Progressive improvements in basic Intensity-Duration-Frequency curves deriving approaches: A review

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1 nterntonl Reserch Journl o Engneerng n echnology (RJE) e-ssn: Volue: 4 ssue: 6 June -7 p-ssn: rogressve proveents n bsc ntensty-urton-frequency curves ervng pproches: A revew Ant Jn, Roch ney Assstnt roessor, Cvl Engneerng eprtent, Guru Ghss Centrl Unversty, Blspur, C.G., n *** Abstrct - ntensty urton requency (F) curves re ongst the ost useul tool n esgnng wter resource structures n prove helpul probble norton bout rnll stor occurrence. stnct proveents re e n the bsc e to generte F curves n the pst. hs pper revews ethos whch suggest the blc box theory n lso the ethos suggestng sngle vrble explnng theory n ouble vrble explnng.e. Copuls etho. hese proveents ncorporte n the F curves propose better es to generte F curves n expln the physcl phenoen o rnll stor ore coprehensvely. Key Wors: F curves, Copul etho, Extree events, Recurrence ntervl, Gubel strbuton.. NROUCON Rnll ntensty urton requency curves re grphcl epctons o the esure o sttstcl chrcterstc o rnll stors tht entl the esgn coptble rnll ntensty or vrous relevnt long stors or prtculr wtershe re. o esgn hyrulc structure, rst t s to now tht the ount o loo schrge t s ble to ccoote. t s clle esgn pe loo. o ece esgn pe loo, Rtonl etho s use where pe loo s clculte s Q p C( tc, p) A () 3.6 Q p = e schrge (3 /s) tc, p C = Coecent o runo A =rnge re (K ) = en ntensty o rnll (/h) or urton equl to concentrton te n n expeence probblty Here, s recurrence ntervl. Rnll ntensty n the Rtonl orul s ece by F curve o requre recurrence ntervl. o esgn hyrulc structure, t s very portnt to now ts crtclty n ters o le pero n ctors ectng ts stblty. Soe structures re very portnt le s n Spllwys whch re e or long le pero n ecte by ny crtcl orces le hyrosttc orce, uplt orce, slt orce etc. n soe unprectble ects le behvour o clte n the prtculr wtershe etc. Flure n such contons y cuse ctstrophe. Whle esgnng, structures re strengthene to counterct those orces. o cobt the unprectblty, hstorcl stuy o cltc ctors s one. n cse o F curves, these ctors re ntensty o rnll n urton o rnll. On the bss o pst, these ctors re use to generte F curves so tht they ncorporte ll the possble conton or the upcong le pero o structures. hese pst t re nlyse to evelop F curves eprclly rst. Wth the te, ore relevnt nlyss turne out. One o the explne the F curves usng sngle vrble rnll ntensty s pronounce vrble o rnll phenoenon then other etho llustrte both ntensty n urton o rnll o equl portnce. Both vrbles re use sultneously wth the help o Copul etho o sttcs. Wth these proveents, very relevnt F curves re generte whch not only sgncntly ncorporte the pst possblty but lso enble to expln physcl thngs up to gret extnt.. LERAURE REVEW.Blc box heory hse Very ntlly, Shern n Bernr tre to estblshe F curve. hey use vrous preters wth the vrbles whch ccoote the reltonshp n erent specl contons wthout cnowlegng physcl unerstnng. o stuy rnll ntensty n urton relton, n eprcl pproch s pple. At very rst, Shern (93); [], erve eprcl relton between these two vrbles n t s expresse s R () c ( b) R represents verge ntensty o rnll n nches per hour, urton o rnll s governe by n nutes or prtculr return pero. Here, three preters, b n c re use. hese preters re use to ncorporte the eect o geogrphcl locton n recurrence ntervl. rtculrly, consers the eect o geogrphcl locton n recurrence ntervl n b, c cnowleges erent geogrphcl loctons. 7, RJE pct Fctor vlue: 5.8 SO 9:8 Certe Journl ge 739

