Flood Frequencies on the San Gabriel River Citation Fox, James May (1936) Flood Frequencies on the San Gabriel River. Master's thesis, California Institute of Technology. doi:10.7907/gacm-2y50. https://resolver.caltech.edu/CaltechTHESIS:10092024-213837010 Abstract No abstract. Item Type: Thesis (Master's thesis) Subject Keywords: (Civil Engineering) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Civil Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1 January 1936 Record Number: CaltechTHESIS:10092024-213837010 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:10092024-213837010 DOI: 10.7907/gacm-2y50 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16785 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 11 Oct 2024 18:09 Last Modified: 11 Oct 2024 18:10 Thesis Files PDF - Final Version See Usage Policy. 19MB Repository Staff Only: item control page

aubm!t-ted 1n Partial l!\4fillment of the Requirements "8:llf"o.r n!a Xnstituto of 'leehmlogy P ~ 08.11.f'<>mia -19,6- ~,m. ~~uet!Qn ·&. ~~iI?!fi~ .ttJrf st.~- 1 1).$ . ffPad, I ~~~8; I. P U ~ and Method& If. Proqu-«, Oltff~ 6 - ll II'!. 'l'he eyti:l1t and it's Intl:u$'rteett 11 - 16 IV. Ffa£eri'1 & ~rf'l-enta lo .... lfl ,q,. , f!~tnsnt ,F~bfrl~l?i! . ' - 6 18 - 21 t.. Ra.!.nMl and ~11i:age ~ o.tsoh~· 18 tl. Annual ftombt- 18 ,... 1.9 19 - ·3 } IV. . Zl;;;, A't.~to- ~~ F'O!!se,a «tlng Floods .~Jmlicat$,~mt o-f, ~$.Jl t.!: . 20 - 21 ~ -- ·26 22- ~ 2, - .26 2.7 De1e l. lii4l ftrdff>gre.phe ·o f Gan. -Gabr'let Rivel' l ~ - 1931 2 :?. Dul"atJ.on l'.1urv-~ a:t O ! ~ ot th& s-an Ga.hwtel River~ P!ot,ted on Pmbabili,ey, Paper, 1@6 - l ~ , . 7 l)tm.tt.1.on OUrve ~ nisnnar-ge 11 on t(Je,nrlth:d.e ~ > 1006 - 19'5 (trpp-01~ 2nd) - :oct the San Gab-rl.el R1Vl»'' li. nood F ~ . 1 ~ 5. ll!soi~ nurati-on ·~ 6. Fiy<tlrograpns for Annual Pree1p1t.at.ion., Ave~e 8 9 10 Annual nisc~. and Annual Floods,,. 1882 - 19'-4 13 15 't/lfl.tf;$ Table I. .l\nbU.nl nooa. M.1 t.hc san Oabrt.e l Mvo~ Table I?. Standard Val":iation and Ooef'tlcient of Skew 17 1'h'4 subject of flood.-:ftequenctee and to-reeao-ting h$8 l,ong been an tmpertant field -of 1nvestigaUon a1'llmg ffflg~;,: r.atneatlotane and p.by.81c1st.e,., lI-.n:MJrCUS ~ · ot awilye!ltt have, been. pl"Gpo.Od., eome of which are :practiotil mi4 in g~nenu use. and otnera wht:eh by ~ o,'f their complexit.y a.nc!. un.._re.nted refttteme:nt have not met With popula:r approval. • The goal of all nttrt.hode .b u been to det.end.ne th& moe,t uni-v&rsally suitable •ans 0£ obtaining a graphical err mathe- matloal relatl.Ol'l.ship between the magnitude of flood flows on a given st.l'8C and the· frequency wtth wh:ieh they will be equaled All L\l'8 dependent upon the pae't reeol'd ot a. at.ream as an index to the fut.ure perfomanec. In epplyi:ng f'lood forecasting t.11:at hist.o?"J will repeat its.elf; that the Brute magni'tudfll and hequeri:ei-es- ot flood dinhargee which occurred during a gtv•n