CHAPTER II

Possible Areas for Improvements

IlJ I~'TRODUCTIOS

P,eviOll' ,h.pl." hll" id.ntifi.d 111'0 kind' of prob"""; (.) ,,,,.;,, ",hnic.1drlemm..; ..d (bl th. I.d of inter"tion tl<,~ ..n the differ.n' ,,'on in lh•..,virOllm<n,1Il m.nqem.n' pro<:<<>- Th. pro.." ,h.p"r Ji... ',,",.1I0ns '0 ",tv.01 >II.." 10 minimi.. ,h... probkms,

Commun".,i"" dinkul".. ori.. from the differinli><TSpO.1i.., of ,h. decision·""'1:.«. ,h. mod.ller. and ,he 'p.dal,., in 'h, "0';0.' wcio!bio!ph,..;.1Il ",ion""di"'iph , This r"LlIt,. for .",mpl•. in ,h. conlli.1inl 'p<ciali>" .."u~.n..lIli".pprood '0 Ki.nliro••n.ly,iI. Th. dl.ho'omy b",,'••n ,h. oinJk-diKiplin.Ki,nti".m! rho ""II' bre'd <>f Inwdi",iplinary .naly", ohould b. recol"i..d. Th."OT< al'" • ".mbe, of 'echni••l p,obl.m, which ohoLild b. dl",.",d.

112 NPRQVBIE"'TS IS SI~IUL\TlQ" ~'EnIOOOlOGY

11,2.1 Modellinll wi'hln • Bro>d<r Conl.x'

Many of ,h. ,«hoi..1 problem' .unufi<d In Ch.p'er 9 ... 1>< ov<r<;om., or"I•.., milip,«I. by pla'in; ,h. rnodeUIn; pro<:<.. ~'ithin the broa<ler .on,u, of"t,., h., com. 10 to< kno~n .. '.ppli<d ,y".",••n.ly,i,' (... a,.pt" 3). Th. b....ph.... in ,h••)'Otem, .n.ly". 'T< ",mm"".d in FlgLl" 11.1. Thi' diaa'''''emph.sizes lh. poin' 1h.o' the nl<>d<11int; .. ti,1t~· " ..If i. n"",...rily .mbedd«l in •seri.. of d«ision, .bou, ,h. d.frnition .nd bOllndinl of the problem, lh.ldenlifl.ltlon of JO>ls .nd priotiti.. Ind th' i.Mlltlon of .I"m.ti.. "'Io'ion', i" ..wilh whit 're 10000Iy 'erm,d th. obj«'i..... of mod.li,"i. By foeU....IIIt.n'ion onrhos< et..rly Id.nlifi«;l ph.......p1ici' T<,,,,,,rlion of tho foc'oll ronlroUinalh.mod.lIin~ pr""," .nabl.. m..y of 'h. "clIniclll problems to b. by-puse<t.Furthermore, lh, itt"'i'" n.tu.. of th. d«i,ion. th.t h.ve to b. m.d••bOLIl thedefinition .nd bOllndina of 'h' problem, 'h. ~oaJ, .nd p'io'it;". <lC .• h,lp. '0

"mo.. lhe r..l.... of <"".uaint that """"lmo. rnhibit tho d.v.lop""n' ofad.quo" mod.l..

11 should perhops be ""...d lholth'" .ro som' probl.m. fot which predictivem:xI.t1inil i. unlik.ly '0 p'Q>"id•• f.uibl. soIulion. FiguT< I U ",m"'ati theb.." deci.i"". which Iud '0 the elIoi.. of mod.lllni "'n 'Wrapri"t " reb"''''SY. """""led wi'h 'h .... which ohOllld lead to • "je.tion of 'h. Stl"'SY. Inparti.ular, p,oblem. ror wbieb i' i. impos.ibl. '0 d.fin. 'h. und"lyina "Iationship'be'"".n ,he ....n'ioJ ,I""'nu ... L1ntil:..ly to 1>< .u",...fully add"...d byrn"odelJinl. Funhm""lO. mod.lh"l i. not usuolly .. inoxi><Miv. '001 .nd tho ,,,,tIf'''' to< ""lob«! by th. 'mporl.... of tho probl.m

,.,

""" ..,,""-----"'....,-­-_.._..

Iu .....,...'_..----,,_.._,.. <--,

I~ ---..,,:::.-:::::.:::- _.~

, ,ooom_.. •"",..- ,

I-- .~."."....-"T"-

If it i. d<dded tlut modellmg ihould be used, tb'n ,h. extent to wbich model.11< >ggr<g".d or dl<aggreg>.ted in hoth tinte .nd .p''''' "'LI1I1'1.I)" h. determined bytb••poeine 1",,1,.1\<1 priorit .., tl'" h.'JOl>e<n Idtntlfoed once lhe problem h.. boe"d<fin.d .nd I>ound.d, There I, littl' point in in'i"in~ on ,h. d."lopment of •hilbly '!!l!"g"ed mod.1 if 'he hlghe" prioriti.. hoye boen pLaced on 800. wbichClIn be uti,ned only by dl"ilIr<~"e<! models, ,nd ,ice ;''''', SLmil>,ly, it '" ",,!domn.." ...,~ 10 d.v.lop .11 the .ub·model. of , dl,""ro~.ted model 10 'be samede~'«, and til< 1.,..1 of del',lupm.n' "'ould b. determin.d by th. priori tie. whicbIu". been identifL.d In ,h. e"li" ph"., t'e""rth.I,,., lechnical dimeul".. m.y

8 _., ,-" ...""', ....'

•-..".~.. ..I ..~". ,,,..,,,.._,.',., , . -''''..,...~,~~"..."""I ,-,.. '... , 1m~':".~... ,...~_--.,''''',",',. ''",

17'"'--''''-'- , ,,_ro...._-- -,,~~ ..,. •.......'v.._" ........,~'.., • ..,."".""'...."".n....,--... ",,,,,,,,,.-' .. oo ..... '"~ .._'" '""".'''"' _"n_~-,,""' ....-..''''' •-,-.Me.,"" ....,. _...",,_.

, ...,""'"

,

Filuft 11.1 Flow di1l>'am for th. use of predict ... model.(b..e~ on ,ie"'. "pre...~ In SCOPE [ 191S.I )

'<qui" the priori'i.. to be re".,,,se<t from nme to time durin; rh' moo,Urn~

proo....Th. cl.. r "'tern.n' of tb, objo",j,.. of th, problem .110 b.lp, to o"wo",'

<Orne or th. te<~nic>l dim"ulti .. ,,1.l<d 1o ,nt .".ll.billty .nd coll"'ion ofd,,,.Ol'er·depend."" 0" p"t dat••tId inform>1ion can ",,,I}' I.:>d '0 d,,-elopm,n' oflb"" p.m of th, model for which ,,1...,,1 d.t> Jr, "'aibbk <Y,n wh'n ,h...p>.1" '" of I",,' priorit;-, Tden,ific"ion of ~0.1••nd priori'i., "'ill f"qu,ntly .nddr"ticolly "duc, 'he '0,,1 d.lO ... whi,b " ..d. to 00 incorpo""d m'o 'h, mooelrnd will Indic,," 'h"" or.., for which n.... d>t. "ill hav' to h. <ollteted if themodd ou,pu, i' '0 mmh lh' r<quirem,n" of the probl'm, Whil, moot scienlimIi'e '0 emph"i« th. b,' of d>t. within th.i, .pec"l field, "peri,n" in theroodelli!tJ of ,n""OI1men..1 'y"e,"" "'u"" th" 'h, ,on"e"" proMem i. oftenmore inhibr1,ni'

