P 452 DETERMINING RELEVANT TURBULENT SCALES AND SOURCE VARIABLES FROM CONTAMINANT CONCENTRATION DATA

Transcription

1 P 45 DETERMINING RELEVANT TURBULENT SCALES AND SOURCE VARIABLES FROM CONTAMINANT CONCENTRATION DATA Andrew J. Annun, Sue Ellen Haupt, and Gerge S. Yung The Pennsylvana State Unversty, Appled Research Lab and Department f Meterlgy. Intrductn Varus meterlgcal varables and cntamnant surce characterstcs can be back calculated frm cntamnant cncentratn bservatns. In sme atmspherc transprt and dspersn (AT&D) applcatns, such as mdelng an accdental r ntentnal cntamnant release, t s necessary t d s n rder t mtgate the cntamnant threat and predct AT&D dwnwnd. T accurately determne these varables ne must ascertan the mean drectn f cntamnant travel fr ether nstantaneus r cntnuus releases, and the puff translatn speed fr an nstantaneus release. Ths ssue s addressed n prr wrk where surce characterstcs, as well as these atmspherc transprt varables are back-calculated frm cncentratn data (Haupt 005; Allen et al. 007; Lng et al. 00). There, cntamnant plume r puff dspersn parameters were assumed t be knwn and were determned frm Pasqull Gffrd stablty classes. Here we elmnate that assumptn and nstead deduce the dspersn parameters frm cnvectve scalng parameters (Deardrff 974),.e. the length and velcty scales f the bundary layer spannng eddes (BLSE, Deardrff 970). The frmer s the depth f the Atmspherc Bundary Layer (ABL),, whle the latter s the cnvectve scale velcty, w, that s gven by g 3 w ' ' w v () v g where w' v' s the buyancy flux. Therefre we v als retreve these scalng varables, whch s mprtant n predctn f subsequent cntamnant dspersn. Here we back-calculate nt nly the cnvectve bundary layer depth and the cnvectve velcty scale, but als the remanng varables requred fr AT&D mdelng f a cntamnant release ncludng the surce nfrmatn. Intentnal and accdental cntamnant releases can ccur n the mxed layer r surface layer, and can be ether nstantaneus r cntnuus. Crrespndng authr address: Andrew J. Annun, The Pennsylvana State Unversty, Appled Research Lab and Department f Meterlgy, State Cllege PA, 6804; emal: aja99@psu.edu Therefre, these varables are back-calculated fr these fur scenars: surface layer and mxed layer surces, each cnducted as bth nstantaneus and cntnuus releases. The number f unknwn varables depends n the release type. Fr an nstantaneus release, we ascertan seven varables (mean puff transprt speed, the drectn f cntamnant travel, the cnvectve velcty scale, the bundary layer depth, the alng-wnd and crss-wnd surce lcatn, and the surce strength). Fr a cntnuus release, we determne these same varables except fr transprt speed because ths varable s nt separable frm the surce strength n a back calculatn frm a steady state cntamnant cncentratn feld. In sectn, we descrbe the technque used t determne the unknwn varables. In sectn 3 we determne the prper sensr dman se and the apprprate dspersn parameters fr all fur scenars. Then n sectn 4, we test the algrthms ablty t back-calculate the unknwns fr all fur scenars. Sectn 5 summares the results, dscusses the sgnfcance f the wrk, and cnsders the prspects fr future wrk.. Methds We wsh t determne, frm a tme seres f surface cntamnant cncentratn values, the mean depth f an unstable ABL and the cnvectve scale velcty as well as the ther varables relevant t AT&D. Ths back calculatn s accmplshed va a pwerful ptmatn technque that tunes these varables s as t match bserved cncentratn values t thse cncentratn values calculated by a dspersn mdel. Thus, the unknwns are determned ndrectly thrugh frecasts f surface cncentratn values as n Haupt (005), Allen et al. (007), and Lng et al. (00). a. Dspersn Mdel Selectn Because ur technque (descrbed n sectn b) requres the creatn f a cncentratn frecast fr each f numerus tral estmates f the unknwn varables, ur dspersn mdel must be cmputatnally effcent. Hwever, t match the bserved cncentratn values, t s necessary that the dspersn mdel captures the prmary effects f cnvectve bundary layer (CBL) turbulence. The structure f the CBL s relatvely well understd frm numercal experments, cnvectve tank experments, and frm atmspherc bservatns (Deardrff 97;

