thesis on the visibility of lunar crescent-4

8/22/2019 THESIS ON THE VISIBILITY OF LUNAR CRESCENT-4

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Chapter No. 4PHYSICAL MODEIS & THEIR EVOLUTION

AI thblclh rhe twen rh .entury and Inro $e ienry ftrst century a tot o,wotk h.s been done on vanous aspects ot the probtefr of vtstli ty ot new tqnafce$.t. thse other t$u65 In.tud6 (t) tonth o, tunar cr6sc6hi {Danjon 1932.1936, yas 19a3b, 1garta, McNa y, schaeisr, 199ft, McN.xy, 19a3, sotran, 2005,Qu6hl & khan, 2006, .rc,) (ia) the mintmun o, timtthg tonga(on of n6w vistbr.lunar cfescenr (Danjon, 1932, ras 19a3b 6tc,), (thr $asohat varaa ons In theanbt vjstblliry oi .ew luna,.r.scenr (llyas, 19A5, Crrdwel & !any, 2OOO erc.).On ot rhe mosr stgntfi.ant or these and olher sffons B rhe hrroduction of rhe-|rrohattomt Lmr D6te Ltne" or |LDL (contras0na rh. |nr.ma onat date ltno(solar)) by lltas (ltyas! 19A6b). Thoogh the td6a h.s nve, D.en !s6d h pbctic oflunar cat.daE but rhe !me has ben erten.ivety usoc |n lonrare (ror insranceluooioat by t{an4r lnd A@urat. llmo by Odeh) as a gu|d for the rcgtons ofvlslblllty or i.vtltbllty oi ths n6w l!..f crs6nt, Howver, In thi. wort the mainemphasts ls on th6 modets rhat deat wlrh rh probt.m o, eaniest vlsrbi ry of newlun.r cesco.t so that other tssues 6r nor constdered.The ri6t [email protected] modet fo, ervtng thls polreh was rhat o, aruin{8tu1n, 1977),Ihis kas ba$d on tho av.rage bdgttness hodetrorru tltoon, rh6averaSo b.tghtnoss ot the twlighr sty and lhe theory or extlnction ((ooman, 1952,B6mporad, 1904, Stedntopf, 1940). Sruh was ,bo rhe rid jn modern rimes roexprott lho v.rtaflons of tunrr s.miii.meter wlth rhe Eaft]vtoon dlsrance,Afioturds, appared lh6 .xtenstve u!6 o,lho phFlca .nd scionce ot vtslblity bySchaetor donng rh6 t6st quarte, o, th twe. eth @ ury Gchaefrer, 19s6, gaaa,19aab, 1989, 1990, 1991., 1993) ba$d o. vrdous racto6 ike armosohoric


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e{inctton .nd sky briShtn* ds to vanou. objocrs l6adtn to th ttmtttngmal tude or the sky. H6 al$ lhe.att2od rhe hportance ot (a) tack ot hrorm.ltonabout seather predrclton st iems a.d (b) necd ot tunher qtlo.6 on ot th6physlolos/ of huhan vi3lon c.pabthbs. Thus,3tnc6$ rheoFltcat modet teadiloLunar Rlpnes law by modtqvat Mus ms th6 only rheoreltcat modts a du roBruln and Schaeter In rhl. york Schaoter'. t$hntque! .16 .pptied ro th6 ,6centobs.aalion.l data and a.e toond to b6 In good aet!metrt wtrh the obsetoalonal

The exptotts or yattop (ya[op, 199a) whlch was .gatn mor of enoticat tn.aruE b ba36d on the ob$da{onat dsta and p.n o, Brutn,. mod6t bur wtrh rhesrmprrcrt ot a 5tngl6 par.meref crito.ton tor the n.w oes.enr usibtr(v, ThlsYallop s modet c.. b termed as a s.mbmpt car moder. one o, rh m6tsrgnlllc.nt connbutons ot y6lop ts hts concept of bst th of vistbfiiy, Tnesonware Hrtatol computes borh th. q_vatues (ya op, 199a) and rhe naCrltod@ntrst (rhe rerm cotned In rhts work) rhal tsthe dnf.ron@ o, rhe r{agnjtud ot thollroon and th. timtflnS hagnltud6 of rhe sky ctos6 to cr*enr. Ihe conpartson otlh tso i3 di$ussed ..d som. ot th6 extra ordtnary oDsendtbns are cdflc.flranaly$d. rlle mosl stgniftcant part ol thts ch6pter ts the dvetopnenr ot a newsrnge psrsmeter crttodon for th fl6r vistb lty o, new tuhar crsc6nt, we havecon3ldred the acruatbnghrne$ ot the cr6c6nt rhat b pnase dep.ndnt(instead ofaver.. bdntnBs ot ihe tul Moon ctos. to horizon usod by sruh).nd rho.ctualb ghrne$ ot lh iw ght 3ky close lo rhe potnt whee rn cesce rs prese( Forlh bighhe$ of bolh (the 63conr and th sky) the loots devoloped Schr.fer.ndotheE hav6 been osed, thts has ,6!utted hlo new vlrtb tty and lmtring vbtb irycunqr lhb te6ds to a nw st of basic dat. whtch In run E.onvened hro a rcwslnge paramoter cdredo. ba*d on . retarion het en aRcv and width o, crescenl.lh6 osr mod.t ts anorhr somfempnbat modot, Our cdterion is lo{.(t to havobettor succe$ percentago than any orh.r crile on devetopod dq ng rh 2Oh

t26


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4.1 BRUIN'S PHYSICAL MODELAtuin bsed his wolk (BNin, 1977) on 1he obseded avedge brigbh.ss of skyagaiBl rhe posirion of th. sun b.los ho,iD, ,ner ssel (0ut natched tnc resuls olK@h{ et. al. 0 952)) and &e bdshrB of rh. M@n s a tu&tio. of ddud., b6ed or

lhe 1h6ry ote inclion dw BnpoFd (Benpomd, l9O4). The fi8ures gi!e, by him, Fie.? $d 3 (Bruin. 1977, pp.339) arc r.poduced here in Fi8 No.4.t,1. On rh. b6h ofthcsesludies Aruin developed the Lund visibilily cuFes (relarin8 atdtude, , of qeeenrplottcd asainst s, lhe els depE$ion blow hoizon) 6d fie Lioiring Visibitiry curyes{Elatine, + r,gai6r r) ed pEenled in fis. no. 9 (intude


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cxnibircd in n8 9 ir is mr.d lhnldif,cFnt vidrh ces@t3 @ girq

aI $le dip r = 0 dgees lh. ninimM dliNds for

2 3a2

Tbh hcms Aar rbe bndrh$ of lh. sky ar rhe* atrirudes (r) G we .s rhe brishrne$ ofth cBent of@ftsponding widrh when lhe su hdjul $r. I. ord{ dul l,rtc ce$. isrt 16r a bright s the sty wilh dftEding ahiludc rh. c@e nusl b. wider ud sidc,.Tnes ar thc sanins poinls of rh. vnibilny c!ryes fial aG aU shaqty d(rtsingf!.crions ol the sotar dip, That heons lhar not only the brighh*s oi cc$e bul $ebrighr&s of sky (har cqul alons lbcs cwa) borh diminish sh!+t, wirh $einc@ine st& deFEssion.