EmOoddin; lbe hiihly ,«lini,>! prOctSl of modellmg wi'hm ,h. con"'l of•.,.,,,m, .n.l.,.,i' .1", h.lps 10 prevent rli. u" of '""rely m.ppropn." mod.I,~mply I><c.u" they .Ir"dy "j... and discour'i" the hun' by "clmiqu" forprohl.m. '0 be 001,''';, Thi. "",y be p"rtkul.,ly imporlanr in d.v.lopinj oountrie,wh." th, lure to u'" ,,,,,,n~ modd. I. par'icul.rly "'ong. Th••mph"i. of lh•.".ly'i' i' on ,h. objectives••nd ,h. g.n.,,",on of v,,'ou••olution. 'nd"""bem.ti,,1 mod.lling '" bo'h dopende"' upon tho .u<<<"ful complOlron of tho"'lrer p/t.<eo, Th, on.ly". 0100 "re.... the n,"; '0 d....lop more th." on. mod.1for .ny OIl. probl,m ... r.nect;on of Ihe ll.n"'tlon of diff".nt ooIutron., Ag.ln .•xpe""';:' in th, moo,llin~ of en''lfonm.n<>1 '; ,"m, .ugge'" t""t it i' diffi,ul, '0,,<eo, in aJ",nc. tho li,.lihood of wc«" of diff.",nl type' of moo,bond mod,1"""gi". It WIll, therefo". u,u,lIy h. n<ceo..,)' to pu"u...""aJ """p"~mul,.nt()u'ly. " 1,.., 1n lh. tarly "'i" or th. mod,llin~ ph.", v.ff",. 19i2J.

11.2.2 Pum,,,I.. E,,im,,H:>n

Any e"'iroom.m.1 moo,l. ,,,.n • ,,1"i"'I' ,impl. on•. will <onuin • I.'S.numb" of p.'",,,,,,,. Th"" at, ."im.t.d flO'" d....ilh" pro"id.d for ,h.rood.I'" or by hi, ..",h of the lit.,,,u,, Cl<uly only th, molt 'o<ura'. "ri",.te'ohould be used, Thus, the p.ra",."" in • ,imul>tion moo.1 rn.y h••"im"e<I rn anumber of ""1" d'p"nd'ng ""y muoh on tho n"ure of th. moo.1 .nd th.,,,:ill,hlll'y of d.,.. P"bo,.. the moot popul" 'pproooh " to u.. '0"" form ofd"'Tntini"io 'rrtlina' proo.dure i" ,,'hi<h ,h. moJo! par"",."" .to .dju",d in>Urn, m.n""r untrl tb. mod.1 output provLd". belt fit (u,...,lly in • Iealt'''lWf<..n,.) '0 the oorreoponding r..l·worid ob..""trooL OubHy. ho...e"OI, th,..tlmatron of po"me",. for. m.th,m.otioaJ mod.1 irom , otl of fl.ld oh"''''>tion." • ".""ie.1 prohl'm ,nd n,.d, to be udd,d u~n~ ,,"""ie,1 m"hoo,. i" ..me,hod, "'hich uk. 00" of th. 't>tiSlicaJ n"ur< of th, probl.m md provide"timo", with ,h, u"""i>ted st,ti"ic.1 properli." "''hik lhor. ar<. ho....v«.numelOU' ".listie,1 "chmqu<' .Viil.ble for ,pp,,,,,hing lhi. prohl,m (l"hniqU",u,h ., "ne,.li"d I• .,t·"!u,,,. ond m..imum I;hlihood) 'h,; "< m.inly.pplicobl. '0 m<XI.I. Ih>1 h.... w.U-4.nn.d ittu""" '" th>t tho ..tlmationprohl,n, i. w.11 po«d. bur <n,iroom.nta] 'y,,,m, are oft.n not ",lI-4.r.ne<l, Inmony CO"'. th. mtem,l ""chonr"". that ,o..m the ob.."od b"h"lour ore iinl,und.",ood and, as poin"d oul p"viou~,.. Iii'" i. ,."Iy ,n opportunity 10

,,l'",fOflll p1_ nptntnen" \II., mipt d."ly , ,"'" ofth... _dlan'...... ]"sud! • .,'....1I01l." io_~- 10 m.ke .. efl'lOlan ~l< of lb. oblt.-l....bI.. oI>'lltIOd "~""l1ll. ·.., .....1opt..'iOa' oftbo O},.t<m ,,,,,Ibn .. ,Ih In,prior ifIf '- !bat ,. • ..n.bl< obaut doe phyoxal""~ff of!llt "SU1Ol- E"On 00.lb< II ' of U1f..-.- ...-.. .. Ib' oysItlll " .•. priD< ..r""",~ an4tlbk.oed 40..1 _1 .liII be _if-=-, ....,...Iy '0 doflD< tho ...t ... of ....-.l.l""" Ih«.... of ......,... _ -"AdU' "'_ ...... b< uUoI.."O1<03IIII.' .. 010) _""1_, "'-111< """""1

Tlw<. _. _ ,1)' 11<. """"" _"""" be, ..""" panmoo.. om...ood-.: o'"p''' u_, T1>t """": .ont_ """)' .....".. fn&.d......' <Iaoop_tbe ,<4 ........ of ID&II} po aad _ po""...f~ ...., II"

_D .,ffo ,. In "'tin po......., I Off}' ....Ifk..' inn~"" 1IIOd.1 "'''1''''.Th .... tho ••:"<"..<)' of tho ",,,,1<1 _'"'PUI w\lI bot ""',••""""••-....,.d .",h III .,jol"".:10f< ,nil ttl< .1'1"",.......... of tho '''''''11On< w.ed [0 ~_o, tho .....,,,.J__",.of' lit p""'lc", bel'" ., "">0<1.

TM", ;, 'IItrer"T< no <>It>er "'Y of do'..mln,... ",od.l 'CC1"",,~ Ih"" b)comp'''''' mod,1 <><l'P"' .,th ,ul·hf. d.... Wlltr. th" 'Onno' b< "<>n. fur ,h •• '(Stt'" " • IOhol •. 'ht" ., 1<", th, "'Utley of tht .uo-moool. ,"oul:,! be kn"",nH"e 'pon. If 'here ore feedb"h btlw..n ,h' I~b-mode], il become. dlff!l:~II (If

not impoulbl.) ". know hoo' Ihe <nO.. asoocl.,ed ..ltIl ..<II sub-model combine inIh. toul mocl<l, Tho.. ou~' 'hu. be no .u,I"l<:oI II>orl "u".nd OI>IIfidcnc< m.~

Iuve to "'" oumly 011 ..""",ualed expe"",," .. ,til the model8..""1 In mind tbe .."nut"", pool>letm 'M' ._ b of tho ilMelln<d

""tUf' of ....ny .....""....nt>l 01_ 1)'_ " is yo ad '0~e 1IOOd<1 _lion b~- ... ex'm6od potiOd of'noodel x1enuf",."",,· h",hdl.ffn,," p1_ibl< _ ItT1l<'1Iffl an 0"-. _oppropru1<. """,,,",,,, .. 01_,hod.. C.nOlllly. 11 --... h,,""- 10 _I ponIIl<ltr ,,"" tl"1b< .."",,,,,a! r_ oflho model ..~ It ..-, r", "' lIIe___ ~ ...... _ffi<;osIll".d.. 10 cNno<ln,.. ~d.u III. at .......