2 nterntonl Reserch Journl o Engneerng n echnology (RJE) e-ssn: Volue: 4 ssue: 6 June -7 p-ssn: Ater yer, Bernr (93); [3], propose slr type o equton wth lttle octon. He ntrouce the return pero n the eprcl orul s R (3) R s use or rnll ntensty cheve or urton o rnll stor n recurrence ntervl n,, re constnts. Wth the te, ths relton s e specc n constnts re ene or soe rnges. Gert et l. (987); [5] n between.8 Hrgreves (988); [6], xe the rnge o n.6 n or between.7 n.85 or the rnll events o urton less thn 4 hours. Kothoyr n Gre (99); [7], prctce the se stuy or the nn regon. hey use rnll t o 78 guge sttons n eterne the vlues o these constnts s =4., =., =.7 n bove equton s generlze s..33 R ( V4) (4).7 V 4 shows the rnll epth or yers n 4 hours n vry ro 7. to 9. ll over n. Wth the te, these bove reltons re custoze n tre to e the ore generlze. Bell (969);[], suggeste generlze orul or F curve tng one hour urton n yers return pero rnll ntensty s nex. Cheng-lung Chen (983); [4], urther propose generlze orul to erve F curve tng three bse rnll epths or ny regon o USA. For one hour yer return pero, 4 hour yer return pero pero 4 n 4 hour rnll urton yer return re ten s bse nex. Bell (969); [], use generl orul o the type: Aln B (5) Bsclly, equtons suggeste by Bell (969); [] n Chen (983); [4], y be consere o type: ) ( ( ) (6) stns or the recurrence ntervl n yers, or the urton o rnll; n stn or bse constnt recurrence ntervl n yer n bse urton o rnll. s the requeste rnll ntensty or yers return pero n nutes urton o rnll n bse rnll ntensty or bse yers return pero n bse nutes urton o rnll. Functon ( ) s the only uncton o return pero n ( ) s lso the only uncton o rnll urton. Bell (969); [], Chen (983); [4] n Koutsoynns et l.(998); [8], suggeste the uncton ( ) s the rto o to s: ( ) ln (7) An uncton ( ) s suggeste s the rto o ( ) (8) e ( b) to Ater ergng equtons (6), (7) n (5), generlze rnll ntensty orul or requre urton o rnll s generte conserng ( ln ) ( b) s bse rnll ntensty. e (9). F curves usng Un-vrte strbuton uncton Wth the te, stues rrve whch use erent probblty strbutons couple wth eprcl equtons to generlze F curves. o erve F curve, extree rnll event re nlyze so to t extree event rnll ntensty ostly Extree vlue type-. e. Gubel strbuton s use. Vrous probblty strbutons re use to ulll the purpose but Gubel strbuton ws opte nly. Bghrthn n Shw (978); [], utlze the Gubel strbuton to generte F reltons or Sr Ln. Oyebne (98); [9], euce F curves eployng the Gubel strbuton or Nger. Ver n e Souz (985); [3], lso use the Gubel strbuton to n out F curves or Rbero reto n Brzl. Sreehrn et l. (99); [], use the se strbuton or Kerl regon n n. Metho opte to erve F curve usng ths pproch s s ollow: ) Fro the rnll t o yers o pero, xu rnll ntensty ro ech yer s selecte. s s: 7, RJE pct Fctor vlue: 5.8 SO 9:8 Certe Journl ge 74

3 nterntonl Reserch Journl o Engneerng n echnology (RJE) e-ssn: Volue: 4 ssue: 6 June -7 p-ssn: ) hese vlues re rrnge n ecresng orer n hghest vlue rne rst. 3) he return pero s clculte usng plottng poston orul le Webull s orul. n () stns or return pero n yer, n stns or the hghest rn n stns or rn vlue or observe rnll ntensty n the probblty s obtne s: 4) he rnll ntensty s regresse wth urton o rnll. 5) Ater ttng regresson, rnll ntenstes seres or erent urtons re clculte. hus, ens n stnr evtons re clculte or erent urton seres. 6) Frequency ctor K or requre return pero s clculte by pplyng Gubel strbuton s: 6 K.577 lnln () s return pero. 7) Rnll ntenstes re clculte or requre urton seres or corresponng return pero usng orul. K s () s the ntensty or requre return pero. s the en ntensty o rnll s s stnr evton. K s requency ctor or gven return pero. F curves e usng Un-vrte pproch re nlyze utlzng rnll seres preene urton whch s not prctcl stuton. Wth the te, ore relevnt pproch s use. hs pproch ncorportes not only event rnll urton nste o xe preene urton but lso enble to cltte to show ont eect o both vrbles o rnll event..3 F curves usng Copuls Metho Copul etho s ctully oern sttstcs etho. t clttes to nlyze ny rno vrbles t te n lso shows the ont eect o these vrbles n ters o ont strbuton sultneously. Every rno vrble tht explns the physcl phenoen s tte nto erent probblty strbutons n the ost sutble strbuton s selecte s rgnl strbuton.. t s ppng whch ssgns ont cuultve strbuton H(x, y) ro rgnl strbutons. the rgnl cuultve strbutons G (y) n F (x) cn be ene s subset o collecton o rno vrble y n rno vrble x respectvely. x & y re two rno vrbles wth Fx x ngy Y y, then there exsts copul C s x, y CFx, Gy (3) 7, RJE pct Fctor vlue: 5.8 SO 9:8 Certe Journl ge 74 H o n the Copul C, t s nverte s, C (4) x, y H F x, F y Y here re vrous Copul les whch re ene over lte vlues o correlton coecent n ths correlton coecent hs xe reltonshp wth Copul s preter. Kenll s tu s one such correlton coecent n t s ene or N observtons s N N sgn[( x x )( y y )] (5) N =nuber o observtons; Sgn = x x n y y ; Sgn= ( x x )( y y ) ; otherwse Sgn=- n, =,,3 N. Sngh et l. (7);[], rst suggeste the e to generte F curves wth the use o Copuls Sttstcs. Supportng the ct tht correlton between rnll ntensty n rnll urton s negtve so the Frn Archeen Copul s selecte. t s lso oun thetclly sple. t s relte wth Copul s preter s: 4 (6 ) s rst orer ebye uncton. K th orer ebye uncton o postve greeent s ene s: t exp t t (7) hs s pplcble or postve. For negtve greeent, ollowng equton s use. t exp t t (8)