Thr.forc, for larger values ot r rh. ee$ent of sne brightne$ @ b. $en atlower od loer alftudc ,. Tlw arc al$ the sianing points or rn cums ttat show lhcb.h.viou of, + s {sh ofglribd. of M@n ed lh. sot{ depb) agaiGr th. $tar dept rAhhou8h the sm of th. atlitude /, of $e cresced dd the r me $lar dip Eoains alnostconsbrt 4 $e ce*enr gos doM dese cw6 coftsponding to fixd crcsnt widthed thcEby ro nxd brighhess. As (he atrirudc of ce$.hl daca*s 0r. sky brighrnessn4l d


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Fig. No. 4.l - ! fic fi8u6 fron BNin s Pap.' ( t 977)

rrr, ?, rc rddb-r rr oi *l

t29


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For thimer c6c.nr rh ,r + s aSaitur r plots Sive thc b.st time of vhibility 6 thepoinr whi.h is the midhum of rhe cwe, h rlso 3ueSens a tug. of tim. for *hich Oecrc*dt my Ehajn visibl- Th* de excellent id6 rhar @uld help cre$ent-hunre6bul untdtunably Btuin has nol pesenld a clear cul ompuratond lrchriqu. Brs.d onsihil& ided Schaefer ha worled out Enorher schehe of computario. lo b discu$.dlatcr. The schcnc for computrtiohs is dduccd frch the visibility cuNes olBruin sd isbsed on ll)e dinimum point of rbe r + It plor againn s. A relarion belken rhe cE$.nlvidth cor.sponding to d r + , cwe sd rhe valu. of , + r ar rhe minimum oi lh.cufl. nay be d.duced fron abularing rheF ratucs. For lhis purpo* rhc data deducrdfiom 6g 9 b, YaUop (Yallop,1998) is d follows:

The valus of ARCV ore the valucs of , + r picked fbo rh. ninimln of rhe, + r cufl esasaisl r whi.h coqespon.ls to the b.sl -tine ofvisibihy ofcresent. Tlh dar! 6 edtoa dird degd polynonial usinS lean sq@. apptuximrion lqdr lo the follovine r.larion

Table 4. L22 3

ARCV =12.4023 9.487arv +3.9512W' O.5632tr' (4rr)Tnis ( an be tEnslomed ro lh. \ Fibitrly oaEmero . r, lunc,ion as to'toq:

v), =(ARCV -(12.4021 9.481W +3.95t2t/) _0.5632W)Dtrc(4.1.2)

Tnis crn be le$6d on rhc obscnarional dara with the visibitiry condilio thal a cssce.lshould be visible if,, > 0 olheNi* it should E@in invhible. Using condiion (a.1.2) onlhe data *t ed ro evatuar. n rhods in ch.prr 3 dlc plor w obhined is shoM in ligu.no. 4.1 ,2. ln this fig@ lhe cue nmed ..Boin\ Limit,, is the plol of $e equrion 4. t .2.

|]0


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Th. rd of th. plor CD$ th. rc|t|iE.Xirtde (in d.8r).gaiMr th. cltsdr wirhh (i.I snd9 l@ldd ar dE bs tinc of visibility for @l obsd8rioi of ttE &tl selcoNid.r.d ii th peioos chl9iq. All !h. pd iE siglding cas .rd ihe @lrs ofcdlculalimr b.$d d (4. L2) @ 31Em in Trbta 4 | 3 TtE @not.r. dda sr b shom i,

2

R.--E-'_;"_

r-r*.rl.sc.G,wu.ca*Fig. No 4 1.2

ApFidix.|u slDB rl| @hs of .rptyin8 Btuin.s [bn, yttrop,s ondid) itdi@ (robe disssd in rexr rnicte) .nd th w dftdim dvetoped in rhj3 woli (ro be repondin anicl. 4 4 betoe) undq rh. hQding -Mod.r tne firn @Enn otriaitu lh. vat!* ofvisibilily pmmetd d.fnd by (4.12). TrE Ddl lh cotunr, e ror the orhq rh

ltl


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t32


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lll


10/47

tJ4


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tlq

?$I;;

135


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Our ofth. 196 positiv sighring in the @pt. t4 cs6 d.qarc rron th. Linjr d@!o Btuin. TheEfoE rh. nodet du! b Bruin is thc best mongsl ql ihe orhe, 20o ccnturynod.k ad is s good $ lh. Lufu RiFn* Law. Ar nx es rhai daiar. f.ooBrbylonid (io.rion atso dcviak froE Bruin,s nodet. A ctoer look in b ttE derails of14 caes $at deviab fron Bruin,s modt sve.ls oEt rhe la cses devi.rilg frcn theLuar Rip.ness Law and lh.e 14 caes have 8 common cascs. rn. fihl I cs.s ofvisiblecNolntable t.3.1 (ob*nation no.286,2ed 272) ofoncrec cros to auruDnal.qunox have !alu6 ofve srlt aboE Bruin.s timi! siyen by (4.r,2). A. n @ di*ussed'n snicle 1.3 the ce!ce.& in 6ese .6es eE older ovi'ibihypo$ibre. rh. Bruin,slt.i,i,b.,.d..rh"b,ich.::,:;f,J:1':;T::cases ae erisfying 1ne Btui.\ lioir despite having sEEll las.

Our otlhe six cdes lhat dviat. fror Btuilt linit bnr not fbn LUM Ripenesraw{obs.4o.413,434,I19,ll5,2S5 ed 290) fiEi fiG havc qalt ^Rm valu6 (o.ol,0.061 and 0.07 rcspedivly) so dc hsginal for Led Ripen*s Law. Sihitdly si, of theIjg that deviat fbh rhe Lu@ Ripn $ t.w but rc! f@h Btuin,, ljnir (obwlrioanumb6 286,2,2?2,314,6t3 ed 716) firsl lbG have b*n dscussed befoE. The n.xr

1lz

t36


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two ll4 ad 613 have smaU v, v.lu6 $ dc m&gitul ds in BNint Mod.l. Tn hslone (obs. No.7l6) is asain u old ag., wide ond bdClt crceoi

Ths sc ob*rve that 6c Bruio's Linit md the Lund Ripen.ss hw ee nolexaclly supplcm.ndng eh oth.r blr thcy @ rh.rically cquiql. Howevd aBrui. s linit is rakin8 brighhe$ into considqation theEloG Bruin's limit h moElogicat ud noE su6sful.4,2 YALLOP'S SINCLE PARAMETER MODEL

To devclop his onc pdndd nod.l of firsr visibihy of luMr clt$nl Yallopused Bruin s wort in order to .xi6ct optimum crc*enls *idth for vdious rehtiveahnud$ o. @s of v'sion ARCV, nedion.d in ptvio6 anicle. Like Folhcdnghandeveloped a lomula cllline ARCV wilh DAZ on lhe bask ofht sunnary ldble da|a,Yallop coroider.d fie bsic dau for dveloping a Elalion blren ARCV md lhe Nidthof crescent W, Hh data (froft pase 2 ol NAO T*hrical Note No. 69 (1998)) isEpioducd in the oble no. 4. | .2.

Hoselcr. d slal.d hy Yallop, f6m 1996 Mdh HM Nautical Aldanac Ofllccddided ro abndon i!3 tcsl bared on the Bruin mlhod (4.2.1) for lh. one baed on lhc''Indi.n" melhod d thc lndie mthod produced mor scnsiblc rcsults fo! old .gcs'-shrings al high alirnd6 thai occuB at l.rsl once d y.r fo.lalnudd rtomd 55 d.sd'Bed on fie sorli of schoch (1930) th. b6ic dara ued in the Indis. melhod h siven in

DAZ 0' I0. 15. 20.I00 30Tatrl.No42l

As rhe width of rh qesent is sivcn by (2.E.9) dd thst @ abo 6e wifien as:tt7


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rr' = ls


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*lich l6ds ro tlE visibiliiy pabr..ld:,ip = (,{XCr. . 01.t733-9.0312W +2011J4W" 013601/ )/10(42t

Fig No 421

. lnda Umir . htsibl.c.eApplyinS Mendd's nodifid ondition to thc daia sr of Ch.pLr I it is fou.d

thal oul of 196 positiw sightings @ iher.27 clg th,l dwiat fron the 6nd;liond.fined by (4 2 5) rhe se e shoM in 6g@ 4 2 2 Thus Me 6s nodited@tdition is dill mr bdd th3r th. ltdiu lr|d rn Btuit's @rditios All thc 14 {,grnat ddilr. iom Bruin s linit tte d6nd. lion rh. Indie linn Ttu rvo tddidonllwr io!! m. 3r4 .rd 33) ttd ddid. fron lndis $nn & Idtd to b. tugjn.l cet(vr = 0 ol8 and o oo2 repedively) in Y.lloP! Indiln dEd.l Thu3 thc t@ hod.ls ar inclore sgr4rcot s Iney re both bas.d on sinilu lpprs.hes a.d onlv slishtlv dillq itr


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i{

Fig No 4'2 2lD addirion 10 @Ndting .ll visibiliiy otditions from DAZ-bas.d lo th. Widlh-

b!*d Y.llop achievd tqo orhd rdeltbl. t8ks. Oft oftheh is hh d.ducion of BBtine of Visibihy The otht r.Mbble ontdbllion liom Yallop is io tkaw lincs

140


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b.twe.'rgiotrs of v&ids vbibility condilions on lh. b.s of viribihv pdma.. ,/}used in lhe Indian mdlDd th|t be cals 6.8tu .