2 Kamal et al. 976; Panfsky and Duttn 984). When cnvectn dmnates turbulence prductn (.e. 0 where L n the Mnn-Obukhv length), L the resultng turbulence statstcs scale wth the cnvectve velcty scale, w, and the bundary layer depth, Deardrff (970). Thus, under cnvectve cndtns, the alng-wnd and crss-wnd turbulence statstcs t depend n rather than the heght, abve the surface (Panfsky 977). The vertcal turbulence cmpnent, hwever, s dependent n bth and because f the exstence f upper and lwer bundares t the CBL (Wyngaard 988). The nature f vertcal dspersn depends n the prfle f w and the skewness f the vertcal velcty prbablty dstrbutn functn (PDF) resultng frm an unequal area ccuped by updrafts and dwndrafts (Wyngaard 987 and Wel 990). These phenmena cause nn-gaussan behavr n vertcal cntamnant dspersn (Wyngaard 987; Wel 990) ncludng cunter-gradent fluxes at sme levels wthn the CBL. Mrever, they cause the plume centerlne r puff centrd t change heght wth dstance dwnstream f the surce (Wlls and Deardrff 975; Lamb 98). The resultng mean ascent f cntamnants fr a surface release and mean descent f cntamnants fr a mxed layer release must be captured n a successful mdel f CBL dspersn. In ths wrk we cnsder nstantaneus as well as cntnuus surces f cntamnants. The tempral averagng pssbltes dffer fr these tw surce types, s we must be careful n chsng the prper dman se fr the sensr grd t enable accurate back calculatn f the unknwn varables. These ssues are dscussed n sectn 3. ) Surface Layer Release The ensemble averaged cntamnant feld fr a surface release ntally spreads laterally and vertcally thrugh the surface layer befre the BLSEs cause t t meander vertcally thrugh the verlyng mxed layer (Wel 988; Wlls and Deardrff 975). Althugh Gaussan dspersn cannt accunt fr ths vertcal meander f cntamnants, t s shwn that a Gaussan mdel can descrbe ensemble averaged surface cncentratn values fr a near surface release wth sme success (Deardrff and Wlls 975; Hadfeld 994). The degree f ths success s dependent n the vertcal dspersn parameters chsen as well as the nn-dmensnal dstance frm the surce (see sectn 3) (Wlls and Deardrff 976). The Gaussan apprxmatn hlds best clse t the surce and fr lng averagng perds. In ths stuatn, the apprprate dspersn mdel s a Gaussan wth a grund reflectn term. C( x, y, t) exp y y exp y Q U exp y where x, y, and span the Eucldean crdnate system, t s tme, Q s the release rate, U s the mean wnd speed, y s the crss-wnd surce lcatn, s the surce heght and y and are the lateral and vertcal dspersn parameters respectvely. These dspersn parameters are dependent n the dwnwnd dstance frm the release lcatn. In cntrast, fr an nstantaneus release n the surface layer, t s nt pssble t match cntamnant AT&D durng the ntal grwth stage because nly ne release event s avalable, s ne cannt perfrm an average. Wthut such averagng, bserved cntamnant cncentratn wll exhbt eddydrven meanderng and dstrtns that are nt captured by ensemble mean dspersn mdels such as the Gaussan. In ths stuatn t s necessary t sample a cntamnant when t s well mxed n the vertcal and back-calculate bundary layer depth by the drect apprach. Fr ths stuatn, we agan mplement a Gaussan mdel; hwever, reflectn terms that accunt fr puff entrapment are als ncluded. Assumng that the cntamnant puff centrd translates dwnwnd at cnstant velcty, () becmes C( x, y, t) exp exp exp y y N n n n y n 3 Q exp U x y n 0 exp exp where U s the puff translatn speed. ) Mxed Layer Release x x x Ut The average AT&D fr a mxed layer release s markedly dfferent than the AT&D f a surface release. Because the average effect f cnvectve elements ntally cause cntamnants t descend t the surface, predctng surface cncentratn values va tradtnal Gaussan dspersn fr a mxed layer release wll cause sgnfcant errrs. A passve () (3)

3 cntamnant descends t the surface at a velcty prprtnal t the cnvectve velcty scale, w, wth ths descent resultng n ensemble averaged surface cncentratns values near the surce lcatn beng abut.9 tmes greater than predcted by a tradtnal Gaussan mdel (Wlls and Deardrff 98; Lamb 98; Wel 988; Brggs 993). T accunt fr ths effect, Wel (988) develped a cmputatnally effcent dspersn mdel based n the prbablty densty functn (PDF) f vertcal velcty. Adptng a smlar apprach t that used t descrbe the vertcal velcty PDF (Msra 98), vertcal cntamnant dspersn s descrbed by a superpstn f tw Gaussans. Assumng that crsswnd dspersn s Gaussan, plume dspersn fr a mxed layer release s gven by Wel (988, 997) as Qt ( y y) C( x, y, t) exp U y y N n N ( n w j ) exp (4) j j j j ( n w j ) exp j where j determnes the nput frm the updrafts and w dwndrafts, j s the updraft