Effect of Terrain on Mass and Heat Transport of Smoke Plume Based on Geometric Properties of Digital Elevation Model and Satellite Imagery

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1 Amercan Journal of Geographc Informaon Ssem 013, (4): DOI: /j.ajgs Effec of Terran on Mass and Hea Transpor of Smoke Plume Based on Geomerc Properes of Dgal Elevaon Model and Saelle Imager Carl Y. H. Jang Cenre for Inellgen Ssems Research, Deakn Unvers, Vcora, 316, Ausrala Absrac The effec of erran on mass and hea ranspor of smoke plume has been negleced for a long me. A novel manner of nvesgang has been proposed b negrang erran wh spaal poson of smoke plume b means of Gaussan dsrbuon. Based on unque feaures of dgal elevaon model and saelle mager, several necessar parameers o calculae dsrbuon of mass and hea beng carred b smoke plume were capable of beng obaned. The resuls of modellng have effecvel ndcaed some phenomena whch have no been dscovered and repored. The new approach of beng epressed b geomorphologc parameers s useful o no onl undersand how mass and hea ranspor of smoke plume are affeced b erran bu also esmae how mass and hea mpac upon he vegeaon closed o burnng spos. The relaon beween smoke plume and burnng zone n mass and hea dffuson has been closel correlaed. Kewords Smoke Plume Modellng, Dgal Elevaon Model, Mass and Hea Transpor, Bushfre, Remoe Sensng Imager 1. Inroducon Bushfre s a process of combuson n whch ranspor phenomena have wdel nvolved. Smoke plume s a b-produc produced b combuson, whch mples man phenomena and unceran facors. Therefore, relevan researches have dfferen focuses. Sudng combuson has been mplemened b man researches for man ears[1-3]. However bushfre has unque feaures whch are dfferen from ndusral combuson. Bushfre happens n an open naural envronmen. Therefore several researchers have developed he bushfre models based on heores of ranspor phenomena and hermodnamcs[1-4]. In hese researches, researchers have also pad a lo of aenon o he sudes of smoke plume [5-7]. However, nvesgang smoke plume has been remaned whn heorecal modellng based on laboraor scale epermens alhough he effec of erran on bushfre and smoke plume has alread been realzed b all researchers n hs feld. So far, he sudes have no been repored on he bass of real erran.. Mehodolog * Correspondng auhor: carljan@pg.com.au (Carl Y. H. Jang) Publshed onlne a hp://journal.sapub.org/ajgs Coprgh 013 Scenfc & Academc Publshng. All Rghs Reserved.1. Feaures of Research In hs research, he concenraon s o be drawn o nvesgang some unknown fac happenng n smoke plume dsperson accompanng wh bushfre spread n landscape, hence how erran affecs on mass and hea dsrbuon of smoke plume when rses from ground. Ths opc has been gnored b assumng erran s fla n he hsorcal relevan researches. Because modellng s based on dgal elevaon model (DEM) and correspondng saelle mager, he manner o be proposed n hs research s novel and unque. The elevaon suppled b DEM becomes valuable when applng Gaussan dsrbuon no model s moke plume. On he oher hand, one mporan parameer such as surface area s also able o be obaned b combnng DEM and s remoe sensng mager; becomes possble o effecvel calculae mass and hea ranspor beng carred b smoke mure. Inversel, he dsrbuon of hem s helpful o provde useful nformaon n esmang polluan and hea how o mpac envron menal vegeaon... Objecves and Scope of Research The objecves of hs research are represened as follows. 1. Revew geomorphologc parameers and how he are eraced from DEM; ncludes mass and hea ranspor esng n general combuson. Classf mass and hea for bushfre and smoke mure n erms of concep of source and snk so as o easl model.

2 68 Carl Y. H. Jang: Effec of Terran on Mass and Hea Transpor of Smoke Plume Based on Geomerc Properes of Dgal Elevaon Model and Saelle Imager. Revew Gaussan dsrbuon n he sascs for developng new model on he bass of new deas. 3. Dscover how he sandard devaon of Gaussan dsrbuon and mass, hea dffusv s correlaed mahemacall and how o locae epeced values no DEM based modellng. 4. Fnd ou how burnng zone and smoke plume are conneced n form of mass and hea ranspor. 5. Esmae how erran affecs he dsrbuon of mass and hea when smoke rses from ground. There are wo approaches o be mplemened. One s usng radonal model o calculae for comparson; anoher s o appl proposed model no hs performance. The eplanaon for modellng s based on he esng saelle mager of bushfre..3. Geographcal Locaon for Modellng Esmang mass and hea released from bushfre n hs modellng s based on he place where bushfre ofen ook place hsorcall n Vcora, Ausrala. The geographcal locaon (-36 70'10" S, '30" E; '60" S, '00" E) s shown b Fgure 1. The dsrbuon of vegeaon s sored n he saelle mager capured b he saelle LANDSAT and he feaure of erran s llusraed b he correspondng DEM (SRTM3 offered b USGS) n Fgure. In Fgure 1, he bushfre spread n landscape downwnd and smoke plume spaal dsperson were modelled prevousl. In hs research, he concerned opc s o focus on one of burnng zones and smoke plumes as respecvel ndcaed b crcles shown n Fgure 1 o nvesgae how he dsrbuon of mass and hea beng carred b smoke plume s performed spaall and poenal correlaon beween and burnng zone. The resuls of modellng are dsplaed and calculaed b MATLAB. Fgure 1. seleced saelle mager for modelng smoke plume Fgure. correspondng DEM for modelng smoke plume

