APPLYING THE MATHEMATICAL MODEL OF FOREST FIRE IN THE SOFTWARE CREATED FOR SUPPORTING THE DECISIONS IN EXTINGUISHING ACTIONS

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1 dr inż. Anna Szajwska, Zakład Hydromchaniki i Przciwpożarowgo Zaopatrznia w Wodę, Katdra Tchniki Pożarniczj, Szkoła Główna Służby Pożarniczj, APPLYING THE MATHEMATICAL MODEL OF FOREST FIRE IN THE SOFTWARE CREATED FOR SUPPORTING THE DECISIONS IN EXTINGUISHING ACTIONS Zastosowani modlu matmatyczngo pożaru lasu w oprogramowaniu wspomagania dcyzji w akcjach gaśniczych Summary Th papr prsnts th assumptions for th computr simulation of a forst fir in accordanc with digital topographic map of forsts and short-trm wathr forcast. To conduct th simulation, a softwar has bn cratd. Th softwar includs dtrministic mathmatical modl of a forst fir. Input data hav bn xtractd from th short-trm wathr forcast and th digital forst maps. Th application rang covrs both planning of a controlld fir,.g. in cass whn th firs ar intntionally startd by th forst srvics to gt rid of accumulatd forst matrial, as wll as to plan xtinguishing actions and to plan appropriat disposal of rsourcs during th xtinguishing of a forst fir. Cration of th dscribd simulation nvironmnt ariss from th nd of optimum planning of th xtinguishing actions in local fir srvic cntrs. Th initial risk assssmnt in th stag of planning th xtinguishing action, will allow fficint managmnt of quipmnt by th local units. It also prvnts from rpating wrong dcisions mad in th arly stags. This nd imposs limiting th us of quipmnt platforms to mdium class PC s. Th outcoms of th papr provids accssibility of a tool supporting th dcision making procss and assssing th damags in th high risk conditions of a forst fir. Furthrmor, conducting a simulation allows to stimat th nd for fir fighting quipmnt in th cas of total and bordr xtinguishing of a fir, for diffrnt wathr conditions, considring fir dnsity. Strszczni W pracy przdstawiono założnia do symulacji komputrowj pożaru lasu, w oparciu o dan cyfrow topografii lasów i krótkotrminową prognozę pogody. Do przprowadznia symulacji zostało wykonan oprogramowani, w którym zawarto dtrministyczny modl matmatyczny pożaru lasu. Dan wjściow pozyskiwan są z krótkotrminowj prognozy pogody, oraz numrycznych map lasów. Obszar zastosowań dotyczy zarówno planowania kontrolowango pożaru, gdy pożary są clowo wywoływan przz służby lśn w clu pozbycia się nadmiaru nagromadzongo matriału lśngo, jak równiż planowania akcji gaśniczych i dysponowania zasobami podczas gasznia pożaru lasu. Stworzni wyminiongo środowiska symulacji popart zostało potrzbą optymalngo planowania akcji gaśniczych w lokalnych ośrodkach straży pożarnj. Wczsna ocna

2 ryzyka na tapi planowania akcji gaśniczj umożliwi wydajn gospodarowani zasobami przz lokaln jdnostki, oraz zapobiga propagowaniu się błędów dcyzyjnych na wczsnych tapach. Powyższa potrzba narzuca ograniczni stosowania platform sprzętowych do komputrów PC śrdnij klasy. Wynik pracy zapwnia dostępność narzędzia wspomagającgo podjmowani dcyzji oraz szacowania strat w warunkach podwyższongo ryzyka zagrożnim pożaru lasu. Ponadto przprowadzni symulacji pozwala oszacować zapotrzbowani środków gaśniczych gasznia całkowitgo i gasznia obrzża dla różnych warunków pogodowych, z uwzględninim obciążnia ogniowgo dango trnu. Kywords: forst fir, simulation Słowa kluczow: pożar lasu, symulacja Introduction Th forcast of potntial fir bhaviour is th ky lmnt of dcision making during xtinguishing of forsts firs. Th problm of simulation of forsts firs is not a nw issu. For th complxity of th contnt, th problm is not compltly solvd to dat. Prvious rsults of works carrid out abound with simulation programs which wr dvlopd for th purpos of work in a diffrnt gographical spcificity. Ths programs ar still of dvlopmntal natur and contribut in favour of incrasing fir safty in forsts. Mathmatical modls usually consist of rang of function which as rsults givs numrical valus for spatial, tim dvlopmnt of on or mor variabls such as spd of dissmination, lvl of flam, risk of ignition or usag of ful. Mor or lss dtaild dscription of bhaviour of th phnomnon is obtaind in this mannr. Dpnding on th typ of function computr programs bas on slctd modls of forsts firs simulation: thortical modls gnratd from th principls of fluid mchanics, combustion and xchang of hat. Vrification of ths typs of modls is xtrmly intractabl dspit thy can b xtrapolatd for various fir situations; dtrministic modls built on th basis of xprincs and fir rsarchs which alrady took plac. Such modls apply mrly for systms in which conditions ar th sam as th ons usd during formation and tsting of modls; smi-dtrministic modls thortical and prformd by xprimnting. Exploration of ths modls is propr in situations similar to th ons usd in ordr to obtain xprimntal data. Thr ar lss difficultis during valuation of ths modls than in cas of thortical ons [Pastor t al. 003];