Fis.No423Fdthc bd rinc ofq.sit lisibililv' hc nor6 ih.t h fg 9 of Btuin tlE siniM

of viribilitv c!tues of , t r agaiin s lor different ges.ent widths, fom a slrsisl]t linewhich whs Drcj.cld nels tn orisin of the @rdiMt svst'm (" r) The 3{m hshom h6e in fi8u.. 4 2 3 s a G{t lir. PNing ttroSli niiinun of @L @rc Th'slop. olrhis saSl lin.i3(, trta/4d,rs 5/{ Itis dnimun @@sponds to lh'bd vilibility @dnio|\ thc b.d cerlln bd}6 rlE N6'ee briahtns ortlt d(v !fl|the b.iShtness oa th. c..stl ..dding lo Bruin Yall@ inrdPr'tt it a 'poinr in tm'rhNt rlivi.!s "the tim lin" beiv@ the Sunst ts ed lhe M@n!t l, in a nlio 5 4 Thusrhie "poi.t in tin" i3 th. b.!i tine I, of c..s..ot vitibilitv Sivd bv:

t,=5\ + 4\rs + LlG) ,9 T. *!1,4c

l4l

(427)


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Finally, Y.llop d.duccs rhe visibihy @ndilios for dillcrcnt M8es oI q_vatu4aic. a detailed dltysk of rhe dlta *r of Nund 256 obsdado6 avaihble in his timc.Our Esulti in lh. sdond l$1 colmn of rlblc in appndix-lll, e lPpliqtion of lhcYalloo s condnion (bascd on bsic dala of schoch, l9l0 or lhe Indid ndhod) io! $edoia selcted inchapter 3 wbich is taLh mostly iion Odh (Odeh,2004) Theconditionsd.duced by Yallop d. Eprodued heE in labl.4 2 4 Ihese conditio.s e iddicalo6 forlisibility eiih or wilhout oPlica! aid.

In all crloldjoE in rhis rcrk rhe coiDur.rioa have b.6 dotu for this besl tim.sivcn by (4.2.7). EsFcially the calculatiotu fo. rhe iable no. 4.2.2 iD $ltich rbe Indidcondition (4.2.4) c used lhc @mputations ac done for this best tim..

The linilins ralucs of t weE chosn for lhc aix cnbria a to F for the following reens(Yallop,1998):

A lo@ limit is rcquird to spdl. ob*talio6 $at d uivial 6on rhos l'ulnave ed. .len.nt ofdifiqitv. Accotding 10 Yallop il wc foud that lhe id'alsirr^ion ARCL = l2o nd DAZ = O" prcducd a Fnsible cut-otl poin! for shich q= +0 216, Tnere aG Ill exmDles i! Tabl. in appendixlll G'cond lai column)whn q exc.eds this value, ad i. 8.Mal it should be vrv ..sv lo se 1he new

Tlble 4.2.4r Thc t-test crileria.

{A) q> 0 216 ENily visible (,4ICl 2 I2'r {EVl(B) 02le,l> {014 visible und( p.rfd condnioN (v U PC)(c) May nedoptrtl lid'o find cerdIMNOA)(D) { 160:4 > -0 232 w-itteo oprielaia o frna crescent tRoet (v)(E) -0 2l>4'-0 29q froivsrbG viii[lcmpe,4nC. < 8 5'tlt (D(F) 4-299>q

-tlor

'sitk, ueto" Dujon tinir;Rcl < 8' I

142


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(B)

(c)

(D)

c@dt in ln.e m, Providcd th.c is tro obscaing cloud in lhc sky Therponed posilive sightings i. dr6e cascs e I 14. Tns it is @mble to considercscs wilh I > +0.216 10 b. lhose wbcn the cccnl is esily visible.Fon obseryc^ rcporls it has been fou.d that, in gcneral, t = 0 is close to lhelowr linit for fi6t visibility ud.r plfecr ahosphenc co.ditio.s 3l s.. lvelwithour Equirine op1ic.! aid. YatloP u$d his Tlble 4lo st lhis losd linn forvhibility mot p@helyand he says thal from inspstion of Tabl. 4 ihesiSnilidcc ofq - 0 @ b. str bul t = -{ 014 is &olhd Possible cul_of val@'Thce @ 68 Aes in Tabl.4 sith q in ihis Ens. in the daia u*d bv Ytllot wirh48 positive siShtings. Th. data sed in this qotk (in app.ndixlll second lst@lu.) thec aE lll ca*s with q > 4Ol4 bul les lhan +0216 Oll of th*l1l cse) rhe!. ae 6a posirive sighnngs withoul oPtical aLYallopusd hisia6L4lo fi.d|hecut ffpoinl *hs opti@laid isal@vs nededlo Iind the crcse.t moon by rutching lhe q_test visibilirv codc wilh scha'Iecs.od.. The rcund.I value of 4 = _O 160 @ cho*n for lhc cut_olT dirclion lnTablc 4 (YalloP, 1998), thcc \,w 26 cNs thar s Gfv rhis diterion t0'16 < q t > -0232) YaUop s Table 4 ha' roo lew enli's ftonwhich lo estinale a lowt limit for 4 The situalion is nade NGe bv thc fact lhatwhe thse is an nl!v. in non cas.s' the Moon ss not scen even wi$ oplicalaid. ln f4t it h @ fot lhc cc.dl to be obedcd lElo* 6 a9pae't clo'galonofabout7c5 (Fatoohi d al, 1998) Ydlop's Tablc 4 h6 14 cs's in lhis dg oulwbicb 6 re positiv sightirgs thdough binoculss o! &le$ope ed one exl6oiilinary ce of uaid.d siShing ln th' r'bl' i' app'ndixlll Gecold 16l

141


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(E)

@l@) of lhb wolk lb@ e 33 .M our of which 18 @ potiliv. sidineswith binoculd or 1el.$op6 dd th@ extra otdinary ces of unaid.d sidli.g(ob$flalion no. 189,455 add 2?4) lh.t is dillcral fren fi. @ @sidercd bvYallop, Al lhe tine of Yallop {1998) lhis wG thc linil helow shich n wsNW.d that il is nol Posible 10 c thc lhin .t snl n@n .v.n vilh a lel4oFAlloeing I' for hoiienlal panllax of lhc Moon, and ienoring th' eff'cl ofrcfa.liol\ fo. & aptent .longadon of ?q5, ,'{XC, = 8c5 lf ,'lZ = 0p rhiscoresponds to . lowr linit of I = -{ 2l2 Wilhout good fidding lgles@p* mdposidoml infomation, obsne6 aa unlikelv [o w lhc crc$"t helow this limnTheE is a lheoEical cul{fi Point *hen th. appatcnl elonSdlion of lhe Moo'frem the sm is ?", knom 6 lhe Ddjon linir (Ddjon l9l2 1936, llvas' l98lbnabohi el al, l99S) This limit is obtained bv extlapolatine obedalions nade allager elongtions. Allowing t" for hori@nul p@lld ofth' Moon a'd i8f,olrngrhe effect ofrefEcion, ah.ppornr elongarion o' 70 is eqnivalent 1o ''{'R'1 = 8'Wirh ,,llcl, = 8'ed D,42 = O! the corespondine lowr linil on I is -O 291'However, in Yallopt lable 4 thE tte 2l enfiies witl onlv ] posilive sightinewith a bin@uld fot I < 4 212 ed no sighting claim wilh s_aided cve ln lablein apFndix-lll (se@nd lst colw) th* ae l8 c*s ir the mse -0 212 2 4 >-0 299 oulofwhich there atc 7 sishdng snh binocuhr ot tlescopes and onlv 2claims of un_aided siShdngs (obsdation los 389 and 455) Both the*obfdrtio.s dcviak from all the crit.ria considered up b lns po'nl