ClIRIM. tl ~'Jg.,..topenb_ of. t WI Indo Iiab..,.·pool>~ "'" fw>d_~' _ ,"pl' " ..... Some inIb>l 1)'_11<

_ ....... ,0""" ptOblo... 01 _ ..""'I ,.."'.."" "- b<ctI .......<d.MIW.. II ..__ [1II_ ..or!< .. tlus (Good '9'.~

',11.., .........1..... '''''''''''' in wIudIl<'CClplUllIo "' orId _ .._ arelltirrored In ponr<ul.. poocn><> ..',til," "'" mod"'. tIlen;' i. ''''''l'tin! '0 .......,....., r......"mulon of til< pa,.._,... for t..... 'ub~Ile"" on tile b_ of.J 10«expe"""n". Such on .pp,,,,,,h <all be .ffcc"... p.n><ul.rt,. if""" un pan til.expe,i....n1 '0 temo" poo.ible >denll~.b,h1y problem~ If ""'h exp",.....",..pllrlllini II not po"'ible, h.... "er. 'h<n I"" "" "''''''Id bo "k.n, ThedccompOiltloo "'auld. for ".mpl., b.lnlO "llIi..ly ind'pendenl ,ub..,."em. Ih.tcon b. Wim.,.d ,n i"'I"ioo.•nd ",h<r' tho ..,im"ed p."""I<" Cln b'COI'IIrdc'«I 10 bo $<n.lbl~ independ<nl bo' .....n suHf",m•. AI..,. ld.n"fllIbllrl)"probl."" can ""CUr wll<n • <ub-t} ",m is C«l'"",«1 • ,tII,n • do..<1 f«db.ok h'l"""re. tho O$t""'''011 0( the .ub..~~,.", p."m.,." lD lIOauon on til. bl... ofobs<r«-d lDJ"lI .....tput ..nobles CID prod_ "'....ad",. fflUl",

Eo....h<n I<ltntlr..brh'y pn>l>lelN h... beC<I ._lOrd tile.. "II ,........ til.

pntblem or obI......, I<b~1y .rr""1 Ci.< """ ,,"'=) "'''''It. of th.~m .. Iho _I As ..,110 tlIo i4<Iltlf"",t_ ... 1m ~ uaIy.........

d ..dy 'om.in m.oy u",=I ...d q.....,ion. _ q....,ltuns ....hich con onll be .ns r<dby zr••ttr r....r<h intO the 'PI'~Cltion of d,ff.r.nt m,th<>d, '0 rul o,k!problems. I\'hlt.'~r ""'th<>d i1 Uliliud in pta,net. hO..·.~I. tt no.... ICmlS ilmolltsSt1Iti.1 'ho' 'ho unc.minry inh...n, in the moo,1 'hould h. quontlr"d in 10""mann.r .00 'hat 'ho ..timotion Ilgorithm 'hould proYid. m...uro' of thoun,m.inty ,swct..od "'ith tho ..timotod por'''''''''' .00 'ho SlCKhas,ic inpu,..OIltpUt> of tt.. .)"t<m. Such """.ut<S ,:on bo til m,ny form•. from oompltt<prob.hlIlty dl.tributlon, '0 moT< I"nitod informltlOn on """tl,,1 momeot>.

11.~.3 T...,tmenl of Unotr"U;",y

S.....I qUit< d"hn<t WU,et' of unctrt,int~· Ill" '" ,,.i',,,,""n,,1 model,. Intho fint plac•• 'h' System i,..lf nay be ,ub';'ot to diff",n' tyP'" of uo«min,y.For in":onee•• 'j'"'''' '" ith • sm.lI numbor of .I.""nts.•ach of "'hi<;h boh.v<."o:;ho"i<;"ly. "",not bo H'''od as <I<<<,,,,,oi"',. Th. diopenion of pollu,ants intho It"""pl,." i, lOO,h.. ob'io'" ex.mplt. ,inet 'h. tr";'ctory of an indi,>:!u"portid' i. imposoibl' '0 prodi". Any ,,!b.n pollution m<>d.1 i,. '0 'hi••x"n,.uneert.in OJIo<p' in. Sloeho"i<; "0".

Other u,"",'tomt'" .ri.. from the proo<1O<S of ob""'''iorl .od mod.Uin& ,nd. "..... ho.....n. lhes< I••d '0 unem";",i•• In both th, "''''''u" of ,h. modellnd thoPO"""'" ."im.". th.. ,h.rlot.ri.. this m<>d.1 .tructu", Furth.."",,,,. 'h, initi.1,,,,,ditlon, on 'h, "ot. of tt.. system (...... ioh ".n .lso. of cOUI1<. bo conlid".d",unm"""" ')'I«m p>r'''''''''') '" of,.o .nbj«' '0 "to'. All of th." ,"Un:" ofuncert.in,y oombin. to .ff." 'ho mod.1 ""'put. ""d it i. very d."ubl, that thilshould be ol••rly .,pT.'oed. For ......, purpo"•• it m.y ""ll b••ppropria" (•• io,h. l<cd.""y in th, "o:;ho"i< """trol lit"alure) '0 oxp'", ,h. '''''0 'ype. ofoo«r"m'y ..po",.I}' _ tlut inh.ront in t.....}''',m ,00 it> diuu!b1n'''.'OO th1touporiJnp<>std 'hr""Jh ,h. pr""..... of ob""'1IlJ and "P"..ntilll it,

Ou.n'i'.'i.. informlti"" <10 .U m.jor un«ruinu•• in lh' mod.1 i,. of 'oul1<•....otill if mod.1 OUtpo"'OO for«as" ... to b. '''''<idtrod In prob.h~i.ti, "ItO•.

Thus. II sboIlld be. o""sid.ration of Ih. mod.lt",. prooess. p..ti<ularly ....h.n themocItl is .pplitd '0 d"I<ion "",ki".. th.. lb. source, of Ihi. un«n.in,y should b.,,.,.d ,. d .. rly 1> po.libl, .nd any """pu' vol", or foro,",' shook! bo.. 'l>OClatedwith it some mu.ur< of un""rUinly Ot ,,,,,M.nce bound" fot ...mpl<. in 'h.limpl. G.uui-on d"trtbu'ion ,u<. Ib, mod,1 ou'put "'oul<! b••upph.d ,,,,,th....,Ib boImd' d.fin.d by It< <tandud .,to'. Also. ,h. provision of .""h IOform.,.,noould .oppr..' tho "cd.ncy of ""oy ,imul.tion mo-d.U<" ,xolu,ively '0 u'ili,.d...,mmi"k mod,1> for fo,,,..ts io hl~y un«rtain oircwnoWl""L If the d.cisionmlbr Jr.... to expoet SO"" mdioltion of ,h. m...u« of oon(>d.n« 1>soct.olod wi'hlimul"i"" mod.1 fo<o<a.... 'hen porn.", h, ,"ould b, I... willms '0 >cetp'd<t",rnni"ic mod,1 """pu"" foe< vol....