3 Amercan Journal of Geographc Informaon Ssem 013, (4): Fgure 3. dealed elevaon of bushfre spos n modelng Fgure 4. December 006 Vcoran bushfre saelle mages, Ausrala[5] Because full modellng hree-dmensonal (3-D) case, requres massve phscal compuer memores, modellng s onl confned o wo dmensonal cases. However, hs approach does no affec fnal resuls. Furhermore, addonal energ source such as solar radaon s no o be consdered n hs research. To race overall s moke plume correlaes wh elevaon of erran, resuls n massve daa o be nvolved n. In hs research, onl paral s moke plume over burnng zone s consdered. The dealed elevaon of s presened n Fgure 3. As seen, he dsrbuon of vegeaon a he seleced burnng zone s uneven..4. Smoke Plume Capured b Saelle Imager The modellng smoke plume s based on hsorcal bushfre happened a he eas coas n Ausrala. The wo-dmensonal saelle mageres are shown n Fgure 4. An nuve undersandng how smoke plumes were generaed b bushfre (red) are provded. I s useful o gude how model bushfre spreads, smoke dsperson especall n assessng how erran affecs dsrbuon of mass and hea ranspor of smoke plume spaall, and reversel undersandng how mpacs upon he vegeaon dsrbung on erran. 3. Fundamenals of Dgal Elevaon Model and Saelle Imager 3.1. Mahemacal Epresson of Terran The surface of erran s able o be descrbed b connuous mahemacal funcons. In he followng case(see Fgure 5), f a boundar funcon b for boundar funcon C n doman D s gven, hus =b(), hen he area of D s gven b

4 l 70 Carl Y. H. Jang: Effec of Terran on Mass and Hea Transpor of Smoke Plume Based on Geomerc Properes of Dgal Elevaon Model and Saelle Imager equaon (1) n erms of Green heorem and he geomerc properes of rapezod[6]. 1 S pj dd d d c (1) c The area of surface over D s Scv 1 f f dd () D Where, he f and f s he second order dervave of a connuous surface funcon f(,) n and drecon respecvel. Ver obvous, he elevaon z n a gven doman can be epressed as z f (, ) (3) The elevaon z represens a seres of pons conssng of a smooh and connues surface of erran. If funcon f(,) s equal o an arbrar consan, hen a he pon P (see Fgure 5), along s normal, wll eld s graden shown as grad(, ) f f j (4) Where, he, j s he un vecor and he f,f s he frs order dervave of a surface funcon n and drecon respecvel. The norm of equaon (4) s named as slope, hus equaon(5). an f f (5) The slope represens he vare of elevaon per un lengh. Is correspondng angle s shown n he equaon(6). arc f f (6) an The range of slope angle s from 90 o 90. When f 0, hen he aspec (see Fgure 5) s epressed as Boundar: C z 0 Doman:D f arcan (7) f P Slope: S cv Aspec: S pj Fgure 5. Schemac llusraon of geomorphologc parameer Area of projecon Surface of erran: f (, ) The aspec s he azmuh of he slope drecon and s angle ranges from 0 o 360. In oher manner, he aspec s also hough of as he drecon of he bgges slope vecor on he angen plane projeced ono he horzonal plane. Anoher useful concep s roughness. The un roughness R k s defned as he rao of he surface area S cv o s projecon ono he horzonal plane S pj for he kh un of surface area (see Fgure 1). The area of surface s poroned no k regular sze sub-elemens. R S cv k (8) S pj The concep of slope, aspec and roughness s an mporan respecvel. However, he analcal soluons o hem are dffcul o be obaned n pracce; usuall he can be resolved and appled n he form of numercal form. 3.. Erac from Geomerc Parameers from DEM DEM s a common used daa. Several valuable parameers menoned above can be numercall epressed. Because he research s o focus on how erran affecs he dsrbuon of mass and hea beng carred b smoke plume, a wndow-lke numerc manner of dealng wh DEM s o be used. The mamum drop slope was proposed b researchers[6]. The local movng wndow s smlar o he prncpal of fler used n dgal mage processng because boh of DEM and dgal mager s based on a specfc mar. The DEM daa flows no hs wndow, he geomorphologc feaures of DEM such as slope and aspec are eraced. Z 8 Z 7 Z 6 Z1 Z Z 0 Z 5 l Z 3 Z W 5 o Fgure 6. a movng wndow of mamum drop slope N S n E 135 The manner of mamum drop slope s selecng one cell as a cenre of cell, s elevaon Z 0 s hen compared wh elevaon Z n of neghbor cells clockwse (see Fgure 6), n=1,, 8. As menoned above, he aspec s hough of as he drecon of he bgges slope vecor on he angen plane projeced ono he horzonal plane. Then, slope and aspec angle n manner of mamum drop slope can be mahemacall epressed as follows. dz arcan ma n dl dzn Z0 Zn j dl l (9) (10)