and dwndraft speed, and the value f j specfes an updraft r dwndraft. The dspersn parameters j depends n w, j, the standard devatn f the vertcal velcty, and j, w j, and w, j are fund by equatng mments f the vertcal velcty PDF (Wel 990; Wel 997). Fr an nstantaneus mxed layer release, we encunter the averagng prblem descrbed abve fr a surface layer release. Takng a smlar apprach we agan mdfy (4) by assumng an nstantaneus release and that the puff translates dwnwnd at cnstant velcty t prduce Qt C( x, y, t) exp U x y ( y y) exp y N n N ( n w j ) exp j j j j ( n w j ) exp j x x Ut) x (5) b. The Hybrd Genetc Algrthm An ptmatn technque s requred t btan an accurate estmate f the unknwn surce and meterlgcal varables by matchng bserved and predcted cncentratn felds. Gven the dffculty f ths prblem, the ptmatn technque must be rbust n the face f a cmplex slutn space. Thus, we use a hybrd genetc algrthm (GA, Haupt and Haupt 004), a cmbnatn f a GA wth the Nelder- Meade Dwnhll Smplex (NMDS) technque. Ths hybrd methd s deal fr ths prblem because t s a glbal ptmatn technque that explres the entre slutn space befre cnvergng t the best estmate f the unknwn varables, and thus, f apprprately cnfgured, avds falsely cnvergng t a lcal ptmum. The GA ptmatn technque mmcs the prcess f natural selectn t btan teratvely mprved estmates f the unknwn varables (Haupt and Haupt 004). Fr a dscussn f the GA prcess, the reader s referred t Haupt and Haupt (004), Haupt (005), Allen et al. (007) and Lng et al. (00). Our cst functn quantfes the ftness f each chrmsme by cmputng the dfference between the resultng cncentratn frecast and the cncentratn bservatns. Instead f drectly cmparng the cncentratn values, we cmpare the lgarthm f the cncentratn values s as t transfrm the Gaussan nt a quadratc, thereby enhancng the nfluence f cncentratn tals. Ths transfrmatn enables the algrthm t better match the spread f the cntamnant feld. T quantfy the dfference between predctns and bservatns, the cst functn sums the Eucldean dstance between the lgarthm f the cncentratn frecast and the lgarthm f the cncentratn bservatns ver all tme steps and grd pnts. Ths sum s nrmaled by the lgarthm f the cncentratn bservatns. Specfcally t s, N N (lg( Cs ) lg( Rs )) t s Nt Ns ( (lg( Rs )) ) t s t s where ε s a scalng factr added t the predctns and bservatns t avd takng the lgarthm f er, C s s a predcted cncentratn value at a sensr, R s represents a cncentratn value reprted by a sensr, Ns represents the number f sensrs, and Nt represents the number f tme steps. The GA fnds an apprprate estmate f the unknwn varables by teratvely mnmng ths cst functn. After the GA prduces an estmate f the unknwn varables wthn the ftness basn f the (6) 3

4 glbal mnmum f the cst functn, the NMDS algrthm s used t quckly fnd the bttm f that slutn basn. Thus, the GA s used t fnd the glbally ptmum slutn basn, whle NMDS cascades dwn the gradent f ths basn t fnd the glbal ptmum slutn. c. Identcal Twn Experment Fr mdel develpment we test ur methd n synthetc data created n an dentcal twn experment, wheren the assmlatng mdel als creates the bservatns (Daley 99). Thus, the cntamnant cncentratn bservatns are created by the dspersn mdels descrbed abve. Ths frmulatn allws us t best gauge f ur numercal experments are wrkng prperly; hwever, t may create an artfcally smple cst surface. These mdels may devate frm actual averaged cntamnant bservatns f the averagng s nt suffcent, the meterlgy s nnstatnary, r f the turbulence s nt hrntally hmgeneus. Therefre, t smulate these effects n a cntrlled manner, addtve clpped Gaussan whte nse s appled t the bservatns as n Lng et al. (009) and Allen et al. (007). Ths nse can be used t dstrt the cntamnant puff r plume shape. It des nt, hwever, represent the meanderng ntrduced by atmspherc fluctuatns whse length scales are larger than that f the cntamnant puff r plume. 