A' p"..nt. in mos, ru1lstio mod.ls. lho only .....y in ..'hi<;h lh. u"".".in'y inm<>d" """pots <.on b........d i' by Monte carlo i1mul"ion. in "'hi'h r<p"'«!"""ho"i<; ."""I.tioo. of ,h. model .'" u,~",od to Z.o<",. ."im,,., of th,prob.bili'y distribution••l>OCu!<d ....ith th, mod,1 OU'pU'L Th, prchl'm wi'h "'elian .pprOIOh i' 'hat it o:on bo compu,.tionolly ,,,h.r in.ff",;'n" uch ,,<>dIuti<limul.ti"" I, d,nned by ..I«,ins the sto:;lII."o mod.1 p'rl"""" 0' Inp"" f,omth<ir ."""",d (it..•"im.o,od) paft1ll probobili'y d"tributron•. 'nd 'h, '0''';

"numl><r of individual Jimubuoo. of this type rtquirM to pr<»'id. 'deSIred OCCO""rIn lho .. ,jnut< of 'Il< OIl'pU' prob.hih'y di>lribu,i""••In l>e ,-try high. """ly,,,,111Ippn>a,h.. 10 'he probl"" >Ie ."il,b1. rOf ,""pI< lin,.. ,}.lOrn. bUI. for ~.n<ral

non-lin." 'j.."m" lllo ool} eu',.., .It.,n"i,. 1o Mont< C.rlo ,unolll;on i. th, ultof ,,,I,, ", polynomial approximation "'''ho'b. •nd th.I< .an b. qui" complex..,d difficult to "It. If mor< 110.,101. lnd oomput>,ion,lIy erf",itn, stati.liealIpp<OICh<. to thi, prOOlrnl eould II< dtvise<l. ,Ii.rtf,,«. it "'oukll>< ...Iooble0<1,..""" (Bum•. 1915). The r«tnlly in"od"<:<d 'm<'hod of ,ompound .imutalioo"(FrlJISz, 1974) "'''''Id 'ppear to be ••i~;f>c:u" It.p in ,hi. d"e"k>n,

1l.Z.4 SensitiviTy Anoty.i.

A, in the co" of ••Iid,,;on, ,tle,. or. diffet<nt inl.",re'";''''' of the tum•..n'i'ili'y JoIlYli" In ,.n<raJ. it i> "ken 10 ",nn ,h. p"""'1S of ......ina ,h.chang« in mod.1 bohnlOur thlt ",SII!' from ohanl" in mod,1 inpUl ."iabl",milial oondillon., pa,.mot." .nd, in ..,.,.. c...., mod.1 otruetUl< S""h lnfOll1\Otioni. of """.ir!<,.hl. impofl.nco both I><oou.. it can lnd ..... 10 rho mod.1 build.,tho« o.pec," of tl>< mod.1 wh'ch or. of dom,n'nt imp",,"n...nd n«d coreful.......... nt .•nd boe."", I' can h.lp the policy anU)'" Il'l fully "-..!"01'''3'h. mod.ir..ul" i, any 'ubO<qu<nt " ... of th. model.

Hoc, apin, how••", •• In 'h. 00.. of p"am."r .,umotion. ""oi'i,;'y .nll1y'"..n I>< con'idered from ."her a d.termini"ic or 0 otod1..,io "i."'poinl,'od m.y b.corried OUt .ith" in 0 oompl".ly in'uiti.. or in a mo", .y.tem..ic m,n"." Itowmucb .ffo" ohould bo iOl'."ed in imprO'l!nlth. ""U'o<y of po,.mo'''' (wh;oh;""01... fUflher HI"'nm.n'oI work or , mol< .xh.u"j". Iite"'u" toh) willr!<1"'n<l ,., how ..noi,i.. the mod.1 oUtput is '0 the pOI"""'''', Thu ",H.bl.poramo'" ..Iu.. should bo ,ubjected to ...n~tivity .noly." bdo.. mot< wo'~ i.und.rt..... to impro.. p,,,m",, ",e",,"Y. VaI;'u, .n.lyticol proc<du... or<

.",il.bl. fo' "",.iU.i'y .n.ly"io, ,,".mly 'oo mony '0 .""mora" fully h"•. In ,h.control .nd syst.ms litor..u,., for exompl., d".rmini,"c tochniqu .. b.><d on·..nsiti';ty' or '!'M.m.,er iollu""''- coeffio;.nlS 0,. .....11 ~"'-''''n and utilized, whil.,in ,b. ",nchao'ic ..... Mon" Corio simulation is oflen use<l in 0 "",."i'ily onolysiorol. (Tomo.ic ,nd Vukob"'''''ic. 1972, MHIe, <1 ,I.. 1976\.

Of"n. mi.I••dinl ,..ul" COn be ob"intd from ..n~",'''y anolyli., p.rtICu."lywher. the an.ly,i. i. noo·';"tem.Uc. It can I>< d.ng<tous. for ..ompl•. to ......mod,l ..nsi'i';ty '0 ".ri..i,.,. in indil'iduol par",,.,,,, under ,h. implici'o..ump'ion 'h" 'h.... r< ind'l'<nd.n' of o,h" p."m".rs m tho mod.l, P"""""..tim.,.. are ""Iy ind.pond.nt of ..ch oth" and ohong" in on. mo" of"n b.occomp.n,ed by .ymp"h.. ic ch.ngos in oth.", Thi' i•. indud, on••d.anug. ofthe mol< .nolytic .ppfooch•• ""Hch """1< ,h...uch rel>tionsllip. 0" !Ok.n in'oOCCOOot, In the ....00'. C"lo "mulari,," .pp,,,,,,h. for ...mple. ,h. rood","po'lu,barion in por,,"."" i. c"""olied by ,h. jorn' pfobabi!lty d"'nb"tion..,rmat<d for the p...mo,er~ in th••impl." G."....n "... by the 00'<>1ion«matrix <If ,be e"into,""" errors. I' should b. not.d 'hot. ,n order 10 oblSin tMc"".rionoo motrl. of th. "'im"ion etrolS for.U por"""e,,, it would b........ ry,hat.lI po"me"" be ,in,ul"n.ously dmrmined no, OIlce. but mony tim.. uod"I variny of ,nvironm!ma! ci,cummtlt!!.