5 Amercan Journal of Geographc Informaon Ssem 013, (4): Where, l s cell sze. When n s even number, j 1 n 1 45 (11), oherwse j=1. The dealed ep lanaon negrang above geomorpholo gc parameers wh some feaures of saelle and applcaon n modellng bushfre have been dscussed b auhor[7, 8]. 4. Basc Theores of Mass and Hea Transpor The mass ransfer s vsble n he form of smoke plume. However he hea ransfer s complcaed and nvsble for human, can be appeared n he form of boh free convecon and radaon. The energ no onl can be carred b ar (hea conducon) bu also ranspored b gra gases (such as CO ) and fne granules n he smoke mure. In oher words, he energ can be sored and carred b he smoke mure and dsrbued n ar lke he behavour of smoke plume s dffuson. Accordng o Newon s coolng law, he free convecon of hea onl affecs he vegeaon close o he burnng zone raher han he one n remoe zone. In order o nvesgae how he energ affecs he remoe vegeaon, assume ha he form of moon for spaal energ ransfer s he same as smoke plumes. In fac, mass and energ coess. Such echncal reamen s o be much easer o undersand how he mass and energ dens s decaed wh he elapsed me respecvel and how he mpac upon he vegeaon n remoe zone. Boh mass and energ dens are eensve proper raher han nensve proper, hus he are vared wh epandng volume and elapsed me General Conservaon Equaon of Mass and Hea Accordng o he concep of source and snk when mass and energ are ranspored (flow n or ou) whn wo dfferen ssems, can be descrbed as he followng equaon. z (1) Snk source In whch n general θ, η, and z represen one conserved Where M D erm (mass or hea), flu (of mass or hea), me and dsplacemen n a one-dmensonal ssem n he lef hand of equaon(1) respecvel; n he rgh hand of, Φ represens he source of mass or hea. The un for he equaon(1) can be lke kg m -3 s -1 for mass ranspor and kj m -3 s -1 for hea ranspor respecvel. In order o clearl llusrae phscal meanng of varables, he S.I. uns are suppled for hem n he cone; he are adjusable accordng o specfc case n pracce. Equaon(1) s ver useful o eplan how mass and hea ranspor happenng n bushfre and oher equaons dervaon also reles on. If he source erm s equal o zero, hen equaon(1) become 0 z (13) Equaon(13) s hen named as a connu equaon. Hence, nohng (mass and hea) s creaed or desroed. I s also useful n eplanng and esmang he dsrbuon of mass and hea when smoke plume dsperses spaall. A. General Epresson for Subsance Transpor In general, for boh mass and hea ranspor, n a one-dmensonal ssem, he can be wren as he followng general equaon[9-11]: A B C Y Y Y z z (14) The coeffcen A, B and C represens dfferen phscochemcal properes conanng behavours cause hem respecvel. B. Mass Transpor In he maer of he burnng, whch can be regarded as a process of chemcal reacon, he bushfre produces a number of speces; n general, s no precse enough o defne mass ranspor usng concenraon f he speces n smoke s more han one. Insead, he mass fracon or molar mass fracon Ψ (=1,,,g) s used o defne mass ranspor. Then he epresson of equaon(14) combnng wh equaon(1) becomes equaon(15) beween wo ssems and n one-dmensonal drecon. M r D v z z z speces mass speces mass producon rae speces nner speces mass fracon change rae mass dffuson flow change Source Snk Snk s he mass dffuson coeffcen or mass dffusv for speces no he mure of he oher speces n a gven ssem, s un s m s -1. The superscrp M ndcaes mure n he cone. ρ s oal mass dens, s u. n s kg m -3. The erm s he rae of producon of speces n chemcal reacons, s un s kg m -3 s -1. r (15)