3. Dman and Dspersn Parameter Cnsderatns The se f the sensr grd prves t be a crucal cnstrant when back calculatng the varables relevant t AT&D. In rder t accurately determne these varables, the sensr dman se shuld nt nly be large enugh t capture the cntamnant spread, but als extend far enugh dwnwnd that BLSE-drven meanderng and vertcal lpng have less mpact n the realatn s cncentratn feld than d plume spread. Ths range can be mnmed fr cntnuus releases by usng tempral averagng. Hw these factrs are accunted fr als depends n the cntamnant release heght as dscussed n sectns 3. and 3.. a. Surface Release ) Cntnuus Release A cntnuus release f cntamnants s advantageus fr the back calculatn prblem because we can average surface cncentratn values n tme f the meterlgcal cndtns are steady. The tme averaged cncentratns then apprach the ensemble average f the averagng perd s suffcently large. Ths averagng wll smth ut lateral meanderng; hwever, t wll nt average ut all f the effects f vertcal meanderng caused by the BLSEs (Lamb 98; Deardrff and Wlls 975). Ths averagng allws us t determne the apprprate sensr dman se fr a cntnuus surface layer release because the ensemble averaged plume grws wthn the surface layer and fllws the Gaussan mdel, as dscussed n sectn.., untl the nn-dmensnal dstance X = 0.5, where x w X (7) U where U s the mean wnd speed (Deardrff and Wlls 975; Wlls and Deardrff 976; Hadfeld 994; Ds et al. 003). Ths expressn results frm scalng tme by the large eddy tme scale and assumng Taylrs translatn hypthess. Ideally, we wuld lke ur dman t termnate at X = 0.5 fr all stuatns; hwever, ths s mpractcal because the sensr dman then depends n three meterlgcal varables that are unknwn fr ths prblem. Als, t s nt vable t adjust the sensr dman n real tme applcatns n respnse t meterlgcal cndtns. Therefre, the sensr dman s a cnstant x km grd fr cntnuus, surface release stuatns. Ths dman restrctn wll cause a slght ver-predctn f averaged surface cncentratn values near the edge f the dman fr relatvely shallw bundary layer depths, but ths wll nt ccur fr large bundary layer depths. Deardrff and Wlls (975) develped a vertcal dspersn parameter that successfully descrbes cntamnant spread n surface layer when turbulence prductn s dmnated by buyancy. Ths nterplates between Yaglm s free cnvectn lmt (Yaglm 97) and the neutral stablty lmt, as well as accuntng fr varatns n spread caused by the surce heght. Ths parameter s gven by where u 3 b' X 0.5X.8 X w (8) w u X b' (9) w u X and u s the frctn velcty. Because we nly search fr and w n (8), t s assumed that u s btaned frm wnd measurements. The lateral spread parameter des nt fllw ths expressn because the BLSEs d nt ntally cause nnlnear grwth f the hrntal cntamnant spread. The lateral spread frmulatn used here s that f Brggs (993) 4

5 y 0.6X X 6 (0) whch was determned frm the Cndrs expermental data merged wth data frm ther experments. Ths y nterplates between the near feld lnear grwth perd and the far feld 0.6 X 3 y grwth perd (Brggs 993). It s assumed that the lateral turbulence parameters wll nt change wth release heght. Therefre, ths expressn s used fr bth the surface release and the mxed layer release. ) Instantaneus Release The prblem facng the back-calculatn technque fr an nstantaneus release s mre dffcult because we cannt average the cntamnant bservatns n tme. Therefre, we must mdfy ur technque t mnme errrs caused by nadequate averagng. In these stuatns, the dman se must be much larger than that requred fr the cntnuus case. Ths dman enlargement s necessary because hrntal and vertcal meanderng may dsrupt the crrespndence between mdel and bservatns t even larger values f X f tempral averagng s nt used. Thus, we enlarge ur square dman such that each sde s a dstance equvalent t X 8. Increasng the dman se whle mantanng the same number f sensrs decreases ur sensr densty. We then determne the unknwn varables by matchng the lateral cntamnant spread and by determnng when the cntamnant s well mxed n the vertcal. The latter effect explctly prvdes nfrmatn n the bundary layer depth frm cntamnant entrapment. Because ur dspersn mdel ncludes reflectns, the vertcal dspersn parameter shuld nt asymptte t a cnstant value. The entrapment s descrbed by the reflectn terms, whch captures the vertcal hmgenatn f the cntamnant wth tme. Wth ths enlarged dman se, cntamnant dspersn s dmnated by mxed layer turbulence. Therefre the vertcal turbulence parameter used fr the cntamnant puff s gven by Wel (997): 0.6X 0.7X () Ths expressn descrbes the near feld lnear puff grwth and the far feld parablc puff grwth. The factr f 0.6 results frm assumng w 0.6w, whch s a vald assumptn fr Althugh the cntamnant release s n the surface layer, dspersn wll ccur thrughut the entre bundary layer, mplyng that ths assumptn s vald. Usng ths frmulatn, the Gaussan mdel (3) predcts unfrm cncentratn values near X = 3, whch s cnsstent wth bservatns. The nfrmatn prvded by ths vertcal dspersn s