tic interest. Several mechanisms havebeen proposed. or,in mid winter,for many days or evenweeks, allow- Inthe warmseason, diurnal CAPs formon near-calm ingpollutants, cloudsand moisture to buildup. For ur- nights byradiative cooling;they dissipate the nextmorn- banizedbasins, air pollutioncan accumulate to unac- ingwhen convection begins after sunrise (P ETKOVSEK , Correspondingauthor: C. DavidWhiteman, Paci c Northwest 1985; WHITEMAN and MCKEE,1982).During the cold NationalLaboratory, P .O.Box 999, Richland, W A99352,USA, season,insolation alonemay be insuf cient to dissi- e-mail:[email protected] 0941-2948/03/0012-0231$ 02.25 DOI:10.1127/ 0941-2948/2003/0012-0231 c Gebruder¨ Borntraeger, Berlin, Stuttgart 2003 230 S.Zhonget al.:Time scale for cold-airpool breakup Meteorol.Z., 12, 2003 pate CAPs andseveral otherphysical processes have aloft continuesto increase, turbulenceproduction pro- beenlinked to their breakupsincluding cold air ad- ducedby vertical windshear mayeventually overcome vectionaloft (Z HONG et al., 2001),frontal passages the turbulenceconsumption caused by negative buoy- (WHITEMAN et al., 2001),air drainagefrom valleys ancyand dissipation. Asaresult, adownwardturbulent (ZAN¨ GL,2002),and turbulent erosion at the topof the sensible heat ux rcpq w is producedand the process of pool (PETKOVSEK ,1978,1985, 1992; V RHOVEC and turbulenterosion begins. When this downwardsensible HRABAR, 1996; RAKOVEC et al., 2002).Turbulent dis- heat uxbecomes equal to orgreater thanthe heat decit sipation orerosion was rst suggestedby P ETKOVSEK in ashallow layer ofcoldair at the topof the CAP,the (1985,1992) as amechanism forremoving CAPs in coldair layer dissipates byerosion. arelatively widebasin. Using an analytical approach, We use S to denotethe horizontalarea at the topof heproposed two conditions that are necessary fortur- the CAP.Asturbulenterosion removes the air layer-by- bulenterosion to work: rst, astrongwind above the layer fromthe topof the coldpool, the topof the cold coldair poolis requiredto initiate the erosionprocess; pooldescends and the area S decreases (exceptin the second,this windspeed must increase continuouslyto special situation wherethe slope angle a is 90 ). The maintain the process.For typical Slovenianbasins he total sensible heat transporteddownward across the area foundthat awindspeed of 7 to 9ms 1 is required S duringa small time period Dt canbe calculated as forshear-generated turbulent mixing to start to erodethe r c q w S Dt (2.1) temperature inversionfrom above. Because the capping p inversionat the topof the coldpool tends to strengthen Theheat decit within ashallow layer nearthe topof duringthe erosionprocess, wind speeds abovethe cold the CAPcan be estimated using poolhave to increase continuouslyso that the increase in DQ r cp Dq DV (2.2) shear productioncan compensate the increase in buoy- ancyconsumption and maintain turbulence.This re- where DV is the volumeof the layer. quirementfor a continuousincrease in windspeed above Forthis shallow layer ofcoldair to beremoved, the the CAPwas supportedby numerical simulations ofan turbulentsensible heat transporteddownward from the idealized basin byR AKOVEC et al. (2002).In their ideal- topmust equalor exceed the heat decit ofthis layer, ized simulations, the windspeed above the CAPstopped i.e., 1 increasing after reaching15 m s .Theerosion of the r c q w S Dt r c Dq DV (2.3) basin inversion,which started at awindspeed around p p 7 m s 1,ceased after the windspeed stopped increasing. Thetime requiredfor removing this shallow layer of Turbulentdissipation was also investigated bythe nu- coldair, therefore,is RHOVEC RABAR merical studyof V and H (1996)as one r cp Dq DV Dq DV ofthree mechanisms fordissipation ofdeep wintertime Dt (2.4) CAPs.Their study also conrmed that awindspeed in- r cpq w S q w S crease is necessary forturbulent erosion to continue.It Thedownward turbulent sensible heat ux q w can be also pointedout that CAPdissipation couldtake along describedusing K-theory (L UMLEY and PANOFSKY, time to complete (upto 11hours)even with windspeed 1964) as accelerations as large as 2.5m s 1 h 1. Theamount of time neededfor turbulent erosion to ¶q Dq q w Kh Kh (2.5) removea CAPis ofgreat interest forwinter weather ¶z Dz forecasting in basins andvalleys. Inthis short contri- Substituting (2.5)into (2.4)yields asimple equationfor bution,we propose a methodfor estimating the time Dt, requiredto dissipate CAPs byturbulent mixing from Dq DV Dq DV DV Dz abovefor different windspeeds, stabilities, andbasin Dt (2.6) Dq K S cross sections. q w S Kh Dz S h Here, Dq cancels in the equationif weassume that the 2 Method depthof the layer removedis the same as the depthof the layer overwhich the turbulentsensible heat uxis cal- Asshownin Fig.1, we assume that aCAPhas anini- culated usingthe bulkapproximation based on K theory. tial depth h,apotential temperature difference qb qc The area S and volume DV are geometric parameters within the pool,and a shallow cappinginversion layer determinedby the shapeof the basin.For a circular basin (CIL)with apotential temperature difference q q . a b with aoorradius of r f lr anda constant slope angle a Wealso assume that windspeed above the topof the the horizontalarea at height z is CAP is u andwithin the
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