6 7 Carl Y. H. Jang: Effec of Terran on Mass and Hea Transpor of Smoke Plume Based on Geomerc Properes of Dgal Elevaon Model and Saelle Imager Where he mass veloc v of he speces s composed of he mean mass veloc v of he cenre of mass of he mu re and a d ffuson veloc V (relave o he cenre of mass) caused b molecular ranspor because of he concenraon gradens of he speces. The un of boh of veloces are m s -1. The relaon beween wo pes of veloc s epressed as v v V (16) In fac, here are wo coordnaes n above descrbng mass ranspor. Dependng on how o observe he moon of subsance, f he bushfre spo s seleced as a saonar coordnaes, he veloc of moon of one cener of mass-based smoke plume s v. If he second coordnaes s locaed a he cener of mass, he dffuson veloc of speces s V. Therefore, equaon(15) ells ha he speces flows no one ssem no anoher. In he case of burnng vegeaon, can be consdered as ha smoke (gaseous mure) n he form of hea and mass flues from ground no sk, and hen form s moke plume spaall and carr hea smulaneousl. The un for equaon(15) can be kg m -3 s -1, n he erms of ha, s eas o verf each erm. C. Hea Transpor If he erm Y n equaon(14) denoes emperaure T, hen he hea ranspor beween wo ssems s represened as(17). C p speces hea released hea rae of change rae chemcal reacon Snk T h r Source T T k vc n c z z z lump hermal conducon C p p, z hea flow rae nner specses change hermal dffuson Snk T (17) c s he specfc hea capac Where p p, speces a he consan pressure. The un of C p s kj kg -1 K -1. The k s he hea conducv of he speces mure, s un s kw m -1 K -1. h s he enhalp of speces mure, s j un s kj. n s mass flu n he cener of mass ssem s defned as. n D z " M The mass flu n s kg m - s -1.Therefore, he un for equaon (17) s kj m -3 s Mass Dffuson and Hea Conducon Assocaed wh Smoke Plume In hs research, sudng he smoke plume produced b burnng vegeaon s he man opc. Alhough s o be dscussed separael, he smoke plume sll has a close relaon wh he bushfre a he ground. Assume ha 1. Smoke plume s a connuous gaseous mure flud, whch can be pared no a seres of sub-volume wh a cener of mass (see Fgure 7).. For a gven sub-volume smoke plume, no chemcal reacon akes place n ner mure and dens of smoke mure does no change wh spaal dsance. Based on hose assumpons, from equaon (15) and(17), leads o generang followng equaons respecvel: M D z T k T c z p (18) (19) Obvousl, he equaon (18) s Fck s second law and he equaon(19) s Fourer s second law n one-dmensonal form respecvel. On he oher hand, can be seen ha mass dffusv of mure D M s equvalen o he hermal dffusv α n form as follows. k c Where k s hermal conducv, W m -1 K -1 The un for boh D M and α s m s -1. Under such assumpons, alhough each sub-volume smoke plume s able o be ndependenl carr ou s mass ranspor and hermal conducon spaall, naurall correlae wh mass and hea flu produced b burnng spo a ground wh respec o me. The flow rae of hem can be mplcl descrbed b he followng equaons(0) (1) respecvel. m z v S W ', b b sp ground ground p (0) Where he concenraon of speces s sk C T ' sp q z, vbsb CpTb WspC p ground ground sk (1) In equaon(0) m s mass ransfer rae (kg s -1 ) of speces, whch ems from a burnng zone wh he surface area S b and rsng wh local geosrophc veloc v b ; hen he speces dsperses from a gven one smoke plume wh volume W sp. The subscrp b and sp denoes burnng and smoke plume respecvel. In equaon(1), q s hea flow rae (kj s -1 ) accompanng