period wi 11 reoul' .1n similar rne,.i,,1itud.ee end f'requenelee in the future. The longer the period of' re(iord• the more dei'in1tel~~ is - flood wen.ts ·may be founded,. Th& euccet.Hsf'ul dm.ermtnation or the co~ree,t magnitude-frequency relationship of a stream would the judg$0en.t c'f the 1nvest.igat.or, ae will be illustrated. In acltl:ltion to -the di:reot- at.t.ae-k at flood-frequency proble!:18,- ma~• othe-r dev1eee have been employed for the pUl'p-oae· of. extending or OOl'T&CUng the dat~ Checking the 1'8ttult..e. M aasisting in their s,pplication to $ngineering probloms. 'l'h.e purp.oa·& of: this- pap-el'- is to utU lze the data of the San Gabriel River 1n an exa~nation or sane of' the mol'!e CO?!:mOn - 1 - milee, -eowd.-ettng almost. entirely ot mountainous tettitery~ 'Otte to ite geogr.aphicsl eltuatJ.on, 1n t.he e-emi-tropleal region of Sout.hem ~alifomi~ a few miles north-east. of Lo.s A.ngeles"' t.he at.ream la allllOtlt entirely· r ~ . Only limited cont.cr-1- but.iona fi'om melting ,mo.w p ~ fi:'01Jl the highest pea.k8.. These oondU,iona result in .a :a t.ream 0£ ex-c.oedtngly varied ... year to peak flowa ef •• high ae 4o.ooo c.f'.e,. (January, 1916) Figure 1, donaf>ed by ~ P a ~ ¥later Oepa:rtr.ent, charts the theee chgacter;t,st.io.a or the ati-$Ql'n. ·The· height and du.rat.ion O'f' flood& are closely. though no"t entirely,. dependent upon the intensity and duration of the preclpi-tation. The recsntly comp:lot:ed f,~rris Dem wae mt placed in operation unt-U 19;4,. and therefore bad no influence oti the data used. Two ,c anals ~ e d by the Southo.m Calif'om.ia Edison Oompany are eupj:i- l .ied by th& etnam a little aoove the gauging stat.ion l'tho.ee :records ar:e u•ed in thi,8 study. (!-fear Az.wm,. aaltt'om1:a) The data ha& been eo-rr-ected, however:. from the .recorded f'low in tru, canals. Thus., the de.ta presented repre- e-0nt natW'-a l~ undisturi>ed co.ndU,ions 0£ stF1::am-f'low on the San Gabriel Rivel". Figure l n.. I,. fulpQ!HJ FLOOD Fru;queNOY' Re"TER1:UNATIO?~ and Met.oho.de 'fhe purpose or flood-tl'eq.u ency studies, aa ment:ionefl before, is to astabli&h a relationship ·between niagnltude of' f'lood& end method o~ anal;rsi& 1e utlli.ud,, la that. the stream will follow, with respect to ~imitud:a and f"4t.tency,. the tlarl.9 tendency as I , The fl.rat procedu?!e 1n making a tlood-frequency plot ts t .o collect. the annual flood-flows en the at.ream under consideration. The annual one-day f'lood is that uaually selected., defined ae the maximum average 2 ~ flew occurring eae:"1 year. 