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<br />MAR-28-2000 TUE 10:45 AM
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<br />I';st.imiltil)n nfthc l-IBC1I...o:lS P;ll':\lncl.CtS ral' nl'll\ling t.hu Prob"ble Mnxunwl'l Ylood
<br />
<br />'II<'t,,,;,,n r."n~tants fall within the 95 perce lit conll-
<br />,1"11"" ['""d of tho norllllll distribution N (33.4 days.
<br />7.11 .)IlY,), Because k is normally distributed, the con-
<br />Ih"'Il"" i 1I1<'rval 011 kayo clln be obtnined hy t-statistics
<br />mil.1 ieI', WOG::l71), The 95 perccmt confidence of k.vo
<br />i:, ; Ioll,;I:l:!..1 ,,(2.093) '(1,6)1=(33,4 :l: 3,351.
<br />i\ILI","~ll the b'Tal'hical procedure is subjective, it
<br />.{'o'I\I. Illat it provided a reliable means for b'lsel1ow
<br />''''I'"ml iOll; tho recession con.tnnLs were reasomluJy
<br />..J,),<o 10 mlch other alld thoy wel'e independent of the
<br />....;"ral! events,
<br />
<br /> ....."..-..---.. -v....--
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<br /> ",- /'
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<br />. 10 ' ",-
<br />.t /' . /'
<br />,~ /' 0 /'
<br />50 ",- /'
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<br /> ......"..-:or-.."_,--.ft.r--....l-r-
<br /> :!.u 2> 30 3' .c .. ,. ..
<br /> RecQs$ion CONIlillnl. k, (day)
<br /> Fib"LlI'1J 4. Pl.:1'iodogr,un Indlcnt.inj.( NonnaJity
<br /> ur llu: Hcct'ssion COJHll;,nt.... Tho dasht'd 1in('1S
<br /> clC'lirnit l.h" D5 [lcn::('ut confithmcl;! 11l.Ulll.
<br /> LOSS I'AHAMETF.RS F:STIMATlON
<br />
<br />
<br />Th" goal hero was to lillll the best Ci,(l" o(>timum)
<br />e"liUlnlc~ or the lo"~ (>11I'a1l1etl>I'. S'l'R'rI. and CNSTL
<br />In )(c(IJlltlllll U)lllvlln vlIIlle", or I'ruc1plttlUon I', YlIlt
<br />l1y,II'l)!l">lph U, total rUlu>IT Q, anti baseflow lI, from
<br />",,,,ll oj' 11,0 20 ~torm evenls. '1'0 proceed, 1!:'1\lntion (1)
<br />w.,~ W I'illcn:
<br />
<br />11'-1.lllJJ = [Q. Dl .. I'll = Ill.1 + Ie]
<br />
<br />\\,)",,.,, I'll ~ [Q - 13] is th" computed snn, [<101 is tho
<br />"i>"NV(ld SRH. and [eJ rcpl'l,sents II vector of residuals
<br />"I' '''''01'.. Tho TU:Cl optimization scheme cOMists of
<br />rl:iIJjmilill~ nn uhjcclivc fun.ct.ion to mntch crnnpulod
<br />Hlltl oU.:;~l'v(Jd s\.II'fn("C! runufr. The objectivo function in
<br />1II':Cl is l(ivcn by tho sqllnr" root of the sum of the
<br />wl'i~l\t.m} l'C~sidualst viz:
<br />
<br />F. ~ ['" '~', - (q~ _ 'I ,)2 * !L]V2
<br />o t:.J J _I J J 111
<br />
<br />(5)
<br />
<br />where m is the total number of nOll-zorn smr ordi-
<br />nates and Wj is the weight for the hydrol,'TlIph ordi-
<br />n<lto j computGd from the equation:
<br />
<br />(q'!+qO )
<br />W.= J . fie
<br />J 2~ 0
<br />qat.,
<br />
<br />((i)
<br />
<br />where '1o.v. is the average observed surface runo!'f.
<br />This weighing function emphasizes accuratc repro-
<br />duction of the peak Ilows rather than low tlows by
<br />biasing the objective function,
<br />
<br />Optimizatitln Scheme
<br />
<br />(4)
<br />
<br />'rhe HEel optimir.ation schemo requires an initial
<br />guess for the. parametel's and uses a univariate search
<br />technique (l~ord et ai"~ 1980) to minimize the objective
<br />function In order to find the optimum value of the
<br />parameters, Due to the nonlinear dependence ot tho
<br />simulated SRH on STRTL and CNSTL, local optima
<br />llre cXJlected to occur, Thus, various initial guesses
<br />are needed to increase the probability of finding the
<br />Il'Jobnl optimum (Lnedon, 1979), However, the global
<br />optimulll is never guaranteed, For this reason, the
<br />present author opted to perform a systematic sweep of
<br />the p~fiIl1luter space and compute the objective func-
<br />tioil for select"d paiu of the parameters, 1'his methud
<br />was feasible because for a selecteel pair of the loss
<br />p<lrameters, the simulation time of H&Cl 011 a PC
<br />486,66 MHz was on ly about three seconds,
<br />'1\", values for each parameter were used with an
<br />incroment of 0.2 inch for STRTL and 0,02 inch/hI' fur
<br />CNSTL, Thus. 100 runs for onch storm were cOllllud-
<br />ClI, which totals to 2000 runs for tho 20 .tor...a, 111"0-
<br />tration of the tcchni'll1l' is shown in Table 2 for till'
<br />storms lIf August 10, 1969 (the remaining table~ 11'0
<br />not showlI for brevity), 'rhe smallest vllriation in UJl1
<br />o!Jjl>ctive function tended to rUll in a diagonal direc-
<br />tion ncmBS ~he table, indicating that best estimates lIf
<br />the parameters compensate for Ga<:b uther, An
<br />incl'euse in one paramct.er usually led to a decrease ill
<br />the val lle of the other parameter,
<br />Although the exact optimum might be located
<br />bctwooUn t.ho pl\rmnotors increments, t.ho largo VUdi\.
<br />tiOll of the nptimum S1'RTL and CNSTT. values (<lis-
<br />c,,"sod in the next subsoctinn) between storms make"
<br />the errors incurred from largG increments negligible.
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