7 Amercan Journal of Geographc Informaon Ssem 013, (4): wh he mass flud rses from ground wh he dfference of emperaure T b. As seen from equaon(0) and equaon(1), once he smoke plume leaves from ground, no addonal mass and hea from ground s added no each smoke plume. I ndependenl carres ou mass and hea ranspor spaall. On he oher hand, one ssue should be llusraed before furher dscussng smoke plume. A ground, n erms of equaon (18) and(19), n sem-nfne meda he concenraon C dsrbuon of speces n gaseous mure(s moke) when s nal fracon C 1 a nal me jumps o be C, C > C 1 due o nsan mass dffuson can be epressed as follows. C C z erfc erfc 1 C M C 1 4D () Smlarl, he emperaure T dsrbuon of gaseous mure can be shown as follows f he nal emperaure T 1 ncreases o be T. T T1 z erfc erfc T T 1 4 (3) Boh ς and ζ s a dmensonless varable havng he followng mahemacal properes as e 0 erfc 1 erf 1 u du (4) z (5) 4D M z (6) 4 The erf s an error funcon and erfc s a complemenar error funcon. Also, erf( )=0 when ζ, hus erfc(ζ)=1 accordng o equaon(4). The mass and hea flu m and q can be wren as follows based on equaon(0) (3). ' " m z, m z, S Smlarl q " D b M C z M D z C1 Cep M 4D z, b ' q z, S T k z k T T1 z ep 4 (7) (8) The mahemacal properes of equaon (5) (8) are useful o be furher used n he followng sucon. D. Mahemacall Correlae Mass Dffuson and Hea Conducon Second Law wh Gaussan Dsrbuon The prevous researchers[1-14] used o nvesgae he mass dffuson of smoke plume b means of Gaussan (normal) dsrbuon appeared n sascs. The spaal mass dffuson and hea conducon of smoke plume s somewha dfferen from he cases of hem happenng a ground because he do no have a clear boundar and nal condons spaall. Therefore o model concenraon and hea dsrbuon of smoke plume, requres o buld a cenral lne based on he cener of mass of each smoke plume. Then dsrbuon happens radcall along hs lne. The approach n sascs s ha, n one dmenson, for he a sandard normal random varable wh dens funcon f(), s epeced value μ can be epressed as Wh f d (9) Is varance σ s shown as 1 f e (30) f ( ) d (31) Because he dens funcon f() s smmerc wh respec o he -as n he - coordnaes, hen 0 f ( ) d f ( ) d When μ =0, hen 1 1 ( e ) 0 e d (3) 0 If le u hen u 0 e du (33) As seen, when +, u +, σ =1. Therefore, n general he normal dens funcon wh parameer μ and σ can be defned as follows n one-dmensonal form. 1 1 f( ) ep (34)

8 74 Carl Y. H. Jang: Effec of Terran on Mass and Hea Transpor of Smoke Plume Based on Geomerc Properes of Dgal Elevaon Model and Saelle Imager Equaon(34) s also able o be eended. The wo or hree-dmensonal form s shown as follows. 1 1 f (, ) ep (35) f (,, z) 3 1 z 1 ep z z z (36) Now comparng equaon (34) (36) wh equaon (7) (8) produces he followng dscoveres. In mass dffuson: M D M D (37) M z Dz In hermal dffuson: z z (38) The un for boh σ and μ shown n equaon(36) (38)s m. Z o X Concenraon profle Therefore he erm of eponen n equaon(36) s dmensonless and hen he un for equaon(36) becomes m -3. On he bass of he unque feaure of equaon(36), s applcaon n nvesgang smoke plume s o be furher modfed n he followng secon Concenraon Dsrbuon A. 3-D Consan Source from Burnng Zone There several Gaussan dsrbuon-based models o descrbe he smoke plume. The smoke plume generaed from ground s usuall reaed as a flud n sead sae, hen he change of concenraon wh me s zero, furhermore, he dffuson of s moke plume n - drecon can be negleced because of he downwnd (See Fgure 7). Then he dsrbuon of concenraon of smoke plume s ofen epressed b equaon(39)[15]. G c(,, z) ep 4 v z Wnd speed v z H z H ep ep z z o (39) Y ( X, Y, Z ) s s s B Cenral lne z c o A H ' Surface of landscape Bushfre Elevaon1 Dsance n X Elevaon Fgure 7. schemac llusraon of smoke plume dspersng over erran