Once apln It must bo <tI\ph..iled ,h..,., in the co" of ....d..ion, moo.ne"

often pay ooly l,p ,,,,...'" '0 the eooeep, of ..n"",..,) .n.t),,;,.nd 'he,.. i" noedfor more r..emh .nd d"'elol"""n' in 'hi' impo'lan' area

11.2.5 Va!irLo,ion

TIlt 'tIm ·valid.lIon' " open '0 differen' in"rp"",ionl ...hen .ppbe.l '0.unul..ioo rnorlellinJ. Broodly, i' i, uoed '0 de""ibe 'he proeeSl of "'''''I "heth"'he sene,,1 beh.v\<>ur 01 the mod.l i' > ',ea"",.bl' rep"..n"';"" of ,h. ,..I·lif.,,."em beln; rnorlelled. or ..heth" 'he me.;h,ni"". inc'Orpur,"d in [he modelroineid. in 1001. "n" "..i,h ,hOle ,",umed '0 ,h.roderit< 'he ..,I ""'m, Such·, ..'i"l· i' de.,I)' open [0. lood dul of ,ubje,tj". )uds-m.n' .nd ,mpro...men"depend very mueh 00 ,",."".-..1 rel>tion>hJ", roth" ,h.n "n me'hooo",,),

(Iearll·.•00idotioo in 'his le",..1 ..n.. II '00 \<>ole [" enrou,og< muehoonftd<oce in 'he model. partieul.rly f'"" ou'"de U"", i.,.. u.." "'ho h.... no'tllemoel... la,en part '" th, mooel bulldln' """". If 'he model i' to hI'" •''''ler eredibili,y. ,berefOf'. i' i' """"'1)" '0 ,""'Id" "'IId"ion in • m"" 'p«if",""i"i,a! "n••" in o,h" "'ord" '0 gi... ""'" qu.n'i'" i," "'pre.."'n uf th. '.,"n''0 ..hi,h ,he model ,har'deri,,, ,be .l....m und" in"..'i,,"on. In 'hi' ..n.. ,I"lllid.,iorl i' "'ullly ,.),;en '0 me.n • prOCflS of ,n",,!, ,be moo,l apin'l dOl. other,I\;on ,h., used In ,he parom"" .... 'mation ph." of ,he """<i<1 buildint _ in ",horword" ''''ina OIl" , d,ff"'n' ob.."""ion ,"'er",1 to 'hot u..d in mi,,,1 modelbuHdi"i- Such te"in, .. ill u'u.lly 'n"i1 eompu'in" [he error v«'o' b""·..n ,h.rood.1 fo'ec.." .nd ,h. ,·.Iid.,ion d." "" .nd ,hen ,,'.lu'''"1 'he " ..;,~"lpropertl.. of lhi' '''OT '<elor '0'" if 'hey eo"..pond '" "hot i' expemd f,om'h, e"jrnotioo ph... of 'he "'.Il..... It .....100 en,," ...Iu>lioo of th. "."".. aJproperti.. of ,h. mod.1 v.rl.bl.. th.m,eI,." te.,__ Ulln& Moote C.lIo 'lI'I1ulo,io"....Iy... Of ""'" 'qu"'aJen, 'echm'l"") ...d 'hen _'OftlP,rl0l th... ,,"i""01prope""', "hich coold be in ,he f"rm of rompl", prob'bili'y d",,,bull""', VI'l,hthOl< "",Iu"od from 'h' dot> in 'h' "alid."on lOt 'nd'o' the valld.lIon .nd.."motion .." combined.

S"',";caJ .alidltion ,n ,h••00.-...... i' oot .osl· om« i' require, no' only ,h.>ppl",,'i"" of ;ood m""ica! melhodoiocy. bo' ']>0 ,he ""I.ilillo" of 'he....lidot;oo dot..., (01 ..ts, Iin« ,le.rly 'he more ",lid"i"" 'h. be""I. In 8'ooroJ.dot••re OIuolly ., • premlUm, .nd IQ ,h••nol)'" must ."h" .n,mp"0 oblainmore d." Of .mph..i« '0 ,be u",r 'hot full ,·.IId"ioo ..... n,,' p.,..ible. 00 'har 'hemoo.l "'n,"u" sltould b. ",.w.d ...ith 'hi' In m,nd,

In 1<"""1. no' ,nou,h ,ff"n i. dir<e ..d t"",,,d. 'h, ,"imotion .nd ••Iid"i""ph.... of rOOdel build,"" prob.bly hee.1l>< 'y"'nuI'", m"hod. of .pp"",chin;mod.l "'II'I11lion .rid ,-.I>d.,ior1 hav, """ r..,i,·ed much ."'""on m 'he~mul'lion'modeWn8 ht">ture. The.. i•• de" need in the fu,u" for ,h.limulotiorl mod.lI" '0 tok. more io",.., in 'he u>t of .",i.I ...l method. of'''inullioo .nd ",Iid"ion. A, 'h, >am< time, ,h.re ". ,orrelp<>f\dinl n.od fOf

''''i''kan' (particul..l), [hOI< 'pec,ali:tln& in """·,,,n" 'n.ll'';') '0 ,,,., more"',n';oo '0 ,h.....,,,1 requirements of ,imulo.'ion..-noo,lIinl'

11.2.' Compu'" Sof,,,·....r>:! Hard......

Th". 'f< b.Slcall,. 'wo .pp,oach" to 'he problem of mod.1 lI.n.f.robihty. Th.nn, 11.. in lh. un,fteotioo of "mul"ion I.ngu"" in'n • COmmon I.n,"'l!'

-,und".,ond.bl. by.1I model bUIld.,. ond. if "",~bl•• to 'ho>st in other dil<ipline•...ho ;",.,oc' "'''' !lit mod'i buildtrL It is, perhap., 100 much '0 bop< 1~" .uch.uni••ruI .irnul.lIoo lool"as< ~ill be ••<>Ivo<l; tht,. It. n..n~ difflCultie., not 'heIta" of ...~i'h i' ,he diffi,uhy of pe ...uad;~ pe<>plt .trudy ,,0«1 to. p.nkulorllnln"1" ,,, ch,ol' m.",ly for conformity. Abo • "";Ie I.nru"l" mip" ,.ff.,,101.. in "rm. of n.. ib;lily Or complexilY unl... d••ii!'<d 'Or}' " ... fully. A mOl<p""'i<al .1l.mOli'-. i' 10 ...OO"di... "I"i>ely ""'all numb« of ",""louont...~ua!", {both 'ootUluon, .,","m ,tmul1tion and doc,". "'<nllth" .re 1''''''olIyocc<pubi. to .yst.m 1<1tn,i"L Sack ,,In<l.r1lized I,,,,u.,.' .rt alrtady beilll..<>I,e<! (•.~., CSSL and SI~1ULA 1(!leny"", 1976~

TOO.y. the mod.ll., " ooofron'O<! with .n 11m,," <mb""""n" n,..'y ofsimul.tiOfl I.nguage., ."",h .. D""A~O.CSMP, ACSL .nd SI\lUl..A. in addition10,lit ..".,.I-purpost" 1aJ11U.g•• '''''h .. BASIC. ALGOL FORTRA 'Ii ••nd APL which,an .100 1>< uO«! r", "mul"i"" pu'posn bu, which do not noc.... rily m..' hi.",,«I. coI1«0...ly, Th, .. " nO doubt thl1 'h, .pecWlZ.d .irnul.llion I1ngu:og..." In

many ....y. , ..itr 10 u....nd ,""ul.. l... P"'II'IlmnI'"1l t.... Th,y.", how,.. ,.,"" c""""entry ....il.hl< on dlff."n, ,,,,"pu'" in",Uarkln.. p,,"cularly "".U..onn. and c<>nuq",ntry p'ogramm....,i".n in ,h.m ... ollen 00' ....,ally"an.f".bl•. Some of ,h... I.n!"'ge' tend to 1>< "ful of compUle' .p.c<. bothIn compilation .nd ""u,;on. Ho...""" 'I"" iJn. th" th" situation i,imp, ""in; (Hoy. 1975~ Th' compUte, r.nau ,Ua«l. 1>< It ,...raI·P"1J'O'" 0'.pociallud. I. on... """,u..d in • m'M" which rna" ""''',ain ,be mod.Der '0"""k in. particul.. mod. -. ,onm.inl of which be m.y 1>< hardly ''01''', Also. i'is importlnt th.,. wh.n u"nll 'peo"Ii"d 1."Iu'S". ,h. u." "'ould be ''01'" of theIl,uetur< .nd proce>... 1><inl .upplied .n'OTJUrlically by ,h. lanll"'" A roodI.ngu.ge .bould. therefo". IOform til. u.., "'Il<" it h.. in..".d f"tu... not.pedfied by t.... mod.II".