partcularly useful n real-tme applcatns, because the exstence f vertcal bundares as the surface and ensure that vertcal hmgenatn wll eventually ccur. In cntract, the bserved hrntal spread tends t be less than that predcted by () f averagng tmes are nadequate (Brggs 993). b. Mxed Layer Release Fr a mxed layer release, we mplement a dspersn mdel that accunts fr the vertcal meanderng f the plume centerlne r the puff centrd. Therefre ur requrements fr the dman se and dspersn parameters change slghtly. Fr a cntnuus cntamnant release n the mxed layer, the ntal puff grwth ccurs n the mxed layer, mplyng that the vertcal turbulence parameter fllws an expressn smlar t (). Thus, fr the cntnuus release ur frmulatn fr s smlar t (); but s adjusted t apply t ether an updraft r dwndraft as mplemented n equatn (4) (Wel 988; Wel 997). Because ths dspersn mdel accurately represents the ensemble averaged dspersn fr a mxed layer release, n restrctns are placed n the se f the sensr dman. T be cnsstent wth the cntnuus surface layer release, we use a x km grd fr all bundary layer depths. Fr the nstantaneus release, we take an apprach smlar t that mplemented fr the nstantaneus release n the surface layer wheren the dman s large t avd samplng cntamnant meanderng. 4. Results We test ths back-calculatn prcedure fr bundary layer depths rangng frm 500 m t 3000 m. Fr these bundary layer depths, w s als allwed t range thrugh typcal atmspherc values,.7 ms - and. ms -. Fr all smulatns we mantan a sensr dman as an 8x8 grd; therefre, the sensr densty decreases wth ncreasng dman se. The number f tme steps, N t depends n the release type; there s nly ne cncentratn feld fr a cntnuus release due t tme averagng, whle we use fve felds fr an nstantaneus release separated by equal tmes steps. The number f reflectn terms, N, s fve fr the stuatns that requre nfrmatn frm entrapment. Ths number s suffcent t smulate vertcal hmgenatn f the cntamnant. The tw release heghts tested are m fr the surface layer release and 00 m fr the mxed layer release. The hrntal surce lcatn fr all scenars s at the center f the sensr dman, (0,0). Because the GA s ntaled wth a ppulatn f randmed tral slutns, each smulatn wll take a dfferent path t the glbal mnmum. Thus, we make 50 runs f the methd fr each bundary layer scenar, and take the medan f these runs t estmate a lkely result fr 5

6 a sngle smulatn. We als test the mpact f bservatnal and atmspherc nse n the back calculatn t determne hw much nse the mdel can handle befre the back calculatn becmes less successful. The amunt f nse added t the cncentratn data s descrbed by the sgnal-t-nse rat (SNR). The SNR values used fr ths wrk are nfnty, 00, 50, 0, 5,, and. Fr ths back calculatn methd, a lw cst functn value des nt always mply that the ptmed varables match the truth. Therefre t s nstructve t valdate the back calculatn wth an alternate metrc that drectly cmpares the slutn t the exact value. The alternate metrc used s a skll scre that gves an ndependent assessment f mdel accuracy and represents the percentage errr f the mdel estmate. It s pssble t use skll scres n an dentcal twn experment because the varables t be determned are knwn prr t the back-calculatn. The skll scre we use fr bundary layer depth s gven by the errr nrmaled by plausble range where a f : a f a l S, f a : a f u f (), a s the actual bundary layer depth value,, f s the frecast bundary layer depth fund by the GA, and, l and, u are the lwer and upper bunds respectvely fr the GA search range n the back-calculatn f bundary layer depth. The skll scre cmputes a percent errr; therefre the clser t er the scre, the better the slutn. Smewhat arbtrarly, we take a skll scre less than 0. t ndcate a successful back calculatn. Smlar skll scre frmulae are appled t the ther unknwn varables. The ttal skll f the mdel s the sum f all the skll scres nrmaled by the number f unknwn varables. Skll scres are used because they prvde a means t quantfy the cmbned success f the methd acrss varables wth dfferent unts. a. Surface Layer Release Results fr bth the cntnuus and nstantaneus release n the surface layer cases are shwn n Fgure ; skll scres fr the cntnuus case are presented n Fgure a. Fr ths surce type and these atmspherc cndtns, the algrthm accurately estmates the unknwn varables when the sgnal s nseless, as expected. In fact, the errr results fr all bundary layer depths s f the rder 0-8, and thus excellent