The table in .ppendixlll G4ond last cotumn) or this wod( shoss 66 cases wtrr-0 299 > q ed therc is one.xtra ordiMry claim of sishtinsopti*l aid (obs .o. 189) Ap&t fron $is lheE is no posilive siehting silb o!wilhoul opdcal sid. In lable 4 of Yatlop tnee is no clain of Esce sisblins $

A@oding |o the visibilitv dNifiorion shosdivid.d into 5 tgions bv four consi&t_q val@s As lne

abovc, rhc suf4 of E nb baclual visibihY of lhe crescent

(r)


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depends on ils width dd oi iis dltilude .bov. hori@n d th. rioc of su.sd accodi.g loBruin (Bruin, l9??) dd Yallop (Y.llop, 1998) a @nsht q'valu. describes a cufre onth. globe i.di@lin8 sinile visibiliiy @nditio.s along all poinc of$e curye' Such aclne is a psldcr@bolic cwe wi$ vicx on the 6l-dost loisitude Thclonpludi.al p6nion of lbis ven x vei* nonih 1o nonlh 6nd th' hnude of |he vqard.Fn& on lhe d.cliMtion of th. Moon ed lhe Sun on the ccle$itl sphere DuingsumheG in nonhem henisphlc lhe sun\ declimtion h extren nodh dd if ihed.climtion of ths Moon is norrh of $c su lhis ledex no!.s to exlEne nonb and lhec6@ visibilily is edier i. rhc nonn hitudes Duing summer of the nodnemladud.s if lhe Mmn is eufi of lhe s6 then ftis v.nex d@s not @ch irs 'xcmnonnern posilion dd still tne .e{ cE*mt vhibilitv is better in 1ne norlhen laitudcsThc situaion h revese for lhe $liheal henisphte Tne palabolu opens westMd above(nonhwardt and below Goutbwrdt fion th vcnex The CuR' A is rhe collection ofpoints on rhe 8tob. fot which rhe q_value is 0.216 All rc8io's $ithin lhc lwo b6nches ot$. p&abola wesl of rhc vertcx e the EgioB wh.e |h. q_vdhe is s@ler lhm 0-216 mdthe cle$ent h ea3ily visible to ln. Mlcd eve in lhis rcgion' Csc B is the colleclion orall points where the q-value is -0014. In all tbe Eeions be$e! cuftes ed B lhecicsc.nl is lisible to thc nai.d ete onlv undet pcrfed visibililv condnions

The Fgions b.(wen cuN. B and C (q_value _0-16) de $e tgio's io wbich dobsen.r suld Gquire opdcal did 10 locatc ihe cr*c'nl dd thn it mav be visible lonaked cye. For reSio.s wi$ q-vdlue I$ t\ai _0 16 rhe cresenl wolld not be visible tothe .akcd eye For a comnon. untaincd obsePer it h highl) unlikelv thal ihe cFscem*ould bc seen in rgions ed oflhe aNe A Thc scienificallt ecoded obsaliom (ohehich all $c sludy of the rwnlith cdturv i3 bNd) do oot Pohibil obedalion of.r.sc.nl wiln mkcd ye in region belwn cwet A 6d C In sucn t'gioN' in facr' lhcprobabilily of obsenation incFdes whh the nlmbef of keen tdined od expenenced

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4J SCHAEFFER'S LIMITING MAGNITUDE MODEI,Ilruin (197?) ued only avfrgc brislhcrs ofsk, duinsrviliehl and rh' vanarion

of brishtrcs oinE full Moon ro obEin appNximlc cohlrsl lb! (csccnls of$rtuussidths ro develop hh crcsccnl lisibility cuncs dhcussed a6o!c ftc t'srltins nodelfornalized in lms of , rclation berwen cRsenl width md thc Elalilc tltiludc ol{*dr ar "tal rime dcduccd by Yatlop (1998) pro!.d 1o b hiShlv succcssful' lihough, the basic data cxtacled by Yallop frcm Druin s visibililv cuBcs- wasrcplaced bt rhc basic das due to Scboch (1930) (lhe Indiah nclhod) lo aFivc ar his q_value coodidons (di$nsed abovc) for rh nN ces vhibilil! n h6 bccn secn rhlrrcsulls iom Bruin s d,tt .re mrlgi.ally bctter dan thc lndian mcthod 'or lhc ddo scl

Schacllcr (1988a. 1988b) oh lhc o$er hand has uscd $c phvsics of \isihilirv'cxr.nsivclt ih rcsulrcd inro a lool (6at Shacrdconvencd inlo a compubr Dmgmm) toddmine $c briebhcss ol sky at anv poi ol tinc dd for di{Icrcnl aftosphencrcmp*tutes aDd rclarile humidil!. Ih rhis {ork Scbaeficls progrm h ep$duccd a'dfrade pad of the lundr crc$eni visibililt software dcvclopcd. Ililalo! ro clal@relisibilily cohdnions. Tlis pan of the sftld is rsi b conpurc thc sk! briSbhcss (orlinni.B magnirude) al points clos to $e cre$eht md the aPPatunt nagniiudc or lh'lunar crcscenr ro sludy $c laryins conmsr dunng twilighr for vanous tcnpcrat!rcs andolativc fiunidny. If rhe appaFnl brighmes of the crc$e.l h morc ddi tlE bighhcs oflhc xrilishi sty lhc cre$e should b. visible o$cNne nor Schacflcr (1988a) himsell'hasap!li.d a sinilar rcchnique lo @lyscthc visibililvor invhibilnv data avnilablc in hisriFc. -l he @hnique is ,Pplied to $e d a*lof rh. chap161dd the rcsulB obbiocd arcpnqntcd in rabt No 4l l Bcforc a discussion 6n rhcs' Esuhs Schrcli'isnldhodology t-or compulins sky briShhess undc! difeEnl ahosphcnc condithns 's

Aner rhc conjunclion thcto tne non&n md lhe Poi oa

ne* lumrcrescen{cd bc seen in rh. scslcm skv ck's-$@r Simildly the last crc$enr cm bc secn i. lbc


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casrcrn st! bc forc sunsd. l hc conlEi bc(wce n lhe briebtness o f crcsccni Nd thai o r thcrwilislr sky dcp{nds on d number of f.clou. Thcsc incllde:

P6nio! of the c@nl which n.elf is significsntlv {fTctcd bv LhcTbc $.nerine orthe tieii ftom cEee fld thc sunliShr dle to (a) thcroial amount oaair-nass the ligbi tdvels-lhrcugh. (b) thc rotal amounr olaeosol pesnt in lhis air. and (c) lhc slratosphctic ozonc thoush shichrhc lighl bas lo ftvel. Th6c *!lt ring souEes cauF th. inlcnsnv of liehrsourccs of liehr rhal includc $c S!n. lhc M@h and o$r sourcG (likeanilicial light lbat G nol considcfd in this work 8lh'v m noi saffc(i!c during lwilisht.The amosph{ic ldp@tuE and the relaive hunidilv

Taling in|o considmrion all lh* alldls |he to|,al brighlncss of lh ikv isconpded at lh point whcE cmcol is pae lf rhe bnsl i$s of $c atv is noE thanor equal to tbe briShine$ of the ccs. ihc cGcent En nor be s(n' Eten ii rhebrishtness of the crcsocnr is marginallv moe $an the bflghtncss ot ihc skv it is vcrvdifilculi lo loc.c lhc (erc6t withour tny oplictl lid ln $e followinS thc q@'rilalivcbols aR di*ussed bricfly for .ll dc$ @nnuaiions:

For alirudc w.ll lbo horian $e lpFcnt Fsnion ofrhc crc*e isEi*d bvanamon.tR. thc angl. ofcfmdion (Snan l953.G@n 1985). givcnby:

x=5s.{#]*' (4.i r)whec P is the ahoq'hcic P6$rc.lhe cEscenr. for ahiildcs closr ro

/ is rh. |cnFatuc and zrhs horizin rhe following

t47


24/47

i = l,.cor ,+ 1i - l (4 t.2)L I+441r rnr Ix- t.ot.corlA,+ ."- | (4.ltjI n'+s.tt I

whcre, 90'r : lnd , - 9ou : R The sollwde Hilalol wo develoi,cd in $is work

ror lh delcrminarion of lisual linitiie naehitude thc major nePs ol calcularionsiadoplcd lion schacf4 s pogBE) rc lised b.low wih bncf de*riPtion Rel4nccsand dcrailed d.sc'iptions can bc folnd in Scherd (1993)Thc prcgEn funcion /drat r'l(,) 1at6 s inpu/pE-c.lculatcd valnes listcd bclow:

. a4r. thcal(iludcofnoon abovehonzon. tdu. ftc azinnth oithc noon. par. the alrillde oflhc place abovc sea kvelih ndcB, Pn,z. cslimlted rclalivchunidny of the place. p/a/. lairud of the plde. PratP. esrinatcd lcnDdlrrc of

. sd/pn4. lhe right Nensioh ofthe $n at the inc of ob.cnstion.. \eshlil (= 0.365.0.44,0.55, 0.?. 0.9) $. {av.lcngths @@spondinS lo U- B. v.R md I bands. b,r.r[t (* Sxl(]iJ. ?x10 i. lx10fr. I'loi3.3xlOI) p!3ncl$ !.lues in lhonish dhc brigihss sssilled snh .rch wvelenglh $lccrcd. a!r1t (= 0, 0.0.01!. 0.008.0) p@eler values in $e cxrinction cctlicicnrcorespondins lo lhe ozrne factor ssdialed wirh ceh wavel.neth sclccled. rr.!.r/, (- 0.0?4- 0.045. 0.031. 0.02. 0.015) p.Bmcrer values in $c cxrinclionceficicnr coftspondi.e to ihe w@ficr facloa (hmidnx lcmpedurc elc )associatcd wilh each wavelengh sel{tcd

. @vh[j] l. -lA.%. -10,45. -11.05, -11.9. _12.7) lhc nagnitude of fuu mooncoftsponding ro dififtnt slel.d warclenlh b6nd5. mschtil (= -25.96. -26.09. -26.74, -27.26,- -27.55) fic $lar magnilLrdccoftspondinS to diffrc sel*ted w6v.le41h bmds

148


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cnschtl ( t.36.0.s1. 0.00, -0.?6. -1.17) @Nrion for lund masoirudcs!! csponding ro difiere.l sleded wavelcngih b6ndsr"a.. the ler ofde obseMtion,c?,,ap.lhc elonsalion oalhc n@n fon lhc sun al lhe line ofob*ryorion'lhc funcrion shs Nnh $lcclinS a poinl I wnh sky position sitnhr lult mdhI O.l.lM tum + 0.r-i-e. a poinl clo* lo th. cstrc of $e tu.e disc Thc ^.ilhdishnce ofrhis poid.:ed,sr is scd lo calcul.k lhc 8as. aeiosl ed lhe o7..c ndss

xr = {cos(?cdig )+0.0286 icxp( to.5'cos(zsrd,ri )r-lx4 = bo(ud'i )+o.or I 1xp( -2a.s'cos( rd,u/,Jl ))l-r. L lsintf,",./,r I l' I"'=l lr.:oro;rrl ]

Ka = o.'chlil'O +0 4'lpto! ' co{satpha ) - cosl3' Ptat )))/ .*,, =,,,,,,r,,.. *.(,i# ).".(tf ).".(- #il )

This is followd by rhe calculaio. of th cx nction @flicicnls componcnlscomspondine ro live diff@r \Evlnglhs cleted in the @v Ydc,ll/:& =o 1066 '*e[- ?s4J'("qrrtl'r) 4 14i7)r, =o r,(xru;'".-,(-#).(' -a##-*,) ",",,,

J, *orr'.^-,0*r!!\' ''o' t

(4.3.4)

(4l.t(4.t.6)

(.r.3.9)(4.i.10)

For cqch wavloslh bed rh.* eidnction ccmcicnts a'c ecumulalcd inkrchli)= K, + Kd + Ko + K" (4l l l)And rheir linearconbinalio. wiih mas componcnls tE gathcrcd inro n v dnvhJl:


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,.tdchltl = K, r ^ s + K,' x, + Ko' x o + X-' xs (4I 12)lbe.qurioft (4.3.?) to (4-3.12) aE Pleed in a loop thal rum nv ddes oncc for ach iO. 1.2,I and 4. Aner$eexccution oflhb loop lhc rir m4ss al poin r, thc tosnion ofrhe M@nandfiarof theSunacc.lculal.dusinS:rrr@/ = [cos{'drd'Jt )+o.o2s icxp(-II'co(z"dirt.)] (4.l.ti)il (nofu < 0) nnposl = 40ar nnpoeJ -lcos(go - nul )+0025 r.xp(-llil (\ah


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lf thc hviligh briebhes rv/, doninats ovc. tne day lieh briehhcs dat, rhc. thc sud.i r,grrb and .' ,1, are slored in ,r.r/t otncffi$ rhe sun of ,'s&r, md etb rR noE'din L.r/t Morcover. ifrhe Moon is.bov. horizln thm de,, C lho addcd to bs.r/t/.l-iially, fic brighbes ,.\rrlt is @neened inlo .m-tanb.6. fon cquaon (4l.16)till rhis point all conpulalion is done id a looP that recutes Ilve timcs again, once forsch wavelrylh bdd *l4td fnc aicula$on ol 6e limitins naghitudc /, is donc .s

(4.1.24)

(4.3.25)(4.1.26)(4.) 21)

la (tel < l5o0) ic,,e=loat..eo lo-re)Els { co,a - I o ! rr . .n o " I 0 r ' }kh = tum'\t + Jctu" tb.t rt.. = t6 i1 -2 t,IVD) d.".htzl\ In(I0) lSchaelcr (Scha.fer. 1988) in his drtshold co.tdsl nodel calculates /i as rhe log

of $c ratio of rhe acrual tohl brigltoBs of th. M@n ad $e tolal biSlttnss oi $c Moonneded for visibiht fo. rhc givcn obsping condiions ln this rc|k we considr rhcmlg.itude oflhe Moon and $e lisual limiliog naennude slculatcd frcm thc alsoinhmgivcn abovc- The diftcmc. of Moo.s naenitude z"d!A and lhc visutl limitinsnalnitude le- is consideted .s nugnitude .onxas de"or.d 4 zDzq A plol (Iig 4l Ibclow) sbows dirercncc ofscbacfcls thEshold cohtrasl I and $c nasnnudo contasl/r43 Scries I sho*s ,1aas lor crcsmls $ wca not $cn and erics 2 shows ,'lu zg rorcrusoent ihrl \vcre sccn Sdies I and series 4 sbow ,4 cot.spondins lo dcsccnc $alwce not sen d lhal scte sen Esp.clively.lheda1a lor this fig is talcn lrom Sch.cfc!(1988). P$nive vales ol cont6$ fo. crcscns $al wrc nol *o ad lhc nesrtilcvrlues lor conlrdt lhal *erc sccn snoN lhc inconsistcncics ol thc modcLs qirh lhcob*ndion. Th6e inconsisteoci.s may E$ll fDn .stiDatcd lalues of tnpcaorc a.dElative hlmidill adoptd for lhe calcllalions.