Sornt Urnul";",, I1nllu'ge. hOI" the ..al""b" r..ture of p,odu,int inle"".dia,ero:lin; in on, of til< JOn"al.puJPO'" lanllu"ll'" Thi, bo'h .nh..",. the ",n.r..•.bili'y of model...,it ..n in them and Il"" tile mod.n" • <h'nco '0 ..~min••nypo..ihl. UIld..i,abl••fftcll of th. <ompilinl pr""....

The" i. r>eed f'" wide discuWon of the meri" of the simula'kln lang..., in<""'P.ri"", bo'h ar,,,,nl th.m..l...., .nd vrith ,h. gen".I.pmp<>ae l.nIlUOll'~ Thi.disc",si"" ohould not "".....ily Iud to the ..I<<tion of. p,,'lcular I'''-Iu.....'the 1><.... bu' ..the, '0 ,n ...........nt of ,,1.,1v. meri...nd drawbxh. andllrid."", .. '0 "tI,n nn, '" \be othe, would be til. mo" 'ppropria'•.

Simutation p'ot-rarnm.. of"n u.. a lreal deal of compu"r spa« and I..... To"""' .xten' 'hi' "n"" inemcient p'oarammi"!. bu, Ihe 'irnutati"" of. compl.x'Y'''m will x1....Y" be d.m,nding;n ,h... "spe,,". H""·...., ,his need sho"1d no,be ,xolI'"t<d, mel ""y .ff"t;'" Urnula'i"". ba," b..n pe'fo'me</ on qui..mod.., eqUipment. On. 'ype of O<x:eUO<y. h""'· ,. i, p,rt;cularly valuable Insimul"",n "",k .nd I> oft.n no' ,v.il,ble; 'hi' uwol phl,x1 display uni"whicllCOn sh",,' ,he time hitlory of varlabl<. in the .ymm tn a V,ph;,,1 r.ohion.Fun...."""'., in"neti... facilltie'. Includlna more p'rticul'rly dIsplay un;". can""Ip a ...ea' d.,1 in brinli"-l tbe , ..till> of mod.llin~ 10 no.-modeDerx••uch ••tlecisioll·mahl1. In 'Iu, ....y. ,.... model <an be m.d. much mo,. ',.01' and thu.lCCtptlblt. u il1ustrmd by pre"OUI experience "ilb .na1oaue cOtnpulen whm, .... pro,,, of mod,l ch"a<:",iulion and ",Iu'ion 're mOre "'sible .nd whe.. ,h.man-maohi i.'Olf.", i. more intm<dia" than I' th. <... with <urr.n,ly .vail.ble

diJ"al equ,pmonl. The nffi! fo' int.".tinn h......n roc"llni••d in r=nt"mulatioo 1lJ\f:uaa<.(Crt»b... 1975~

11.3 STRATEGIES FOR l~'PROVI~G HU"',I.:-'· I:-''T[RI\CTIO~S

11 ,J, I Improvirc ,lit Int<rfoces b<~n Sci<n'im from Diff"",n' Diociplin..

A. model. inc..... in .iu and """'pl.xi'y. they ..qui,. mn...n<! mo" poople'0 oOllcop,u.liu and 'OO"to.t them. Usu.lly. 'h' wo,k i' partitioned .lonltrad"ion.1 di.<iplin.ry lin.., .cd each rubmod.li. 'h, "lIpOOsibili'y of >Oien,imf,om • po,'icwl1 discipline, Ord.o"..tion of tho ",b-modolt '0 yield the 'otalmodel i•• diffi.u[tUtk

Th. ooIu'i"" d'pond. largoly on th' .ircum".n... ,h., .har""'"i" lII. ty."mand ,lie problem. If, for in"ano<. ,h••yst.m could I>< mod.lled by th' upper"""f'JUr"i"" of ,ub·mod.!> in Filu" 11.l. th.n i' ...0Ilk! b. quit. ' ..y to oarry ou'all in"o"lption. of .y",m porfonNnr:< usinJ lII' rub-rnod'ls on. 11 a trm. ini>oIati"". If. how.ver, ,h. 1"""" .onf'Cu"uon ...." n.""",ry '0 rep....n' tho.)~"m. th.n.•lthouih «".in qu<o'iono ""old I>< .n "oJ u.inl ,h. individual.ub-modol•••n que"i"". in.oIving ""<tall p<rfonn.nr:< ould requi.. ,"ooinJ.n.ub-mod.l. oimul"ntQu.i)', (It m!&hl. ho..'....... I>< po••ibl. ro u.. simpl" ....ion.of th. ",b-med.is 'n th... """all porfo,,"o= 'ludic, 'h.n Ih"'" orilinallydeveloped '0 "udy tile p<rfo,m."", of tllt indi'ldual .ub-oy".m,) Th. """n whyI,;, no, tuen,ial,o openlo 'ho .ub-mod<b aimultooooudy in 'ho rust """flilura'ionIs tlut no""" plI.nom....an 'PPO"' In tho full mod.1 that would not olf..dy b.appar'nt '>f could b< .",po,'ed f,om tho I><h.vicul of tho ..pora...ub·modok Inth' mo'" compl.x cooflJUra'ion, on tho other h.nd. n.,. ph.n"""na (wdo ..i"".bWty) ,""y _II ,,",,'-

Sill« lh. ><i.n"" in each di.dplin. vie..., the 'otal problem from h1> ownP""p«trv•• ho h.. po""ul.. id<a. on ho... h••an b.., contribute to a solution, Hi.1<no..'led.. &nd d... ba.. m.y be 'lui.. diffo"nt f,om 'h"" of .denti". 'IllIOled In

prudl>Cillll O'beT ",b-mod.I•. In some c..... the p",,;e.... may b. deocnloed in I"'''dot..!; in o,h" ...... tho p'oc......'" only v'i""ly p"rceiv.d in • quolitativ• ....y.Th"". tho" ,""y be. mi"",,,h of '00 much ...ith '00 linl. information.