9 Amercan Journal of Geographc Informaon Ssem 013, (4): In whch (See Fgure 7), for s moke wh consan source, he smoke plume s alwas descrbed b usng he effecve sack hegh of smoke H, s un s m. The v s he average wnd veloc a sack hegh. G. s emsson rae of source; s un s kg s -1. σ, σ are he sandard devaons of he concenraon dsrbuons n he crosswnd and vercal drecons respecvel. The un s m for hem. s he dsance downwnd from he sack; s he crosswnd dsance from he plume cener lne and z s he vercal dsance from ground level. The un for hem s m. B. Smoke Plume Based Dsrbuon Equaon (39) s esablshed b assumng he ground s fla. In fac, he smoke plume especall caused b bushfre s serousl affeced comple erran. In order o se up he correlaon of plume wh elevaon of erran makng use of he advanage of DEM, assume ha 1. The smoke plume s puffed from one burnng zone whn each me nerval.. The mass and energ released from burnng are remaned n each smoke plume havng dfferen nal spaal surface area and volume and dffuse a specfc spaal locaon. 3. Smoke plume s composed of massve fne parcles. 4. The solar radaon s no consdered. 5. Each smoke plume has s own mass cener formng a cenral lne. Based on above basc assumpons and he concep of equaon(36), he followng resuls can be generaed. 1. The pon (μ,, μ,, μ z ) represens a spaal pon locang a a cenral lne and specfc me respecvel.. The vercal dsance of each parcle n each smoke plume z s equal o s vercal spaal poson mnus s correspondng elevaon of erran. If he dffuson n -drecon s no consdered, he modfcaon of equaon(35) for spaal concenraon dsrbuon n and z drecon can be rewren as follows. M 1 z z C(,, z) ep z z (40) A 0 W sp In whch, M s oal mass of each smoke plume, kg. σ, σ z have he same meanng as ones defned above. A 0 and W sp are surface area of smoke plume a nal me 0, m and s spaall epanded volume a one specfc me, m 3 respecvel, hose wo parameers can be elded b oher modellng. The un of C(,,z) s kg m -3. The oal mass M of each s moke plume can be obaned from equaon(0) for speces whn one me nerval of burnng b, s o produce, whch s shown b he followng equaon. M m (41) ' b In pracce, drecl seng up hree-dmensonal relaon beween smoke plume and landscape requres massve phscal compuer memor. Therefore he comple case s descrbed b wo-dmenson based equaon(40) whou drecl consderng -drecon dsrbuon of mass and hea Hea Dens Dsrbuon Smlarl, he hea dens dsrbuon and oal hea beng carred b each smoke plume and combnng wh equaon (1) are shown as follows respecvel. Q 1 z z E(,, z) ep z z (4) A 0 W sp And ' Q q b (43) The un of E(,,z) and Q are kj m -3 and kj respecvel. Up o hs pon, he necessar conceps for hs research are alread nroduced. The resuls of modellng are o be dsplaed and dscussed n he followng secon Esmae Dffuson Coeffcens In general, here es wo manners o esmae mass and hermal dffuson coeffcens of smoke plume σ, σ, σ z. One s usng equaon(37) (38). Anoher s o use esng daa and fgures[16] (see Fgure 8 and Fgure 9). The laer manner s ofen appled n nvesgang mass dffuson n vercal and laeral drecon. However, more precse manner s o use power law. z a c (44) The values for a,b,c and d shown n equaon(44) can be found n Table 1 and Table accordng o downwnd dsance(see Fgure 7). 5. Resuls and Dscusson 5.1. Common Used Parameers and Values n Modellng In he modellng, here are several parameers used n calculaon. The are lsed n Table 3. In whch, v and v b are assessed b local geosrophc wnd accordng o elevaon and hegh of smoke plume when bushfre akes place a specfc geographc locaon havng burnng area A b. The manner of esmang above parameers has been nroduced n he prevous repors[7, 8]. α, α z, D and D z are manl esmaed b he hermal and mass properes of carbon dode (CO )[17] a nal me. Smlarl, ρ and C p are modfed b consderng smoke plume as a gaseous mure. T b s a emperaure jumpng from amben emperaure o mamum burnng emperaure whn a me b d

10 76 Carl Y. H. Jang: Effec of Terran on Mass and Hea Transpor of Smoke Plume Based on Geomerc Properes of Dgal Elevaon Model and Saelle Imager nerval when smoke rsng from ground. A 0 ma be dffcul o be assessed, whch s appromael reaed as 1 square meer n order for s moke o be phscall observed a nal sage. Fgure 8. vercal dffuson σ z vs. downwnd dsance from source Fgure 9. laeral dffuson σ vs. downwnd dsance from source

11 Amercan Journal of Geographc Informaon Ssem 013, (4): Amospherc Sabl Class Table 1. power law eponens and coeffcens for σ Downwnd Dsance, meers <10,000 Downwnd Dsance, meers 10,000 c d c d A= B= C= DD= DN= E= F= Amospherc Sabl Class Table. power law eponens and coeffcens for σ z Downwnd Dsance, meers 100<500 Downwnd Dsance, meers 500<5000 Downwnd Dsance, meers 500< a b a b a b A= B= C= DD= DN= E= F= Table 3. common mass, hermal and phscal properes used n calculaon Term Smbol Value Veloc of cenral lne n drecon Smoke rsng veloc n burnng zone v 6.16 m s -1 vb m s -1 Effecve sack hegh H m Burnng emperaure Tb 100 K Specfc hea of smoke mure a consan pressure Dens of smoke mure n burnng zone Cp KJ kg -1 K -1 ρ kg m -3 Currenl burnng area Sb.8419e+06 m Thermal dffusv n drecon Thermal dffusv n z drecon Mass dffusv n drecon Mass dffusv n drecon Inal surface area of smoke plume α.00e+06 m s -1 αz 3.190e+06 m s -1 D 4.71e+06 m s -1 Dz.560e+06 m s -1 A m The mass and hea emsson rae produced b one gven burnng area S b are presened n Table 4. Those daa are calculaed b usng equaon(0) (1) and he correspondng daa suppled n Table 3, and hen appled no all calculaons of mass and hea ranspor. Table 4. calculaed mass and hea emsson rae for gven burnng area Term Smbol Value Mass emsson rae m e+07Kg s -1 Hea emsson rae q e+10 KJ s Spaal Dsrbuon of Concenraon Invesgang how erran affecs dsrbuon of concenraon s carred ou wo approaches. One s usng radonal equaon(39) and suppled daa n Table 3 and Table 4 for relevan parameers. The resul s represened n Fgure 10. σ and σ z are assessed b usng equaon(37) and he relevan daa are shown n Table 3. Fgure 10. concenraon of smoke plume dsrbues whou consderng effec of erran