l5r


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Thdhold conExl vr| f.e.ltld. conbtt

i-

Fig No 4l lTa!t.4.1.1 is d.v.lopcd sina the sc prcssn Hildol i4 o!&r !o sDlv* $'

crts@t ob*frarion @rds t Ln tod ti|c E (S.h&Lr' 1988t Ydlot' l99E Odeh2004). In @h mw of thc l'bl. obsfrrion Dmbq (s sign d bv Odch (Od'lL 2004).dde of ob*darion. ldrlud, longrld. &d.lcvstion tlove s l.v.l of lh' ple ftoswh.d th. c'l6l is ob*dc4 followEd bv $. diMr.d ldp.tat@ 3nd 6ri6aldlElarivc h@idny. Th .ext thF @luld @nr.in $c uit.6,l lim' &d th'ldf,rdlig Ms,in4le .dr6t wh.n th. ru&ttn d" co,rr/dt b4om$ j6t f!vo@bl'for siShrinS of c'lsdt (@lum vith hddinS .3l!n) *id n is bsl for sidlinS(@lwn wi$ lsdins 'bd-) ad whd i is favo@ble io' sidtina ror th' lar rin'(6ltm wilh hddirg 'ta'r). This 8iv6 lh. tine Engc lor $e posibl' Et'd cvevisibihy ot $. c'ls6! TIE rus,,'& .otdr i3 @Nid.ied onlv fot @id'd visibilit,oa crcsdt. Th. lan $E 6ll,!m @Duin th. i.fonMdo. E$ditg *tEths lhcclt* M claincd b b. vi3ible widout dv opdcal ai{ wi$ a bi'@ulu ot eith a

t57


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Tt. ob*Mtio6 @sidered in th. llblc 4.3.1 e ody rno* *lq il wr claimrhar rh. cc@ 6 sn by dy n@s .s ll|e rcordi enen rhede not El.ver. Moeov.r, by vrryiog thc Grinared tnpdt@ dd Glatirc huidily iln valual.d 10 oblain oplimm @ndilios for nr}d eye visibihy ol $. asc.nl, If thntaEnituda co"na is obtairea ro b i. favour of visibihy onlt dcn lhe lim. ra.8. ofnaked cye crescenr lisibility Ee delemined md included in thc rzble.lt thc nagnitudeco"rf"rr is nol found b be in favou. of u.aid.d visibility the l6t posiliv. value of lhenagritutu conn$t is c5lculaled md th. se vatue is included in aU the thRcoGpoodins columns. 'rhe s,m positivc vahe in all rh* @tM.s it rhc indicalionthat under lhe walh.r ondnioN consid.Ed the crsccm ws Evr visible to lhc naked

]-his table shows tbal $erc d ll cases ofposidve sighting claihs {ilhout opiicalaid when nagnilude contmt was nclq in iavour otunaided visibility. All tsc positilecss e aho nor in aetemenl wilh tbr conditions due io Folhqi.ghm dnd nalndeuLunar Ripeoes las d@s nol allow l0 of thcse dd the two of lhen e oily ntr8'halcses a.cordins b n. Only one 6e mlcdly diffD fiom Lllm RiF@ss law. Onl, I of$csc 13 ces ue not allowed by B.bylo.id cdknon. To or thesc ces m notallowcd by lndim nlhod ed rhe !6t of th. thrce m n&giMl c66 i. Indid method.Boih Bruin's limit 6d Yallop s critcrio. do not allow.ine ol rh.s cases ln cae ororher tou dlaims Ellfoutcs* are marginally lllowd by Bruih's critelion bul Yallop sdlsion difieB a lot in one oflhem.

Thc liBt pase of the lahh 4.1.1 shows t$o etaa odinarv claims of nakcd ctevi.ibihy of crc$enl, ob6 No. 189 &d 455 wilh q_values -029 dd _0 216 Thc Yallop sc.it.don d@s nor allow naked y. visibitilt for lhc$ q Qlrcs 8d tlE naanittde.o"r'4r, b ale nor favoMble ev.n wirh hiSlly exassenled wealh.r condnions TheModifid Ripene$ Fuciion (chapb 3) !alu6 corespoldine to lhs oberations eaho noi favoudbte G0.95 md -0.62 in tablc 1.5.1) for cEscni vkibililv Therefole th.*obsedations, as lhey fdil to etisry evoy model, de highly melilble ahd ar. outlie*

l5l


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TheE is only onc noc clain ofnajcd eye vilibility of ffiant wilh t-Elue lcsrnd -0.16, obeMtion no. 2?4, with q-BlE -0.22 | (AR- = - l .l9)- I1tis obs.dalion itnot allowed by both the Yallop s crilerion dd th. Lunar Ripenes Law but wnh highd.tevariotr (1524 n 16 ahove s lcvel) dd loe hmidity (6linat d to bc lo'ld lhetuEnitude cohftast is favourabl for uaided visibilily lnd $e ob*nolion is notuNlidble. In rll the esl of lhe cB@nl oben rions *ith I-valB ls lnd -0 16 lheclaih ofvisibilily of cressnt is with binocular or wit lelescope. Thee claiN de alsonor ucliable 6 out of25 s@h claim 8 harc favounble uas,itt.L cotun lor n*.dete visibility with oplimm 4tinales of lehpcdtwcs ed rclative hunidiry'

The hagnilude conrAr for sme other r.porledly Positivc cE$nl sidrinss{ithoul oplical aid n nol favoudble. Th6e e obeFalion nunbe6 14l, 3 19, 416, I16,315. 2a6. 611, 314,272, 2. The q-values (and A\"J fo! $ese descents & _0 153 C0.8?), -0.1r (0.07),.0.101 c1.06). -0.047 (-1.t. -0.02?(0.167), 0.00? (-3-5),0.01 c0.7?),0.012 (-1.01).0.018 (-2-88),0.109 G1.47). For 341.416.Il6 rhe thrc. crireda (Yallop\.Lumr Rrpcoess Law md ihe nagnihde oi!r60 e. co6islenl- For 286,633,114,212dd 2 Y.llop's citerion allows.alcd cye vGibilily udr "perf*l lkibility condnionJbut bolh lhc Lumr Ripness Ls* and lh naerrilude conltdt are nnfavoulable for nk.deye visibilily. Thu ir apFd thll Lus RiFmss L3w is nole coNistcnl with them.Snilude conlrdt rcsulis.

Io rhis work limiling tlesopic hagnitudes &e not coGidcrcd as lhe rponedccsem ob$fr.tions wnh bineuls {d lclcsP.s do.ol pevid. approPriale d.iails.ThcrefoE lhe appopiale limiling lelescop.s cm not be conpnled MoEover, out wo*is horc conccmed wilh visibility of n w casd witboul dy otircal aid

154


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t!.2131)

-'.gr""il-,,;* I ",.;;; I,.!('!,"];;; t"

r-?tp!!

,,;p,{ I155


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t56


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l5?


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t58


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4,4 A NEW CRITERION TOR NEW CRtrSCENT IISIBILITY

while dvcloping rhe "vbibilitv cudcs" (it againsl 5) $d the limi$n8 visibilitvc!ruJ (, + r against r) for.onstad brightn.ss Bruin @nsidcrcd the avedgc brightnesof w$m horian duiog rwiligh od fi. ldistion of lh. bdgltN of lh' full M@nwith tlE alitude above hotian c me ion d @lier' Instcad of @cid'dtrg av'asebrightness oi sky we hav coNideEd dual blighrnds of skv and fte cr'scent calculakdsing the techniques developcd by Shefet sd olh'6 (Schmier' 1988b, l99l) i' lhe$nw@ Hilalol. W. $lslcd c@ent vi.ibilitv circUmtarcls of ldious rcw Mm6css whn lhe crcscenl Ms rponed b hav. beo sn For cFs415 ofa pan'culdwidth we found lhe altiludes I oi skv points with btighhess equivalent lo that ol thoparticlle crc$. at dilltnt $l& depEsio.s r' Th. ovcdgd of the 'ltiludes of skvDoinrs for difl'rnl $ln dctr.$ions for plirhuld sidlh d Lbllatd in T'blc no 4 4 lThe left most column of lhe lablc contains ihc solar deptssions r and ihe toP rov grvsrh {idrhs r oflhe crcsenrs sclaled ed thc n xl one giv.s its na8lnude Thc enties of$e 6r of rhe blc ue lhc aldtu&s , shcE lhe stv hs rh' sm brighhAt 4 lhcbriehtness of tnc cresknl ofthc width al th. top of lh @luon.

It should b. nold thal duins ihe twilighl 1ne widrh of the crc*dt vd'es up b adc seconds for very wide d.sc.nls. Se6on to eason ed for dif|ere'r lalitldes the skvbddrlnes fot th. sdde altitu.l cl6e lo th. poid ldee ihe sun sts also vdi's lor qchcolumn of th. lable 4.4.1 a numbq of c!*s of alnosl eme cE$enl widtb wE@nsidered md each ahitudc is aveEg of lh.se cdes Thc dtla of lhe tabl' 4 4 1 is $e'plottd on a sraph shown i. fsw 4 4 1.lb lhis figure n as a fuhclion ofr (i' =/6,) @d r+ ,' = s 6 a fuclion ofr (rl = sat) aG bofi ploned /ft represnl the "visibilitvcwea &d the s(, rc9dnc the liniting visibilitv cudcs" sinild lo wh'l Btuin(Bruin. 1977) developed.