Th. ooIu""" '0 ,hi. ,n1<rf.". p,olIkm Is rather '\mple in principle. a1thouJhdiffkult in pra"i"'. Th' ",i,n,im wo'1<i1lll with u,h .ub·modol ohould bo ..ked todtfine tho '''P''' th.y ..qui.. f,om oth" lUb-mod.ls. ""' iu", the t)UtP~l whichlhoy a" ,,"pobl. of pruduclni, or r..110 be 'ppropn.1<, Wh.n the mod'l-build1n&pI""''' i. vlo...ed in thi. w'Y. th. mi""",do., quickly lIt.om••pp."nl. ond in""'" 0.... tho" i. th. posoibll"y of ,u<hillll a ".",noble CompTonti.. byoimplifyin! 00<It< of lb••ub-mudd. Of by ",ducin.lh, numb" of qU'''ion. ,h.,tho ,""in mod.l <lIQuid 1>< d..iJned '0 on....". Wh.n final 'lr"rnent on Inpu' h......n r...hed...ch wb-mod.1 ohould b< Ii.t<d.......n .. lII. lh.ory .mploy.d to"lato input ond outpu' of the tub-modeL Tho IOUIC,.1td "",thod. used to I.nerate<Qn.".inU mult 1110 b< pr''''nled, Un..... sci.nti...or:eptr"aa .ub-mod.1 ou'pu,.. inpu' '0 hi' ,,"'n .ub-mod.1 I><liov.. th. input to b. v.ilid. h....iIl inmt on",conmU<'inf; • roo" .ppropn.1< inpu' or .n,ot into dot"uc,i•• "Ium'na"""""'ni"ll mod.l "edibili'y, In othor c..... of cou .... the diff."",,,. in

fillu" II,J Altern.tI.', mod.1 "'uCh,,., oompared

philowphy ''''''''i ""ion' .." from diff,,,n' di'<ipUn" wiU b< i,,""'ndlablo••ndthe mod.l·building 1""<;<:'" <lIould prob.bly be 'bondon«l.

An oI",""iv. "'Iution i' to d"'dop ,ub·mod,l, ,ach of which indud.. ,I,mont<of ......1 ditcipHn<1 13th" 'hon being divill.d oIong di"'rphnuy lin... Thi'.pproath '<;eompliu.., ltu.. ,nd.. Fin,. i' m.lus for '''''r inpul .nd OUlput.second. It m.x.. fOf' f., mo" pr«i .. jnl<lrotion. fin.lly. il bringo ,h. diff."n'di,dp!in.. log<'h<r " 'h, ."It", po..ibl. "'I' lh' .It"nlli., .pproath ofdivioio<l .10f\l1 ditcip!inary lin" do« nol do lhi.. In fa,r. if anythinl. it "nd, '0koep Ih. dilf",nl di",lplin" .p.rt. &xn< of the .ril<ru lhat .IIt ....., in d.cidinllhow 1><" 1o 'ubdivid. lh. mod,l .1001 other thon discrphnary bn.. hav, I><,n,ummlriud by 8<nyon (l9n}.

Th. bIOi, ""'choni"" '<qulred 10 rmpro.. lh. in'"f",-"", bel.....n indi>"idLIII,participating in mod.l ,M",",UOn i, '0 ke.p ,h. "'oc'u" of ,h. whol. mod.1cl.uly in rrund; no p." of Iii< mod.l 0' ito 'ub.,."O<lol, <lIould bo hlddon f'om .",,'nor be dopendonl on impli.cll ..",mp'ion, or un"'plaintel 'blacx bo...•. Ono wayof .dli.....iol dialocuo i' ,t!< "'o'l:shop ..Hin!:. in"ohioll fOClWinI on mod.1in'"f",. i"u...nd ""in"n.",. of a hi~ d.g«. of und.."ondml of Ih, Itrn';tu«of 'h, mod.l by .11 por'i,ipont<, Sio", • mod,' m.y "pKlI}' und'fJo chonl'. Iformal "".hani"" b '<qull.d '0 dOt"""n' th'" chan." for.U p."kipmto••""ndu'in•• ,h"..doy wor""'up.

finally. mention <lIould I>< mad. of Ih, fl" IhOl. In ,on" , ..... mod,lI." or<no' in do« COlI'''''' with ,h. ",i,nu",......n 'ho"~ th,,. may I>< ",iubl. link<be,w«n ,Ii< mo<l.lI", ond Ih, poIi.cy-mak.... lhi> <i'u.lrOn moy .n>< wh.n.bWld.n, lmow1telll' con I>< found in the publithtelltt""u" thot would "mp' th,m<>dollor ro <M"rutl • 'ub·mod.l withou' 'ped.liztel .ci.n,lfo< >d..-k,. or ,..h,nthe" m.y .JUt! in"i'uhOll.1 Or pe"""al p'oblem, Ih" p""n, ...."tim fromparticrparinl in the mod.Urng >eli,'ity. Th. 'pecioliz.d "";en,i,, may b.U."". fo'".mpl,. that lbo ,ub-mO<lol of hi' port of th, ,nvironm,n' h., boon 'implrfitel '0the poin' tha' i' n" longe, yield, belle.oblo pr«li.c'ion .. !hi, diffkulry can b<""<room< OIIly by 'ubJ«lrng the ,ub-mod<l '0 KNliny by the ""i<ntifIC sp<cioli" ..

11.3.2 lmpro'Vtrc 'b< In'«1"'e< be'-'n Mod<lltt-.rod Decillion-Maker

Whet. "liobl, rnod<l, oxi"... 'hoy do in '0"" fi.ld, of hydroqy. fluiddynamic>, ""'«>,oI01y••nd ,0Iin«'iJll;. thoy aro U1<d.,. m"«r of ""u'" Mor<compl'" .nviron""nlal mod.1< h..... ofl<n r.iltel 10 pr",'. th.i' "Ii.bmty - by..,,,f.ctOlY valicLtliOll - arid tto.,. no' pined ,I>< confid.n", of d«won·m.h... A'• r"LlIt. ,h. inl<,f."" I><r"'o" on.ironmtn,al mod.I1".nd d«worwn.k" i' "ill.problrnl, Thi' I. p"tkul.ul~ '" in 1.'1' ,ov.mm,,,111 inltitutkm'. who" commu,,~

,",iOll' btl"""n ,,,,..ch Of "dwcal bronoh.. of lovemm.n, ond h'lh".I.",,1

-_.....",'" ­......... --...... -­

""""~"'"_c _",_"_......'- -~...

~.

--c::- """"~-- _....,,,­

_R~_'_

--I

-"_.,,.,..,

,

~_._~

" ' .....

policy-nukinl ",hel"". m.} 1>< I"'kina. In oddl,iO<l. the diffe",.. ou,loo•• lOdb.ckgrounrl. ~ the mod,lI." .nd de"i>lon-make" i.bibi, 'he ,o,,,,, ..ful applic.,;,,"of ,ironl";",, mod.llinl '" 'h, e""i,,,,,menuJ o«;"oo.",.k"'l P'''''''''-

",,,.mp,, to bridge ,h. PI' sh"""" in 'he oon".1 port of F,.ort 11.4 h,,·.involV«! ..,...,om" oJ I>x ",,,,,<du,u in both 10<01 .nd o";on,1 pohlical ..Uil\p.On, import"'" (althou'" orten d.r",...,) ....hid. lh11 h., b«n "",d to imp",..commonk>tion invoh... 'policy ..aly.lf Of ';nttnntdi.ri<.. who m <"."run'",j,h bolh ,h. ,,,hoi,,,I.nJ ",leo tin" ,,,,,,,,,n. of ",icn,i", .nd ,h. pollti"l i......and obj",'i... of ..oior polk-y m.kers. II"",..". thm ". m.oy ",unui•• whore.""h ""."".oi.n.. do not "i" or may hl" p,,,,.n 10 be <oun,.,l'roducuV<