12 78 Carl Y. H. Jang: Effec of Terran on Mass and Hea Transpor of Smoke Plume Based on Geomerc Properes of Dgal Elevaon Model and Saelle Imager Anoher s usng proposed equaon(40) and relevan daa suppled n Table 5. σ z and σ are esmaed b usng equaon (44) combnng daa suppled n Table 1and Table. In hs case, he smoke plume s assumed as a moderael sable gaseous mure, hus F pe (see Fgure 9). Table 5. parameers and values used for mass and hea ranspor calculaon of smoke plume n wo dfferen cases hegh. Tradonal research manner s reang he dsrbuon of smoke as beng n dea sae (see Fgure 10 ). Therefore, he resul shows ver smooh and sead sae. I resuls n a bg error n esmang mass dsrbuon n nvesgang smoke plume. Term Smbol Case Value Dffuson coeffcen n z drecon σz m m Dffuson coeffcen n drecon σ m m Volume of smoke plume Wsp e+09 m e+10 m 3 Horzonal dsance beween mass cener of burnng zone and smoke plume Mass cener of smoke plume dbs (μ, μ, μz) m e+03 m 1 (5.731e+03,.145e+03, ) m (6.0871e+03, e+03,.9064e+03) m Fgure 11. concenraon dsrbuon affeced b slope for case 1 Mass cener of burnng zone (b,b,zb) 1, (5.6778e+03, 1.975e+03, ) m Dscusson The resuls shown n Fgure 11 Fgure 16 provde he followng nformaon ha 1. The dsrbuon of mass s serousl affeced b erran descrbed b geomorphologc parameers.. As seen from Fgure 11 and Fgure 14, he mamum concenraon s presened n he locaon where has mamum slope angle when smoke plume rsng from ground. 3. Accordng o he prncple of he mamum drop slope, he locaon havng mamum slope accompanes wh he mamum elevaon. Therefore, he concenraon of mass s alwas hgher han one dsrbued n oher place. Such phenomena have been approved b Fgure 3, Fgure 13 and Fgure However, he aspecs shown n Fgure 1 and Fgure 15) offer anoher mporan nformaon, hus he mamum drop slope unevenl dsrbues n erran. 5. For vsble mass dsrbuon, he comple erran easl causes he urbulen sae of smoke plume. In oher words, he concenraon dsrbuon s uneven. Above fac can be approved b saelle mager shown n Fgure 4. As seen from, he concenraon dsrbuon s serousl affeced b adjacen hlls (slopes) and vares wh Fgure 1. concenraon dsrbuon affeced b aspec for case 1 Fgure 13. concenraon dsrbuon affeced b elevaon for case 1

13 Amercan Journal of Geographc Informaon Ssem 013, (4): hea (such as solar radaon) are no consdered. Dscusson In accordng o he varous resuls shown n Fgure 18 Fgure 3 and he feaure of erran descrbed b Fgure 3, can be found ha Hea dsrbuon s also affeced b adjacen hlls (slopes) In erms of he scenaro shown n Fgure 4, hea conducon s also n a urbulen sae; however canno drecl be demonsraed b he curren saelle mager (Fgure 4). Fgure 14. concenraon dsrbuon affeced b slope for case Fgure 17. hea of smoke plume dsrbues whou consderng effec of erran Fgure 15. concenraon dsrbuon affeced b aspec for case Fgure 18. hea dsrbuon affeced b slope for case 1 Fgure 16. concenraon dsrbuon affeced b elevaon for case 5.3. Spaal Dsrbuon of Hea As menoned before, he hea ranspor s analogous o mass ranspor. The resul shown n Fgure 17 n a radonal manner s obaned b he one smlar o equaon(39). Neverheless, he emsson rae of source s replaced b hea q. suppled n Table 4. σ and σ z are assessed b usng equaon(38) and relevan daa shown n Table 3. The hea dsrbuon s calculaed b equaon (4) usng daa suppled n Table 5 and assumng he hea loss and addonal Fgure 19. hea dsrbuon affeced b aspec for case 1

