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BrsE - {/tili:,qTl/reo} * root (lit) Elror ln peak Bstlnate {PEAK) PBAK = uh€te P P D { ( lpo-P&l),/Po} x loor - oba€rved peak dlscharge = nodelled peak dlscharge (1v) Error Ln predlctetl Voluhe (VOL). lrls 1€ only a usefut neaSure If tjle voluneE a!6 not congtralneal to be equal. vot m Tlne to Pea]< the rnoalelled TTP whele TPo = observed tl$e to Peak TP = Dodelleil tine to peak n (vi) Paltial htegral Squar€ Erro! (PISE), an objectlve functlon r,|hich rras lnteoaled !o be a codprcml9e bet$een the IsE and PEAK functlons. Ic is deflned as: PrsE = fio;gl {(lv -v l),/v } x roor volurne of obgerved runoff volulde of predlcted runoff zrtoo) x loor fot eo>P o/2 nhlch i6 the sane as Eq. 3.1 but over a resttlct€d lanqe fo. ehlch the obsorved dischatg€ is at I€ast one half the dagnltuale of t}le observed peak dlschalge. Part of the study was an lnv€stigation of the lelatlve nerlta of sevelal of these objective functlorls. 3,4 Conparison of optl'llzat'lon schepes (TfP) gives lag !in€s. a beaEure of the acculac!' of ttriee catchsents rele chosen (1 Dutch, l seteall,sh, I Britlsh) fo. the study of optinlsaclon nethoda, one nodef nas useal throughout - the {3.2) (3.3) (3.4) tlm -m lt rine increnents (3.5) I t. t t t I t I t t I t t t I I t t I
I t t T I I I T t I t l I I I I I I t con6t.nt proprotlonrL loas cubrcdel q.orlblnad wlth t}a lfash Cascaale lurf,ace loutlng aubood€l (tbis cholcr ras neccgaallly albltrary). troul obj€ctlvc llrDctlotra uete us€d fo! cooparlson ar folLot's! Integral Sguara Error Blaaaed Int gral Sqrrare E!ro! PartLal lttt€EraL Square Error (ISE) Equatlor 3.1 (BISE) Equatton 3.2 (PISB) Equation 3.6 Poak Elroa (PErrR) Equatton 3.3 Each objectlv€ lunctlon was appued to t}le flrst s6ven events froD each crtcbnent (a) on aI1 events corDblnad to glve a global beat f1t (Sufftx C) (b) on all 6v.nt! lndlvldually, than taklng t}e average o! the palao.tor vrl-ues (Sufflx AV) , Itrua for each catctEent. elght aeta of palaneter valu€s nere obtalned (for each objcctht€ ftrnction on boti coeblned and indLvlduaL events). Otlng each of tltaaa el,ght palanetor 6ets. the leorlnlng events ln each catclurent w6r€ aloulat€d (th!e€ €vant9 frorn the Dutch catclEent and fo\rr each froo the BlltlEh and S!.edj.ah catcl,sents). Fol eech of Ul€66 lnilependent everlta on eac]r catc]E€n! uging each of tlre paraDete! s€tr, a t ble waa tkatan up of the value of each obJectlve (€!ro!) functlon (tor €x..ople, aee Table 2 below). TABLE 2 Error sumary for catclment 4376, event 400120 @tiolsation tech.tqu. u!.d to obt!1D p.!a!.t . PE^x"., - 3.89 - 5. rt 23.93 16.50 I 3 2 5 6 7 IS! I PISE t v.Iu. Rdk value RMk value Rek 2.65 2. S8 2,96 2,36 3.13 2 7.23 -t.5} { 3 ?.15 5 7.80 I 6.71 3 13.3r 7 10.56 2 a 6 8 a.o9 5 6.4e 2 7.93 4 5.53 r 9.O5 6 1,6.?2 I tt.36 7 Each palamet€r e€t iras ranked accorillng to the value obtalned fot each er!o! functlon, (It 13 lnt€leatlng to note that values of the Paru.al Integial Squale Elror (PISE) ar6 for each parae€ter 5et greater than val\res of the total htegral Squlre error (ISE), ltoplying that sbsolute erlorE aae not unlfor ly dtstltbuted over the hyalroglaph anal that large! e!!o!3 occu! ln the legion of Ure F€ak). 1I
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I T I I I I t I I I I I I I I I I I
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T I I I t t I I t I t T I I I I I I
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II .l I 't I t I I a: I I I --^-.r-
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I I I I t I T I I I I t I I I I I I
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t I I I = sinul-atlon run 2 = optlm
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I I t I I t I t t I t t I I I I I 5
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t I I I I I I t .t t I t I t I I AP
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t I 'l t I I I I I I I t t I I I I
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t 'l 't I I I I I I I I I t I t I I
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I 'l 't t t I I t I .l I I I I I I
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I 't 'l ' ?lrl I I t I I t t I t t
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