4 nterntonl Reserch Journl o Engneerng n echnology (RJE) e-ssn: Volue: 4 ssue: 6 June -7 p-ssn: Sngh et l. (7); [], suggeste the generton o F curves usng Frn Archeen Copul s s ollows: ) Fro the vlble t, nnul xu events re oun out n ther corresponng rnll ntensty n urton re note own. ) Rnll ntensty n rnll urton re tte nto sutble probblty strbuton n ther cuultve strbuton s oun out. 3) Correlton coecent Kenll s tu s clculte or rnll ntensty n urton. Hence, Frn Archeen Copul s preter s clculte. 4) Usng cuultve probblty strbuton o rnll ntensty n rnll urton n Frn Archeen Copul s preter, ont strbuton uncton s generte s: h C U, V u, v ln (9) h h u h v Here, h hxs genertng uncton s: x exp x 5) o erve F curve, rnll ntenstes re C clculte over prtculr rnll urton usng contonl strbuton exp r exp exp exp r exp R () 6) Contonl strbutons or erent urtons re clculte n contonl strbuton s relte wth return pero s 3. CONCLUSONS R () C R Eprcl etho s tre on vrous regons o worl n every te new equton coes nto conserton whch epens on the portnce gven to erent vrbles n the eprcl equtons. Mny trls re e to generlze the equton but equton s generlze up to soe extent wth lttle constrnt o rnll urton n return pero o pst sttstcl t. t s lso observe tht very less physcl nterpretton o stor phenoen s explne. Un-vrte etho s oun out to be ore pproprte s t s oun out to be generlze etho n sttstclly nlyses ntensty o rnll n ore logclly relte wth return pero vrble but lttle unrelstc s rnll ntensty te seres o xe urton s consere s t oesn t sulte the rel phenoen. Copul etho s oun out to be the ost pproprte etho out o three. t sgncntly explns phenoen sttstclly n physclly s t nlyses both the vrbles rnll ntensty n rnll urton sultneously. t nlyses rel rnll urton whch solve the unrelstc etho o Un-vrte etho. t lso shows correlton between both vrbles whch shows hyrulc senstvty o regon. REFERENCES [] Bghrthn V. R., n Shw E. M. (978). Rnll epth- urton-requency stues or Sr Ln. J. Hyrol., 37, [] Bell F. C. (969). Generlze rnll-urtonrequency reltonshps. J. Hyr. v., 95, [3] Bernr M. M. (93). Foruls or rnll ntenstes o long urtons. rnsctons, 96, [4] Chen C.-L. (983). Rnll ntensty-urton-requency oruls. J. Hyrul. Eng., 9, pp [5] Gert, A., Wll,. J., Whte, E. L., n unn, C. N. (987). Regonl rnll ntensty-urton-requency curves or ennsylvn. Wter Resour. Bull., 3_3_, [6] Hrgreves, G. H. (988). Extree rnll or Arc n other evel opng res. J. rrg. rn. Eng., 4, [7] Kothyr, U. C., n Gre, R. J. (99). Rnll ntensty-urton requency orul or n. J. Hyrul. Eng., 8, [8] Koutsoynns,., Kozons,., n Mnets, A. (998). A thetcl rewor or stuyng ntenstyurton-requency reltonshps. J. Hyrol., 6, [9] Oyebne, L. (98). ervng rnll ntenstyurton-requency reltonshps or regons wth nequte t. Hyrol. Sc. J., 7_3/9_, [] Sngh, V.., Zhng, L., (7). F curves usng the Frn Archeen copul. J. Hyrol. Eng., [] Shern C. W. (93). Frequency n ntensty o excessve rnlls t Boston, Msschusetts. rnsctons, 95, [] Sreehrn K. E., Jes, E. J., n Sseenrn, S. A. (99). Regonl rnll epth-urton-requency nlyss or Southwest n. J. nst. Eng. (n), rt AG, 7, [3] Ver. B., n b e Souz, C. Z. (985). Anlyss o the relton ntensty-urton-requency o hevy rns or Rbero reto. C Bull., 34, , RJE pct Fctor vlue: 5.8 SO 9:8 Certe Journl ge 74

5 nterntonl Reserch Journl o Engneerng n echnology (RJE) e-ssn: Volue: 4 ssue: 6 June -7 p-ssn: BOGRAHES Assstnt proessor, GGV, Blspur (C.G) M. ech. (Wter Resources Engneerng ), elh B. ech. Honours (Cvl Engneerng), N Rpur Assstnt proessor, GGV, Blspur (C.G) M. ech. Honours. (Constructon technology &ngeent), NR Bhopl B.E (Cvl Engneerng) 7, RJE pct Fctor vlue: 5.8 SO 9:8 Certe Journl ge 743