agreement wth the knwn slutn. As the SNR decreases, we expect the mdel skll t als decrease because the nse mpacts the nfrmatn cntent f the bservatns as seen n Lng et al (00). Fgure a cnfrms ths: the mdel errr scres ncrease as nse s added. At SNR 5 the mdel has an errr scre less than 0., errrs ncrease rapdly, hwever, wth further ncreases n nse. As SNR decreases frm t, the nfrmatn cntent f the cncentratn feld decreases t the pnt where the multvarate back calculatn s n lnger successful. Table dsplays the errrs and percent errrs f just the bundary depth predctns. Fr SNR 0, errrs n bundary layer depth are nt large and, n ths SNR range, the errr n bundary layer depth predctns remans belw 0%. When SNR s decreased t 5, errrs n bundary layer depth reman mnr fr 750 ; hwever, errrs becme larger (between 0% and 0% errr) fr deeper bundary layers. These errrs ncrease as the SNR appraches, where errrs n bundary layer depth becme greater than 0%. Fr a surface layer nstantaneus release, the dman se must be suffcently large t sample the cntamnant when t s vertcally hmgened. That ccurs near X 3. The back calculatn skll scres are shwn n Fgure b. As wth the cntnuus release, the errr scres are clse t er when the SNR s nfnte, mplyng that the estmate fr each f the unknwn varables s clse t ts true value. As the SNR decreases, the fgure shws that the algrthm handles nse better fr the nstantaneus cases than the cntnuus cases; skll s nt sgnfcantly affected by the nse untl SNR. Even fr ths nse level, the errr remans near 0. mplyng that errrs n estmates f the unknwn varables are nt prhbtvely large. It s nt untl SNR that estmates f the unknwn varables devate substantally frm the true values, as seen by the large ncrease n the mdel skll scres. Fcusng n just bundary layer depth n Table, when SNR 5, errrs are less than % fr all bundary layer depths tested. Bundary layer depth estmates are stll qute gd fr SNR wth the errrs beng less than 7%. As wth the errr scres, errrs n bundary layer depth becme substantal near SNR, where t grws t between 8% and 36%. When the cncentratn values are crrupted by nse that s f the same rder f magntude as the cncentratn value, the nstantaneus release estmates f bundary layer depth are mre accurate than thse fr the cntnuus release estmates. There are tw pssbltes fr why ths ccurs. The frst pssblty s that the nstantaneus case has mre nfrmatn avalable t determne, the extra nfrmatn cmng frm cntamnant entrapment that s captured by the reflectn terms n (). The cntamnant entrapment allws a drect calculatn f the mxng depth, and ths nfrmatn alng wth nfrmatn frm cntamnant spread allws accurate determnatn f. A secnd pssblty s that the tempral dependence f the puff allws multple 6

7 bservatns f the cntamnant feld, each crrupted by uncrrelated nse. Thus, the sgnal can be separated frm the nse. An equvalent mathematcal effect culd be acheved by samplng a cntnuus release ver the same number f tme steps and averagng the feld. By effectvely averagng befre nse crruptn ur test penaled the back calculatn methd. We undertake the test ths way, hwever, because n a real-wrld applcatn, an answer s desred n the least tme pssble. b. Mxed Layer Release Fgure dsplays errr results fr cntnuus and nstantaneus releases n the atmspherc mxed layer; the cntnuus release errrs are presented n Fgure a. These errrs appear smewhat smlar t thse shwn fr the cntnuus release n the surface layer. The errrs are small fr the nseless case and ncrease wth lwer SNR values; the errr s less than 0. fr SNR=5 and s abve 0. fr SNR=. The nfrmatn cntent s n lnger suffcent fr successful multvarate back calculatn nce SNR reaches, as seen by the large errr scres. Whle the pattern n the multvarate back calculatn errrs are parallel between the cntnuus mxed layer and surface layer releases, the errrs n bundary layer depth devate smewhat. As shwn n Table the errrs n bundary layer depth, when nse f the same rder as the cncentratn sgnal crrupts the bservatns, are smaller fr a mxed layer release, beng less than 5% when the SNR 5. Ther trend as SNR decreases s smlar thugh, wth t becmng dffcult t back calculate bundary layer depth when SNR. It s nterestng that estmates n bundary layer depth fr the cntnuus mxed layer release are mprved frm the cntnuus surface layer release. Ths dfference ccurs because the rate f plume descent frm the mxed layer s a functn f bundary layer depth and the cnvectve velcty