'fhe t.c)te:1 length oi' the ree:ord then. iepMSents 100% on tlle· time sea.le" and eao-h individuel flood now oceurred k100 percent oft-he n tme. wb&l"e n is the total TlUlm}~J' cf !:tans in the record .. It tollo-ws that- if' the floods are arranged in desc&nd.1ng order of magnitude and numbered c«teecutively from 1 to n, t ho percent of time ant flood waa equalled or ,exceeded is !!x100, where m n is the number oe:n-esponding to th& flood. In plot.ti~ however, t.he &C'tual per-een.tages are mt ua,e d .. Instead it is a&BU:lilBd t.l1a~ eac..1-i flood has an equal chance of f'al ling anywher.e wit.hin the rang& of time it repeaenta, and . therefore it 1.e plotted o.t th«1- mid-point or the int,erval or at - U p •c {2m · • 2n ~100. · 1 ;1..,.,., This p1!~edure bae '-uven f'oL.owed,. us....:._.g a 50 year period of reeord. in 'l'@le I. In plot-ti.rig, eithel' th-e actual £loods or thoir ratio to t.he me$'1 :flood are tal~n as the ordinat.ee. and the time soale as the abscl&ae.. All .standard t.ypes of: paper,. ae well as specially ago~ artt.tL~ie or legarl t.bmie pa.per were used, but -the t.rend &!nee then hae boon toward the use of what is termed 11 hydr-aulin probability paper11 • On this paper, the oriinate ia either arithmetic or logarithmic# and the ti."118--seale abecinaa 1e t,aken from the tnt.egral. o:f" the probahiU.ty curve. If plott.ed cm this pcq,er data fo l lowing the normal law of :error will f'e11 on a et,raight. line. st.Nam,-tlow data doea net follow the normal law of el'l-«>rhut approaches it closely enough that a plot on probability paper has t.he c:ombined e:f':fect- or 1tetra.1ghtening outn the curve and magnifying the end& o-t the ~!.me-scale .. If it la desired to project the cun·e beyond the rtm..:s"-e O·f t."1& data, this is done with 1'1l01"e ce:1"ta1nty with a. et:raig.'lt line than with ·a n empirical curve. The use of p·robability paper acheivea this reault. It is po&sible, tho.ugh rarely neceuary., to detal"!nine mathematical expre&&.i~na which .&l'proxi:mate the emplrical date.. 'l"he st;raight line: Which closely apprcmim.at.es the 29 year curve ·• in Figure 4, ie of th• form Q, • ,1.,ooo;e-¢485p ., where q is t he flood dieeh~ge in q_.. f.a . ., p th& percent of t.ime Q is equalled or exceeded. ~ · e t.he baae of na:tural loga:rl.t.hms. The method now in general use was dev{Jloped mainly by Fulle,r Fo.:ater and Hazen. I't involves obtaining, through the use or three coef"ftoienta and a set of empirical logaritiimic factors,. TABLE I. ANNUAL FLOOOO ON TUE SAN GABRIEL MVtR Ohronologically Perc,ent~ or Thie In Order of ~tude Y-eu- •Fl• e.f,.a,. NO~ f'b)w e •.f.1t.• Aetual 186~18&5 leaG-1587 1887-1~8 it,000* 1 2 ·2· ·_ 2.. -~,00 . 2 % 4 188e-l009 ~:~= , ~ •.~ i5 5,200"" ao.~ 1,000* e,o1891-1892 1~~18~ 14,.~ 1~1894 2701' 4,00()=I' t8J4-189.5 1t395-1896 2'0* 189(5-1~7 1897~1898 •. ' 1899 l~ 1g9,-.1,oo •.•. . • .... •. • • ." · . 1,00-.1901 1901-1902 1902-190'1_ :·· •.. 1904 _.·. 6 7 8 9 10 11 -~~ 12' 200llc ~ 1: 15 ~ro• 17 ti 185♦ 5~~ 5., 500* a4s- 16 18 19 20 1_·., . 1905 10..0001900-1900 9,-4,0 21 1906-1907 1907-1908 1908-19® a, 1;909-1910 1910-1,911 1911-\912 6*810 1atw .•.• . . ··.•. 1..100 12...000 9,-160 22 199 1922-1924 ,,2 "~00 9.160 8~200 ~,.-000• 7,100 6.,.81.c 5,910 5,,,5',0 ·-5 -~ 5.,aoo• ,,..aoo-+ !)