14 80 Carl Y. H. Jang: Effec of Terran on Mass and Hea Transpor of Smoke Plume Based on Geomerc Properes of Dgal Elevaon Model and Saelle Imager Fgure 0. hea dsrbuon affeced b elevaon for case 1 Fgure 1. hea dsrbuon affeced b slope for case 6. Conclusons A. Achevemens n he Research The effec of large scale erran on he dsrbuon of mass and hea beng carred b smoke mure has no been nvesgaed for several decades alhough some researchers have alread poned ou hs ssue. Accordngl, n hs research, he followng opcs have been eplored n process of seekng for a possble resoluon o. 1. The correlaon beween mass and hea conducon n erms of feaures of smoke mure s esablshed.. Sarng from mass and hea flu, he mass and hea flow rae are hen consdered b mulplng hem wh correspondng burnng area. 3. Gaussan dsrbuon s a radonal manner n nvesgang unknown smoke plume, whch s sll used n hs research. However, of mporance s how o deermne s sandard devaons and epeced values. In order o buld relaonshp beween landscape and spaal poson of smoke plume n vercal drecon. The sandard devaons n vercal drecon are alread consdered and he epeced values are deermned as a cener of mass. 4. Accordng o he resuls of modellng, s dscovered ha mass and hea dsrbuon carred b smoke mure are serousl affeced b adjacen hlls (slopes), her aspecs and elevaons when rses from ground. Concenraon and hea have a srong endenc o dsperse ono hlls and are n volen sae. 5. Based on hs dscover, proves ha radonal model of nvesgang smoke plume n spaal dsperson of mass and hea has a bg defcenc. B. Fuure Work The energ beng carred b smoke mure s usuall released n form of radaon. In he fuure work, he focus of research s o be moved ono hs feld. Fgure. hea dsrbuon affeced b aspec for case ACKNOWLEDGEMENTS Auhor wans o offer specal hanks o Professor Jng. X. Zhao a Shangha Jao Tong Unvers for supplng desred daa used n hs research. REFERENCES [1] Séro-Gullaume, O. and J. Marger, "Modellng fores fres. Par I: a complee se of equaons derved b eended rreversble hermodnamcs". Inernaonal Journal of Hea and Mass Transfer, (8): p [] Marger, J. and O. Séro-Gullaume, "Modellng fores fres. Par II: reducon o wo-dmensonal models and smulaon of propagaon". Inernaonal Journal of Hea and Mass Transfer, (8): p Fgure 3. hea dsrbuon affeced b elevaon for case [3] Vegas, D.X., "A Mahemacal Model For Fores Fres Blowup". Combuson Scence and Technolog, 004.

15 Amercan Journal of Geographc Informaon Ssem 013, (4): (1): p [4] Babrauskas, V., "Effecve hea of combuson for flamng combuson of confers". Canadan Journal of Fores Research, (3): p [5] Onlne Avalable: hp:// hfreimages.hm. [6] O'Callaghan, J.F. and D.M. Mark, "The eracon of dranage neworks from dgal elevaon daa". Compuer Vson, Graphcs, and Image Processng, (3): p [7] Jang, C.Y.H., "Modelng Bushfre Spread Based on Dgal Elevaon Model and Saelle Imager: Esmae Burnng Veloc and Area". Amercan Journal of Geographc Informaon Ssem, 01. 1(3): p [8] Jang, C.Y.H., "Dgal Elevaon Model and Saelle Imager Based Bushfre Smulaon ". Amercan Journal of Geographc Informaon Ssem, 013. (3): p [9] W.Dbble, J.W.u.M.R., Combuson. 4h ed. 006: Sprnger. [10] Wllams, F.A., Combuson Theor. 1985, Calforna: The Benjamn/Cummngs Publshng Compan, Inc. [11] Lghfoo, R.B.B.W.E.S.E.N., Transpor Phenomena. 00, New York: John Wle & Sons,Inc. [1] Jackson, A.V., Sources of Ar Polluon, n Handbook of Amospherc Scence. 007, Blackwell Scence Ld. p [13] Franzese, P., "Lagrangan sochasc modelng of a flucuang plume n he convecve boundar laer". Amospherc Envronmen, (1): p [14] Venkaram, A. and R. Ve, "Modelng of dsperson from all sacks". Amospherc Envronmen (1967), (9): p [15] Onlne Avalable: hp:// h-envron/ssems/plume/gaussan.hml. [16] Durrenberger, D.A.C., Gaussan plume modelng. 00, Unvers of Teas. [17] DeW, F.P.I.D.P., Fundamenals of hea and mass ransfer. 00, New York: Jhon Wle & Sons, Inc.