scale. Therefre, mre nfrmatn s avalable t back calculate. As wth the surface layer release, Fgure 3b errr results fr the nstantaneus release are mre successful than fr the cntnuus release. In ths case, errr estmates reman belw 0. untl the SNR =, and these errrs d nt grw as fast near SNR. s f bundary layer depth estmates fr the nstantaneus mxed layer scenar parallel thse fr the nstantaneus surface layer scenar. As seen n Table, errrs n bundary layer depth estmates reman less than % fr all bundary layer depths tested as lng as the SNR 5. The nly dfference between the surface and mxed layer release scenars s that errrs n bundary layer depth are nt as substantal fr a mxed layer release fr reasns stated abve. Here, percentage errrs n bundary layer depth are less than 0% when the SNR. Fr a mxed layer release, results dsplay mre errr fr a cntnuus release than the nstantaneus release.. Ths mples that the ncreased errrs reprted fr cntnuus cntamnant releases are caused by bth factrs prpsed at the end f sectn Cnclusns We have ncrprated a back calculatn fr bundary layer depth,, and the cnvectve velcty scale, w nt the surce term estmatn prblem. These turbulent scalng varables and ther varables relevant t the AT&D prblem were back calculated frm the surface cncentratn feld va an teratve ptmatn algrthm and a frward AT&D mdel. Wth knwledge f these varables, t s pssble t frward mdel the AT&D prblem nt the future, allwng authrtes t make decsns fr surce mtgatn. By ptmng the surce characterstcs and relevant atmspherc varables s as t match the cntamnant spread n bserved and mdeled felds, t s pssble t estmate these varables skllfully fr cntnuus cntamnant releases n the surface layer and the mxed layer. estmates f bundary layer depth ncrease, hwever, when nse f the same rder f magntude as the cncentratn sgnal crrupts the sgnal. In cntrast, fr the nstantaneus release case we extract nfrmatn frm entrapment as well as spread f the cntamnant feld, thereby achevng a better estmate f the varables sught. Fr surce term estmatn t s essental t accurately determne the surce characterstcs f a cntamnant and relevant meterlgcal varables n a tmely manner. Unfrtunately, the averagng tmes requred fr the valdty f many dspersn mdels are large n the cnvectve bundary layer because the rat f the length and velcty scales f the BLSEs s large. Therefre, dspersn mdels may nt accurately descrbe the cntamnant transprt and dspersn n real tme applcatns. We smulate ths prblem n ur back-calculatn methd by addng nse t that data, usng ths nse t mmc atmspherc fluctuatns and sensr errrs. Althugh ths nse cannt accunt fr vertcal meanderng, at lw SNR the nse s f the same rder as the sgnal, causng the bservatns t devate cnsderably frm the dspersn mdel predctns. The effect f vertcal and hrntal meanderng als has mplcatns fr sensr stng. The cntnuus surce cases are very practcal fr ths back calculatn apprach because the sensr stng grd need nly have an adequate densty, the dman se relatve t bundary layer depth beng much less mprtant. Ths s pssble because we can average the cncentratn data n tme and match the hrntal and vertcal cntamnant spread t determne bundary layer depth befre entrapment 7

8 prvdes addtnal nfrmatn n ths varable. Such averagng des, hwever, mpse a respnse tme cnstrant that can lmt the tmelness f subsequent cntamnant frecasts, a crtcal ssue n the event f a harmful release. Whle back calculatns fr an nstantaneus release can be dne n small dmans usng nfrmatn frm nly the mean lateral spread f the cntamnant, nfrmatn frm vertcal spread must als be explted wth nstantaneus surces. Ths extra nfrmatn s needed because the effects f meanderng cannt be averaged away. Rather we requre a dman large enugh t encmpass the eventual vertcal hmgenatn f the cntamnant feld. Thus, the dman shuld extend dwnwnd f the surce fr at least the dstance traversed by the cntamnant puff n fur turnver tmes f the BLSEs. In real tme applcatns t s nt practcal t change the dman n respnse t durnal and synptc varatns n ths scale. Therefre, t s sensble t cnsder a 5x5 km sensr dman se and a hgher sensr densty fr the nstantaneus cases. Ths ensures that the sensr dman s large enugh t sample the cntamnant hmgenatn even n hghwnd, deep bundary layer stuatns. Here we have explted surface cntamnant cncentratn bservatns t fnd surce characterstcs as well as the meterlgcal varables relevant t AT&D. The dspersn mdels used were basc and cmputatnally effcent. In future wrk, we may nclude a mre sphstcated mdel lke the Secnd rder Clsure Integrated PUFF mdel (SCIPUFF); hwever, the same dman cnsderatns wll stll be necessary fr nstantaneus releases because ths s als an ensemble averaged mdel. Ths methd can als be appled t ther passve tracers, such as pllen, n the atmspherc bundary layer. 