-,,0 ,0 . .* 4~ 000 ~-020 ·· . ✓- ,, • ·* '000 . . }:, . i,J '6 ' ,1 ;~ ,9 4o 41 42 4, ;a 4o 42·· . . . 44 46 ·Jffl 00 52 ~ 45 47 1+9 51 5; 55 76 75 17 754 (;68 492 49 185* 50 4, 69 71 r; 200* 48 ;:5 ,1 59 41 70 72 755* 47 4.6 '' 620 5,910 1934-19;5 31 '4 ·'6 2:7 29 t,7 45 1,690 2,;00 2,6oo• :,i:-a ,o 68 476 984 19., 2-1,,, ·25 8,0* 1~8-1929 1929-19;0 1930-19,1 193;-199+ 26. 28 6, ?.A 44 19 !1 2, ·54 192t;<19!8 1951-19;~ 24 17 57 ·668 5,5'0 492 22 r; 58 60 19214-1925 1~192.6 1926-1927 ll,4oo le 20 V. ,2 7 15 .,,¾ '° ,1 5 !6 '6· ·•,oo a-,. ; 12 14 / ,:rt 1 ,,, 9 11 t.960 1,690 l,~* 1,-4;0 l,.2'ro •984 29 19tt-:i92~ i1.1too t~OOO* 8 10 ~ 1913.-19.14 11~800 1916.i--1915 1,4,0 aao 1916-1917 1917-1918 5,0,0 146 1918-1919 2,400 1919-1~ 1920...1921 16.900 1921-1922 8,:200 14.,~• li"ooo 11.eoo l..900* ~-e0" :2·.< .,ijoo "- :-· .27 1915-1916 22,,,00 6 24 25 26 ,.020 l.,s.,6tJ 1912..1913 c20,.ooo• ·1• 6··1- 900 · ··.• Plotting 476 ,oo• ,,2 ~ 270* ~,,. 245• 199 146 62 66 7ti 78 So 82 84 86 88 5' 61 65 19 81 e:, 85 87 90 89 94 9' 92 96 98 100 91 95 97 99 -6- 4at-a. These coeffieients are: a.ee area -o:'f the stream-basin. Ooefflclent. of Vad.at1on • 0V = ~ . 42 . n - 1 when d = ( flood - mean fleod)J.aean flood and n ""' length oft reeo-rd. . . . Oo&ffid..ent cf Skew, o.s . .., da. j 6vi . cs is further ·,:n - l .:X •. • . adjusted by means o2 an empiric-al · :f'e.O'tor t = ( 1 -.,. 8t5 } . . n f The· <:ri ta e. me-asw.e of t-he V'!"t'iat1on or t.he data fr<iJm tho mean II1 fl'!93¥!9U ,9:£!,o Figm'eril 2., ,,, 4. ~ 5 an- all Val"ioue form& of frequency . .curves derl.ved fl'Om the dat.a ot the Sen Gab-riel Riv-er.. We:t.et' D&parl.nrent. Fi~ It repn,.sent& e. f'lo► durat1on cttfl'.~ on which ' all flf'-wtJ for the pttriM 1$9o - 19,0 are plott.ed on p:robabiU.ty peper. • '!'he pldt.lng po.tnts are de\-e-mined in the same l!UL"ln&r out.U.ned ab&ve, bu.ts tbte aeate oaoh flood or flow rep:re-- se:n..te only one.· day dunng the p~riod,. ra-t.h&r than one year. A epeolal ·a cal• 1e e upe~$d cm t.he chart locating -the yea.r-ly .-r pere-ent chance floecte :fu:r vari..ous interval.a. 1.e elmply made.. The conve-nion For -ex.ample., t.he 100 year, o-r one percent clt&n-o.e • tlo.od. on tM;• c)hari, o'CeUJ'& ~lM -.xlOO • .00274 percent or -~ - 8 - Figure ; - 9 - Figure 4 - 10 - Figure 5 - 11 - time. The otraight-U.110 extension of- t he upper end of the curve a-e arns s0ll'1ewhat arbi.trarJt but unless th~ law fullowed 'by the vai-ia:tio-na e-hang~s abruptly beyond the ranga of ob served di:tta., carried t.o p-o-nition.e of' ext-reme floods. 'l'he values obtained f'1•-0t1 t.hia curve .a re closely eor,1parable wi.th tho9e indicated by Figure 2. r:rost of' the exiat.ing di.f'fer-ence is probably due to the diff erence in tho perio·da of record. From "thi e 1t is ap- parent that in t..1.e ~aae of the Son Gab.riel Hiver, log paper ie as usable as probabiU:t.y p-a per, and will achiev-e th-0 name results. Figure 4 plots frequency eurvea for- two sets of :flood data, as indicated in the legend. On this curve. the annual flooda only are :plotted, end the titll-&-acale gives directly the percent ch-anee of aey i'lood flow.