3 probabilistic modls using known distributions of probability for occurrnc of phnomna accompanying firs. Dspit larg numbr of modls, thr ar only fw of thm which ar succssfully usd in practic. Matrials and mthods This thsis prsnts dtrministic simulation modl of fir dissmination which was laboratd in th aim of facilitating th analysis of probabl dstruction and watr dmand ncssary for fir xtinguishing. Computr simulation is basd on th cllular modl using Frmat s rul with a matrix of spatial rprsntation in which a singl cll of two-dimnsion matrix rprsnts a projction on a surfac of actual ara with a shap of a squar. It is assumd that conditions prvailing in on cll ar homognous similarly to avrag conditions prvailing in a projctd ara. Squar clls ar commonly usd for simulation of natural phnomna. Propagation of fir may follow xclusivly by nighbourhood of clls, in this cas clls adjacnt by sids and vrtics. In th accptd modl of fir dissmination th Huygns rul was usd which is known as of light wavs propagation. This rul which is usd for applications of fir simulation was adoptd by Sandrlin and Sundrson for th first tim in It is assumd that a shap of fir can b rflctd by an nvlop of particular llipsoidal sgmnts of fraction simulation. Each inflamd cll constituts a nw sourc of propagation of fir wav. Th front of fir wav constituts th nvlop of llipsis of partial simulation. For th fact of rastr natur of spac rprsntation, actual llipss cannot b usd. Th nvlop of progrss of fir in vry stp of simulation is approximatd to th narst vrtx as coordinats of location can only tak valus of whol numbrs [Knifht t al. 993].

4 Pictur 1. Propagation of fir with th us of llipss in diffrntial nvironmnt Ryc.1. Propagacja ognia z zastosowanim lips w zróżnicowanym środowisku In homognous nvironmnt undr conditions in which thr is no wind, th shap of wandring fir from th point of ignition is assumd to b round. On th othr hand, whn homognous wind blows, th shap of fir from th point of ignition taks th shap of an llipsis [Lops t al. 00, McAlpin 1989, Pastor t al. 003, Richards 1993] (pictur 1, ). A simpl mathmatical intrprtation and th asinss of srvic in th scop of ntranc data hav mad contribution to gnral accptanc of such shap for computr modls simulation of dissmination of forsts firs. Accptd modl, in accordanc with Huygns rul, bst illustrats rality taking into account invariability of conditions. Dspit th dirction of wind may chang in rality, with rspctivly small tim intrval stp of simulation th variability of wind is of marginal importanc. Pictur. Transfr from windlss conditions into conditions with wind factor ar shown in th

5 Pictur. Transformation of dissmination spd dpnding on vctor wind spd in rlation to spatial systm. Ryc.. Transformacja prędkości rozprzstrzniania się ognia w zalżności od wktora prędkości wiatru do układu przstrznngo Point P is an origin of th fir for windlss conditions; point K is th position of fir accssion for givn tim t. Angl Φ is containd btwn th dirction of wind and th straight lin PK. To includ wind thr should b mad transformation of position of point K, rcumbnt at th circl, with th point locatd at th circuit of llipsis in th dissmination modl. This point will b locatd at th intrsction of th straight lin locatd undr th angl θ to th dirction of wind. Sourc of th fir P is of th sam actual coordinats as point I. Sction DB t is th distanc which will b covrd by fir in th opposit dirction to wind. Dsignation of angl Φ allows application of pattrn 1. Φ = cos 1 0,5 ( b cosθ ( b cos θ + ( a c ) sin θ ) ac sin θ ) b cos θ + a It is known [Lops t al. 00, McAlpin 1989, Pastor t al. 003, Richards 1993, Willr 007], that not only changs of th spd and dirction of wind but also othr factors such as kind and ful typ, asymmtry of changs (topographical conditions) influnc th shap of fir dissmination. Cofficints of llipss ar conditiond on ful typ and spd of fir. Proportions ar also influncd by humidity and typ of forst bd. Dsignation of spd of dissmination allows application of pattrn. sin θ [1]

6 ( c cos Φ + a ) b V p = [] b cos Φ + a sin Φ Simulation On th basis of th modl th softwar which uss spatial data as wll as short-trm wathr forcast was dvlopd. Entranc data ar obtaind from numrical maps of forsts and short-trm wathr forcast (pictur 3). Pictur 3. Contxt diagram Ryc.3. Diagram kontkstowy programu As th spd of wind which is input from a short-trm wathr forcast is of a discrt charactr, with a crtain intrval of tim which cannot b changd, it was for th aim of simulation to allow obtaining this valu at any tim of simulation. Thrfor, th valu of spd of fir is avragd with adjacnt forcastd valu for any tim of simulation within th scop of validity of wathr forcast. Th sam mchanism also covrs dirction and a sns of forcastd wind. From th digital map of forsts th significant impact hav: kind of forst, ag of forst, prcinct of forst, obstacls in rlation to fir (accss roads fir, rivrs, tc); placs of spcial dangr. For th xcution of th simulation it is ncssary to introduc 4 initial paramtrs.