159


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T$LNa43.ltf t li rl!.a.l a, -r.81l t3 4.5

1 tt.a955 2a5_a5 32 2.1 12,5 1.f 1,1 0,8, 3.05 0a ot5r,e 0.t 0.552f r.t255 0l o5 o3o,7 o250,2r.t o22 1 oi5 o.t

Fia. r!b.4.,1.1

532

Altdav.r 6ot Oap,Ebo

!I

t@

12


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Alttudo v.6 Sohr Oottesalon1913

l:!9

Th. @rdin rs oarn ninid ofafi, Ghom i. figurc 4.a.t) e lhd b.sic dals for lhe@del pe nrv dseloDed Sou tu dE i.ble 4 4 2l

Using tubi. l.e sque appronn rion * oh.ird lh. following El.ro. ben*cnrchtiE .ltilud. ot@rf ARCV !d tu widd r

ARCv = 435t 37tvt +2222O75O57W2 5.42264J1tt! + t0.4341159(4.4 D

I6l


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On lhe bais ofthh dlatioo wc tlcnre th. visibil,ty p.m.tr v, 6 follows:v e = QRCV - ('-O.35lg$7W3 + 2.22207 5057W2 - 5.422643U t/ + 10.4341759) / l0

(4 4.2)Our model for .adi.sl visibility of n w ls& *s6! ir that if rp > 0 (w @ll the

visibility paEmctcr v, in (4.4.2) s th. r-vtl@) lhc ceml moy be lisiblc withonlopdcal aid olheei* noi Applting this o.dition on thc dat set ued in chaflet I &d inlhb chaptcr qe present thc rsulls obtained for whole data set of463 cd* in d.ltncolunn of table in appe.dixlll. Fid fd .ss when rhe visibilily is claiocd wjlhouloptical aid in odcr of inccGing r-ralrcs @ sho$ in 1abl. 4.4-1. Oui ol0tcs csesonly I I 66 d4iatc ton ou nodel. our of rhese I I c6es 8 de coosisteni sill thenagnitud conlrast 9 arc consisle.t wirh Yallop s crirerion and 8 ats consislcnt Mth theLund Rip.o6s Law, Tbe oberyaiion Nnbes 3E9,455,274, 341 dd 316lhal d.vialefrom lhe Lmr Ripen.$ I-aw, ihc Yallopt crilerion ed 1be Dagnnude conlrdt d alsonegrdve i. our modcl. Howvcr the obseorion nwber 4161hat is negalile in orhermodels is allowcd by ou!nodel. ille Een is th.t in this ce ARCV b redonably hish(9.41 .lg@9. Txe widdi h small (eund la @ sondt bur |hc M@. is rcry close roperige s closr ro $e Efih.

In fisuE 4.4.2 the minima of each visibilily cw. is joincd resulrins inro onFi8ht linc stich $nen .xlodcd inr.e.l tn oigin of rhe (r. t) c@rdjnde stseo. Thesrope of rhis linc is found ro b (lh + sys -) 9-3t5 ot t'/s - 4.)15. This lqds ro a Dodi6.d''b*ttine" of cesenlvisibility a:

,3 = -=-i:s1:s+4.3(Ts+LAC)

l(2.163)rhpanofLAG

9.3

besl tih. of crcscenr visibiliry is give.in conp&ison ro l(2.25)rh panoflAc in

(4.4 )B

t62


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l6l


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In gendl l@kingd Lhe @npt.rcdsl! $ rn ubtr jn atFndrxtlt rl (m b nor.d'Ihr t no clain of visibiliy by ey n{s who slalue < -O.t9l. In f{r asobrdolion nunbf 389 is not coDsin n( wjth .ny nod.l w dject n edihercrore we claim $at th@ js no aulhotic obstuation (wi1h or wi$our optical.id) ofneq lunar cEsenr for s-vatu. < 4,162. Thus cFsccn! can not be senwnn vcr r-value < -0. l6 evs wirh a rel*cop.For -0.16 < r-value < -0,061h.rc e 26 (45olt clains ofcrcs vrs,bihy wirhopncd aid our of58 rcporled sd coNidercd obse(arions. ^s unaided visibilny.laims 45J, 274 and l4l d lol coNnlenl wirh ey nodet s w @nclude lbalfo. lhis tu8e ofr-utues the qscenr cs be secn wirh opdcal ad only.Ih 49 c6es wi$ -0.06 0. 15 rh.

For 0 05 < r-vatue < o. I 5, rhce dc j5 sishtincs wirh dtuar ai d (1[r/r) and 14$'thour oprical ad t2ra,. I hus rh. tuflr hay b easit) *.n qrh opucdt aidnr h! r4se ot s-htr &d !m be seer wirhour opticaj dn under ver) Comcondnion (sarh{ coldiriotrs and heichr above *. lerct).For r-ulue > O. t 5, oul of nexl 2 t3 obeR.rions th.oplrcal aid I 65 timcs (77.5yo). Th@foE wc concludecEeent can bc esity seen.Thus ou oodcl $ar we @ll .euhi & (lh critcnon..cd be sleheizd 4

164


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Calculate r-vdu. (or vp @odins ro 44.2) fo. th. c|lsdl a1 ilc besr tineTh. vbibilily condnior a girn by our 6odcl @ ihq givn in Tabte

The success of our hodet in t m3 of nuber or posniv ob&fradons in.gene.r wfth orc suggqrd c,itcrion is achived dE ro lhe f&r rhat we halr u*dSchrc&as brigblre$ hodet, i.e. actul brjghrness of sky rnsread of the avela8ebnghD.$ ed acru.l brighbcs of ces@r ins&ld of 1h. b.ighh.s of ftU M@n. Thnudber ofposnivc ob*pations in agreeme Mrb a cnterion rs mostty int.rp,ted 6 th

2.

l

vhiutc uaer pertco onairiii'lili[May rcquirc opricar aia o iiiiFitii?MFoliRequi( ophol ad (ROA) .0.16


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Wlen a ctirerion allows oprielty uaid.d visibitiry of rhc ncw crcsnr dd ihecFsnt is nol sn thcn it is a ncgativc.@t. Th.re c& be a.mbd of ree.s tornegativ em6. D.Airc rhe f&r rhal s obsdi may b .xFrioed ed r.ineddlononer &d lmws the loerion offie cEsent rhe armosphdic ondilions od thePhysioloey of dc obw.at cy6 @t stil lead lo non-vbibilny of ihe crent ThesfacloB ae sdlt nol wll exploEd rhus the high frequency ofrhc..gaive crc6 shosOil the probLm is srill nol eh.d conpl.Iety. A posniv. emr @cG when a nodel do*allow visibihy oa cesc. sd thc visibitiry is nor claimed Snaltq rhc n!frbr ofposirive ercB dd b.ttq is a visibility c.irerion.

The hbl 4.4.5 slmdises the posnile ed negative obseNarioB in 6greoe.tor d'esrem. with diafcEnr oilcrion fmn ft dara sr w h.ve choen for $is M,k,Tte labl is aEanScd wirh dercsing succe$ pcrce age in tems of vjsibiliry claihsaruirenl wirh lhe $ircrion. Surprisingly lhe Babylonim cnrenon ha rhe besr succcspercenh8e ti)ttowd by our r-vatu. crilrioo, Th. l.btc funher shows lh Btuin,scnrenon (4,1_2) and th. L@r Ripens law e.qudly suae$tuI, Thse @ followedby $. q-valu. critcnon of yalop dd rnc ARCV,DAZ_bdcd Indid ncrhod (1,6.t3)Tlle crn*ion duc ro Ma@dd (3.6.10) od lo$erinsnd,s crjterion aE dD lc6tsucessful ofde mdhods shom in rhc |2bte, Ir sbould i, nor.d lhar tess succdstut amodd is in d$nbine pGilive sighdnS gncEr it is. Moreoler, strcrer a hodel jt shouldbe nore coosislenr wirh .cgaljve obsryatioDs (wl|en fte cGsc.hl ,s nor sn).