6. Acknwledgements The authrs wuld lke t thank the Defense Threat Reductn Agency wh supprted ths research under grant numbers W9NF-06-C-06 and DTRA0-03- D and the Educatnal and Fundatnal fundng suppled by the Appled Research Lab at The Pennsylvana State Unversty. Als, the authrs thank Jhn Wyngaard, Kerre Lng, Luna Rdrgue and Yuk Kurk fr ther help and suggestns. Lastly, the authrs thank Jhn Hannn and Chrs Kley wh mntred the prject 7. References Allen C.T., G.S. Yung, and S.E. Haupt, 007: Imprvng Pllutant surce characteratn by better estmatng wnd drectn wth a genetc algrthm. Atms. Envrn. 4, Brggs G.A., 993: Fnal Results frm the CONDORS Experment. Bund.-Layer Meter. 6, Daley R., 99: Atmspherc Data Analyss. Cambrdge Unversty Press, Cambrdge, UK 457 pp. Ds A., J. Vla-Guerau De Arellan, A.A.M. Hlstag, and P.J.H. Bulthes 003: Dspersn f a Passve Tracer n Buyancy- and Sear-Drven Bundary Layers. J. Appl. Meter., 4, Deardrff, J.W., 970: Cnvectve velcty and temperature scales fr the unstable planetary bundary layer and Raylegh cnvectn. J. Atms. Sc., 7, -3. Deardrff JW, (97) Numercal Investgatn f Neutral and Unstable Planetary Bundary Layers. J. Atms. Sc., 9, 9-5. Deardrff J.W., and G.E. Wlls, 975: A parameteratn f Dffusn nt the mxed layer, J. Appl. Meter., 4, Hadfeld M.G., 994: Passve Scalar Dffusn Frm Surface Surces n the Cnvectve Bundary Layer, Bund.-Layer Meter,. 69, Kamal J.C., J.C. Wyngaard, D.A. Haugen, O.R. Cte, Y. Ium, S.J. Caughey, and C.J. Readngs CJ 976: Turbulence Structure n the Cnvectve Bundary Layer. J. Atms. Sc., 33, Haupt R.L. and S.E. Haupt, 004: Practcal Genetc Algrthms, secnd ed wth CD. Wley, New yrk, NY 55 pp. Haupt S.E., 005: A Demnstratn f Cupled Receptr/Dspersn Mdelng wth a Genetc Algrthm. Atms. Envrn., 39, Hsu S.A., 003: Nwcastng mxng heght and ventlatn factr fr rapd atmspherc dspersn estmates n land. Nat. Wea. Dg. Lamb R.G., 98: Dffusn nt the Cnvectve Bundary Layer, n F.T.M. Neustadt and H. van Dp (eds.), Atmspherc Turbulence and Ar Pllutn Mdellng, D. Redel, Drdrecht. 8

9 Lng K.J., S.E. Haupt, and G.S. Yung, 00: Assessng Senstvty f Surce Term Estmatn. Submtted t Atms. Envrn., accepted Panfsky, H.A. and J.A. Duttn, 984: Atmspherc Turbulence: Mdels and Methds fr Engneerng Applcatns. Wley, New Yrk, 437 pp. Panfsky H.A., H. Tennekes, D.H. Lenschw, and J.C. Wyngaard, 977: The characterstcs f turbulent velcty cmpnents n the surface layer under cnvectve cndtns. Bund.-Layer Meter., Stull R.B., 988: An Intrductn t Bundary Layer Meterlgy. Sprnger 680 pp. Wel J.C., 988: Dspersn n the cnvectve bundary layer. Lectures n Ar Pllutn Mdelng, Venkatram A., and Wyngaard JC., Eds., Amer. Meter. Sc., Wel J.C., 990: A dagnss f the Asymmetry n Tp-Dwn and Bttm-Up Dffusn Usng a Lagrangan Stchastc Mdel, J. Atms. Sc, 47, Wel J.C., L.A. Cr, and L.A. Brwer, 997: A PDF Dspersn Mdel fr Buyant Plumes n the Cnvectve Bundary Layer, J. Atms. Sc Wlls GE and J.C. Deardrff, 976: A labratry mdel f Dffusn nt the Cnvectve Planetary Bundary Layer, Quart. J. Ry. Meter. Sc., 0, Wlls G.E. and J.C. Deardrff, 98: A labratry study f dspersn frm a surce n the mddle f the cnvectve mxed layer, Atms. Envrn. 5, Wyngaard J.C., 987: A physcal mechansm fr the asymmetry n tp-dwn and bttm up scalar dffusn. J. Atms. Sc., 44, Wyngaard J.C., 988: Structure f the PBL. Lectures n Ar Pllutn Mdelng, Venkatram A., and Wyngaard JC., Eds., Amer. Meter. Sc., 9-6. Yaglm A.M., 97: Turbulent Dffusn n the Surface Layer f the Atmsphere Iv. Atms. Ocean Phys., 8,

10 8. Fgures and Tables Fgure Cntured Skll Scres fr Surface Layer Smulatns. Fgure a s fr a cntnuus release and Fgure b s fr an nstantaneus release. Fgure Cntured Skll Scres fr Mxed Layer Smulatns. Fgure a s fr a cntnuus release and Fgure b s fr an nstantaneus release. 0

11 Instantaneus Release Cntnuus Release Table : Bundary layer depth errrs fr nstantaneus and surface releases n the surface layer Surface Layer Release SNR Inf Bundary Layer Depth

12 Instantaneus Release Cntnuus Release Table : Bundary layer depth errrs fr mxed layer release Mxed Layer Release SNR Inf Bundary Layer Depth ,