• Figure 5 gi vea the entire curve of which Figure 3· ia a portion, with the exception that in the :fonnor an arith.>netic time-eeale is ue-ed ao as to c:ova:r the entire ra.ng;e of the eurv~. !JI. If the-r e were such a thing as a definite cycle, it would be a simple matt er to cho-oso the correct length of :record on which to ll aae futu:r.e f'oro-easts., and even to :ahoo~:e t he e.'{act size of :flo-od: that would occur in any given year. - Sueh simplicity doea not exittt in na:t ure,. however, though at one time U .l!Jh the potdt.ive t.l"Uth 4f' thte 's upr•J:Uon do net #X"in. It 1-a generally '/tt»Tnl that the.re .a re fluctua'tiona ftom high to admit -e:r wc:e&Scsfttl analyst•. ?hat. auoh nuc:tuat.ione do OCO\U' o.n the San Gabriel le :readily eeen ftent Jl\l~ 6. en whi@a..·r e plotted hy4rogl'e,pns I f,e-r rainfall., tl\Yffage· annual dieeruu-ge, and ~ l y fl.coda r-or th& penod t88,-.t9'4.. 'the record le not 1~ enough, nor ia ·t he o,ole d•t'iftit.e •nough to w.a;f'l'ant -~ - al te,:ation of -th& flood tnqueneY -met-hods. N u- to include qclte e-: ffeets .. Se-lecting a period o~ r-ocof'd tor tlood :f'reqaeney study ho expected once in the next 50, 100, or 1000 yea;rs.. .o'bvloua-ly a f'allac·3 .. This is fitol'eOast-6 based on record periods of leas than 20 or ,0 yea.rs a-re VSf'!/ likely to lead to erroneous temteneies than are .actually t he eaee. Figure 6 - 14 - While if,. 1a aasu.11Gd., for went o:f' bettor Womation. t.ha~ ftt~ure floods wi 11 be of the same magnitude and frequency as thoae in the paat_. it would be wore• than Mile to make a similar aeaumptlon aa t.o the o-rder of their occi..1rranoe. If any att..snU.on ls to he paid t;c, .cycles at all, it should b& for the purpose of d.eteminlng the co'r.reet. pe.r lod or record upon which t.o b8:8e :future forecast& wit..h the gre.e.t.eet degrM of &afef.y-. Insp:ection er F4,.~:e 6 .a :zwu that the period .fTom about 1906 - 19;5 1Wuld give a falr rep:resenta't.ion o'.f the put performan4e of the st.ream$ whereae a record fTom 1893 to 19:55 would be deng~rously prejudiced on the aide of small fl01'1:e. ln ord-er t.o, compare t.he effec.t s of using varying length& of' record, it was found neeeaael"y t.o. ext.end the flood data. further back than recoroa could l}e found. It watt supposed that., td.nc13 the San Gabriel ie almo&t. entirely rain.tea, 'that there would be aone correlation b~ween In Figure 7, thla wu annual pNJC1p1'tat1&n and t.tmual flood. attempt.ed9 While th.ere is conelderable error for 1ndiv1dual floods~ tbr a long reeot-d t.her-& le a tendency to compen.eat&~ and t.he results obtained ar-e aeeun1ed to be a tai.r 1nd1cai1on of the act.ual pe,r formance ot 'the