, The number of iegarive obsrnadons in ag@mc urh lhc diterioo is at$omrdkd 6 a resl of a cnr.non by sodc alrhos (Fatooni et ot, 1999). Howe!e!! iishould be notcd $ar rhe exploration of Schafcr shows fior $e bneh|ness or nagnnudecontra$ is highty dcpendenr on rhe w.alher .ondir io.s. All rhe single pameter cn&riaconsdsed in the rable 4.4.5 do nor conlider wea$er ondiriotu of indilidu.lobsw.'r'on.If ay ofd* qitcdon alom viribility in soh cae il ,. sl,U possibte lhallne setbq @ddirioN &c rcr f.vour.bk for vkibiliry &q oe crc*en is not acrualty

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Tl|rcforc, if Fothcdnghd's criGdon is nosl s@4stul i. b.i4 cotui$dr fotnegalive obedadon rhG dcs not at dl htu thrl it ii h.tcr or noa d.p.dabl. thdYdlop'3 mod.l. Bolh Mah&E $d FolhdinSldt hod.k @oa resative oh6d6tioB (whd ctlsdr is mt *n) but e lc.st sussful for pciliv.ob*d.lion. Ihh is tre sinply b..!4 the criteri! a. sficlcr s @nFGd lo o$dcrireria. On th. oih6 h.nd Babylonib @ndition, i-v.lue criedon ed lhe LuarRiperess law e highlt cotuistent with rhe positive obervalions but l4t coNislent wilhthe ncgativ. ob*Nations. The* dd other crit.ria (Bruin's limn dnd Yallop\ 4.valuconedon) arc noF conc.hed with condnions udr rh. visibihy o{ n w lutu oesenl i3tossible .nd not *nh fte .onditions un


44/47

visibihy cws inii.lly corceived by BNin, Thb clss includes Bruin's lidit, Yallop\a-EIu cntrion md th. s-value cilerion th.l is d.velopd in dis work

w. hdc ucd Schafls algo.nhn ro cxploE rhe Epoaed ob$natoN out donot cone uder ftc "Edily visible ' @ndition duc io YolloP md when $. cEse mrponedly sen, AnohSsl ths ob$palio$ ces lhal have ufavouiablc ha8litudecont6l are critically exoined md some sft Gjccted (esp4iallv obs.nation nlnbcts389 od 455) s $ey de lol consislent wnh.ny of lhe visibililv ctit rion consideEd inrbis work. Bo$ lhce rcponed cses m nol .oDsi.lercd Fliable as .ven undq niehlvexrgeerated .hosphdic t nFEtw md Glativ. humidny rhc magiudc contrdt isfoud ro b. unfavoubL for cE$ent visibilily ve foud al lcdl onc ob*oation whnile crc*enr sd Gpondly *n wi$olt.ny oflhal oid (obs. no. 274) ed thal is nolco.sistent wilh any cilcrion bul havc 6 lalourable nagnifude co 6t fo! tlalivchumidiry less than 50% and atnospheric lefrpcrature aound l0 deglee centiSBde

Apan fron obervarion nDmb.6 389 sd 455 1nee e ll olh.r caes shen thecEse w4 r.poncdly s@ without oPlical .id but ihe ma8lilud. .ont6l ws notfavowbt.. Howvcr,olee m ofFsitiv. ob$nado$ re consined wilh ar lcsl onoder crilerion consitleed in 6is sork A3 the brighhess model tE still nol pedeclrneEfore thcs. I I obsenalio.s ce nol bc dl.d out .s umliable.

The models $at @ dedued Iioh rh Bruin's isibilitv cud6 ud linilingvisibility cud6, th. Bruin's linil md YalloP s single p&meter (it .ion drc found to beconsisr.d qith.{h other. Bolh hav. stmosl.quivaldt succGs Frcntagc br Bruin s

We ha!. developed new visibihy curves and limiting visibililv curlcs using thebrid nss mod.h due 10 schaeler md o$es O. the basis ofthese n'* cuBes a newdara *t ad a ncw sinsle pmetei cril.rion b d.duced The .s liniting visibililvcufl* havc lcad lo a slishdy nodifi.d "h.st lime of cE$nt visibilnv Our nwvisibiliry cril..ion, thc r-value ;ilaion, is found lo be norc succ6sful fot posnive

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obsMriom bul lcs sue.senn in @mpdien 10 thc Bruin's I'mir dd Yallop'3 ctil.tionfor n.g.tiv. obsdaliors.

In vieq ofthe facl rh.t all th vkibilily oiroia de ai6ed al explorin8 conditiohsundd which rhe new luM rcsert may b. seen the suc@$ oI a modcl lor positiveobsrv{ion is hor inporlrnl d i$uc as cohparcd to ils succe$ fo! ncradleobs.F iions. None of lh sodel h limcd ai deducin8 condnioa und.r which lhcvieibihy of ftw lbr cJsMt is Dposibl.. ThcEfo&, a nodcls see$ for bcingconsblcnl wift $c positirc obsmlion b lh sses ofthe nodel.

In vi.s of the nagnitude @nl@r model bed on brienb6s of [email protected] dd ofrwiligbr sky il h6 ben *en lllar rhc lbibiliiy of .ew lun& cr$enl is Sreatly aff.cted by(i) $e eleelion above sca lv.l oflhe obs.Nation sne, (ii) rhe almospheric lenpcdurcand (iii) lhe relalive humidily. Higher is the.levation morc islhe maghiiudc contrasl rnfavou ofvhibilitt. Lowd is lhc lenpcEiuF or hunidily the nagnilude contdt is motefavouBblc for cEse sighdne. Evcn if *niampidal diteri likc Yallop's g-vtlu.cril.rion or ou s-value critdiotr


46/47

Thercforc, a possiblc slralgy for vedliatio. day be to usc eslituted alevalio.,t, esriMtcd tcmp.rarurc, 7, dd $dnakd Glaive huidity, l/0 md get thc rsults forg-value or r.value. lf n allows crcsccnr visibilny for lh. eve.ing in question dd fte claimh nade, tbe clai6 is acpted lf1h. s.mi-.mpiricsl cribnon d@s nor.llows ccsc.nrvisibility dd cresccnl sishtins is claim.d, .voluare mleniludc contBsl M,. Iftlo > 01heprogran Hilalol alloqs for vElidtio. i. elvalion, rempctur dd Elrtive hunidny eonc con adjust for thse quanfii* and qiry whether a favoulable ma8nirude contmsr (M< 0) is obtaincd or nor If rhe new mgnilude contmsr is favoldblc dcepl lhe claim

On bsis of the d!r. generaled by pDgEn Hilalol GhoM io ngu6 on the n xtpage) Elations berween magnitude coht6$ and rhe quantiries on wbich ir dep.nds {t Iahd I, ar obtained 6 aollows:

nay be considced for an adv&k pGdicliotr. I. cdc of vdifyins a visibilig claim $.dual ahosbh.ric conditions mv b. 6oded.

M = i 8177 -1.autE + O.0Ao000zeM= I t626e40n22)M = -A 4 368 + 0 Ai26T _ A 0008f +A OAOA6t'

ThG for meter inc.edc in elevalion M dece66 by O.OO0OO0I4' _ O,0O4l, for achpcFnlagc ircre4 in relaive hmidity rl' vdies by incrss by O.O3l 56e(0 o,o:d) ed forach degce cenrigrade inc@sc in tnpqarue / incrcdes by 0.0126 - O.OO08T +0.000006T?. This n6y ledd to the alproprjat elcvalio,! rehriv hhidiry ddathospheric lenperarure tequjEd for faloldbl nagnituo conrsr An applopnateerclation my b tbe elvation of . hill top o. buildirg Mf fbm wher m obseFalionnay bc @de or oay hale be. @dq The apprcpiare lchlsar@ ed rclalive hMidity

t70


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may 6ose that nay b. lhe ayrlse for lhc eson or lhc valB $at wE acNallyre@rded ar rh $ne of obsc(ation,

ELEVATION VRS NAGXIIUOE CONTRASTy= ?E.ri.odtr+ 5 af?

HUMIDIIY VRS IIAONTUOE CONTRAS1

t8B2

3.E3

$,3.33

TEIIIPERATURE VRS MAGNITUOE CONTRAST

thesis on the visibility of lunar crescent-4

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