In IQme inmnc....pe<ial '''<'''pn h". b«n m.d, '0 '''<:QU''S' u""fflOi.oldi.logu, bo,,,..,.n mod.II." .nd d,<i1ion·m.k.,.. On••ppr<>acft i. '0 form""1'<"';,,""y c""""in... ''''''i>li''i of r<pfO"'''''~''' f,om ,h. dtci,;on or,n.s,mod.II"l,.nd ,,·.n. i" oom< co.... ,h. pubhc (Holling. 19751. In oth" in".n« ..g..phk" di,p1.y. thot .n"p'ul.l1< the prtdkuon. of mod.1 '<'1.1" h.vt b..n u..d,Sp«r" 'ffu,," to ,,,.,,,1.,, comp."r OU'P"' i"'". comp",h'nsible I.ngu.~ h",""",ti"". 1><,. h<lpful, frn.lly, IOfIl< mod'lIing proJ«" hovt in."I.td ,h••,,,.from the oul"", lh, ,.,·,,,,,,m,,,,,1 prohl,m i. lhu' d,fi"td jornlly. ",rmini", thepo"nti.1 limi"';""••nd .OSIJmplioo. in ,h. mod.1 to b. fully app"d.ttd by the<!<crsion·m.k<r. hi'" ,x",""ro'" or. lhu. rI'\I"Lrnrltd, It mu" I>< r<ctlllrultd thot,hi. rn1<,oe,i"" 1TI1~' I>< difficult for. "umber of ,,,<on,, fur tXrnlpo,. mod,lI'"and u.." "f"" h"'" quit< differinl pt,,,,,"iv,, ,u''''ming the probl,m", h....d.

Th<.. pr"".du.... h", ...ductd the problem> occurring ot 'he in,,,f... h".."nmod,II,,, .nd d.dsion-m.k.r1. S.I"tTlhtl<... 'h.... i. "ill room for imp",.'tmen,.and some i<I... will .. gi...... r\' lh. oUl..,. h"", ..·", j1 Ihould b. ,mph.'f,td ,h".Ih't1l lh, ""Ur< of man••"vir""m,.,,1 probl",,,. 'he ,,,,"m, 'ppl".ch m.y I><'h, only viabl. tool to und..."ndi"i .nd in 'u,n .""'ing .nvironm<n'"1TI1n.s~m<n, prohl'lM

-,In m..y In"a"".., d,,,;olon·make,, Ire "<jth" farnili" with nor en""",ured of

SYO'"'''' ""~'>i. and modelling_ I' >hook! b. " ...>Sed lhal .y".ms a".ly.i. do<' "0'"'plio« 'h, d«wOIl prOCflSc ,..Ii«." Ihonk! aid in imp"'''''; ,h. b.~. for Il'1O"

,,"Ion.1 .rwnonm.ntol ""nagemeo'-Tlie ,imulali"" mod,lI., Or,," """,rib",.. ,,, lhi. lock of empathy by lI.ins

toclink" j'TJ"" .nd '''Iking do"'"' '" the """...,.<i.liit In <00\1'"'" "ct1noIOf;Y_Tho d«i.iOIl proc<» ,m ""I)' benefit f,orn the .y>«rMn<>d.Uin.apprnadl if ,Ii.,.is • 'p"i' of m"'u,1 underSl.nd,,,, be"..." decisinn.,.,,"" and mod'U,,,,Communi,,,;,,,, ";lh lho <l<m,,,,,..,,.k,,, ..ill be " ...Iy r."I,,,,«I if h. is ....d. 10und,'mnd ,h, g,"",1 "'""'1" of m<>deillng, .nd '" .pp",-im 11. poteot;"! 10 ,hepoint ..n." h. i. keen (0 "so ,hi. '001 and to In";,,, 'lie mO<lolliog ,,<tc,s<h;"""lf.

Willi 'hi' point ....bhllled. some mo... speCIfIC reCOfJ\JI\<r\d"i",,' un I>t madeThe apP'OI"i.,. in..,f"", 1><[."0 <ei'Oli". arwl d..iloioMn,km d.pend, IIIgol;­upon 'h, nlluro of ,h. probl.m. AI'hough ,n ,xh,,,,,;>-. in'-.ntor)" of problem, i'beyood rho ",ope of 'his "»011. rho follo,.'ioZ zen.raliuti"'" "" b. mad.

(1) Probloms d.pendrnl upon ,«h"I<" q",,'tion' ,.-h"h ca" b. a".w.,«1 wi,hrelotiv. cer'ainty will ",ually b. ,...,I>',d "'ilb ,he help of <oo" • .,tion,1",i'ntifi< adl'ioe from ,uitably q"alifi.d Indl,ia",I. 'nd ~ro"pl_ M.,h,om..k" m<><l.h ",-ill ofren b. "'oJ i" ,he ba,klmund in..,"puoo. fo,.""h ""'k', ,nd ,h<.. m<><I.1s may ",,<_lion_II; indod••lntul.,i"" modd._

(2) for problem. which "qu", moT< ",<Ura" d""np'ions of <","pl.xi"1OH.lltiooohipl b",.,«" ,,,,"»On."" Or nrb""od,l. of lh. probl.m, aJOInl worbhop b"..«n mod.lIe" and decioion.",um ha. been found '01>< helpful_ S""h , work.hop ",,,,,lei <oo..n"." on ,h. d.fini'ion andbounding of th. p,obl.m. on 'h. id,o'ifk>tion 0' ~oal. 'nd prion'ieI, andon ,h. ,nnmerall"" of op"onal ool"uon., with ","al plrUoipatlO" of lh.m<><I.U<rI .nd d.."ion·m, • .,..

(3) Problem. whi<h mm from • mUluph'i'y of <hoi,.. <an f"qotn,ly 1><darif,..a by z,n.""ng a raneo of =n"io,. of1<n ob"in.d f,om a'imulalion m<><I.1. bUl ,.~uiring.xpli<i' de..np'lOn. of ,h. combrn"ion off.. ,OT' produci". ...h ",.n.rio.

(4) Whe" ,he probl.m " m'rnly con..med "ilh ,h. r.,olu,;O" of u""mullbe,w«n ,l1em1111'< pohc,.... pmins...,.,ulatlOn of the u""lIkll ,na 'h,moo.. of r..ol"""", in ,.-hi<h til. v,nou' a"i~QfI.",ak,n pla;- ou' th.irr..pe<lil'< ,01... m.) be h.lpful. Simulation modeli oan provide' fil11l buefor "",h pming_

!'robl.,." "itrd! reve" «ohm,,1 nneertainlY ar, 1."."lIy ,h. mo.1 diffi<ul' 10solI'<. Anempu m.y 1>< mad, to obl';n' """"'MO' ,-;0" f,om .u'Ubly qtu.l;fioJpour< of expo,,, lhrough l><lphi pr""..... •. In eoneral- h,,·.'...r. furth., ",...,.1;

wiU be "",""ry. 'nd ,II< d",ision-m,k" mU'1 ....pt d.lay ,

'Delphi ,'"""'" Til< i1<r.. i" of 1n.:l1vio:l".1 ""D.., Or '"rme''"'''' '" d,fi.. r><T",,,,,1_"""", .... __ ." .." dh.,_,,, (l'ill. 19' \ l