7 1. location of th fir sourc,. simulation tim of th bginning and th nd, 3. th tim intrval of an individual simulation tim, 4. rastr of ara. Simulation is bing carrid out itrativly. Th numbr of itrations ncssary for xcution of simulation is stipulatd by tim of nd, tim of bginning and rastr tim. Paramtrs ar dtrmind by an oprator. During conducting a simulation a matrix is cratd in which rsults ar kpt. Dimnsions of matrix dfin lngth and width of siz of th ara. Th siz of matrix X,Y dpnds on rastr ara. Aftr ach itration scors ar ovrwrittn in particular clls. Each itration rquirs mathmatical modlling of ach cll of matrix and saving data to its nighbours. A singl cll of matrix kps data lik: dirction and spd of wind, ful typ, vctors of spd of fir for nighbours of a cll, stat, passag of tim in a stat of ignition. During a simulation a pictur of procss of fir is gnratd according to th condition of clls (pictur 4). Pictur 4.Graphical illustration of th cours of th fir Ryc.4. Przntacja graficzna postępującgo pożaru For th aim of calculation of watr dmand ncssary for xtinguishing th fir total numbr of inflamd clls should b countd for th complt xtinguishing, and

8 rspctivly th numbr of inflamd clls within th circuit of fir for a givn width of xtinguishing rim. Dmand for watr for full xtinction isw was dtrmind basd on [1]. wr: P Wop isw = CCP P- fir surfac [ha] f c - complt combustion cofficint 0,7 CCP- watr vaporation hat [kj/kg] W op - calorific valu [kj/m ]: f c W op ( 498 5, w ) 4, 1868 = Qd s wr: Q d - fir load kg/m (th valu takn from a digital forst map) w s - matrial humidity [%] For th purpos of dtrmining dmand for watr to xtinguish fir rim, th surfac of th rim knowing th width is calculatd, complt combustion cofficint is xchangd for flam combustion cofficint which is dpndnt on fir load Q d. Having known th currnt location of a fir, duration, tim ncssary for arrival of xtinguishing units, it is possibl to stimat a watr dmand for a crtain xisting situation by firmn raching a plac of fir (pictur 5). Application of computr simulations can in a simpl mannr facilitat planning of xtinguishing actions. Pictur 5.Graphical illustration of watr dmand for full xtinguishing and xtinguishing of th rim ara Ryc.5. Przntacja graficzna zapotrzbowani na wodę do gasznia całkowitgo i gasznia obrzża

9 Summary This program has ducational and training aspct for analysts and civil safty srvics. Computr program was dvlopd with th usag of programming tool RAD including th packag of Dlphi compilr. Application which was obtaind in this mannr is adaptd for launching within PC s with oprational systm Windows. With th aid of th dvlopd program, simulations undr variabl conditions can b carrid out within diffrnt forst aras. Bibliography 1. Instrukcja ochrony przciwpożarowj obszarów lśnych, ORW LP Bdoń Knifht I., Colman J., A fir primtr xpansion algorithm basd on Huygn s wavlt propagation. Intrnational Journal Wildland Fir, 1993, 3,(), str Lops A.M.G., Cruz M.G., Vigas D.X., FirSsation an intgratd softwar systm for th numrical simulation of fir sprad on complx topography. Enviromnntal Modlling and Softwar, 00, 17, str McAlpin R.S., Tmporal variations in lliptical forst fir shaps. Canadian Journal Rsarch,1989, 19, str Pastor E., Zárat L., Planas E., Arnaldos J., Mathmatical modls and calculation systms for th study of wildland fir bhavior. Progrss in Enrgy and Combustion Scinc 003,9 str Richards G.D., Th proprtis of lliptical fir growth for tim dpndnt ful and mtorogical conditions. Combustoin Scinc Tchnology, 1993, 9 str Wilr K., Ochrona lasów przd pożarami. Cntrum Informacyjn Lasów państwowych, Warszawa 007. dr inż. Anna Szajwska Adiunkt Szkoły Głównj Służby Pożarniczj w Warszawi. Wydział Inżynirii Bzpiczństwa Pożarowgo. Zaintrsowania naukow: symulacj komputrow, mtody numryczn, tchnologia podczrwini. Rcnznci dr hab. inż. Ryszard Szczygił, prof. IBL dr inż. Bartłomij Bdnarz