st.ream. The dotted po;rt.ione or both t.he annual discharge end flood hydrographa were obtained in this manner. (Figure 6) From this ext.ended lat.a , the dot.ted eunre on F1gure 4 waa wol"ked out., aa illustrated in T:abl(t I. Wh11e 'the curves hav-e the &ame charact.er1.e t1c fo~ t.he longer :record yield:& lo:wer results than the 29· year cune. This te attributable 'to - 15 - Figure 7 - 16 - t.he, incl uaion by t.he fu-rme-r o-f an exceptional ly dl"y period f'r-om. 189;, to 1904. Unfo-J'tuna.tely sufficient. reco.r ds d() not exist. to determine which curve is the oorre·c t one. the do't.ted line repreaenta a Ev-e n though lon.ge-1' po.riod: ot dats.6 one would be inclined to place m.ol'e t-:rust in the aborter,. 1n this ctaa. lt euld b$ en the side of s.af'e,1-~ and 1a known t.o lwle been a tair. unpN!j'u dicad sampl(;! of the past history of thea trsa'"'l. xv!_.. - ~ OOUFlOIElti'S 11. wu disc-eve-red that in the ·o nae ot the San Gabriel" Hazen'a Ooocf f'icients could not be dep:,nde4 upon to givo a pe!'m$nent indication of the tom o:f the frequency 4trve. In a trt.ream of eo va:l'iable a nature, the inttlusion ~ one high £1.ood in addition to a givon set 0-~ d.a-ta would ca.use a tt3umpn in the av and ~ -of about ~ . ?a'ble tI U~imtr«tea the method o-£ computat.ion f'o.r these oaef"fi:Ci$flt.a as applied to the shE>rl.., 29 y&ar nteGrd. re.a ulte SN:: The av = 1.. 07 and OS • l/12 • The determination waa rape,ated .i'ot" ·t he fifty year period# and even though the plott.e-d frequenoy ,c urve was- lO:Vtered6 the eo&f't'icients became: OV • l.42 $ld OS = 2. 11 • Then. sinc,e some doubt wae entm-tained as to the accuracy of the- ft'OOd tlow ohottt~-n fGJ' 1889. the factors ware ~mputed~ estimating th1e :f'loo4 at- 40,ooo c .. r. a. instead of' 20*000* T-h is Ume- the value-a ti the eoe:t:f'ielente rose f.o• 0V Cl 1.6, OS = ,.71 . Thie property ot the method nseeasita.tft extreme eare in eh.cosing a period o-f record tor det.e:rmination of the flo'Od-fretpency ea.e ffio-ients. The above disousaion ia not an at.tempt to diseredit. a method - 17 ... TABLe ll. !WA!raARD V.tlU' ATION ~1> ®E.FFIGIEffi' OF SKEW . -~ • l 2 -i 4f;28 ,.__25 ' 4 a.4o 2']·27 5 6 ~ ,S l .~;oo • 7 1~74 9 1~1'6 8 lt> u la i, 14 15 l6 17 l8 19 20 ~l 22 23 24 25 •26 27 28 29 tt_;,57 1\,,1 1•;14 1~06 •~96 ~58 ·• ·•·~ •• ._i,e •.. ;a ;;,2· •.. 28 ~24 ·.19 -,.16 •.11i ~1, ~ 09 •· .· + ,f, ,.aa + 10-~7;0 ~25 + 1·.. 40 + lA..,27 ♦ 1-,.00 + -.;.81 + •~ jl + j·•' 5. 7, + ~146 :1 + .-,. 'fl' · · • · 1 ·4 + ,, . + •. ,-·0.6 --- •....o4 - .-~55 !.,42 ,•• ·54 .... · •.. :&,.070 ..· 1..•·900 ' 1~610 l~.000 •656 '· •~!¥50 • r • . • :-'-26 '...2ll ~•.()96 -.oao . • 004 •.002 . *.68 .ag1 •;ca • . , ·- · .;s4 .. .· ·.46:! ·- • . ~,578 -~446 ·- •.81 ~84 •705 ..... .: •...86 ~l 4,.69' •.. 74o - · ·- ...,._ •.. 62 - .·.7276 --- -.,87 ... . -.s,o .97 .94{} Tot.ale •~tti~nt.. ,Of Varta.tiiffl '«1,6~ ~655 -...1m ·~ · . - ,..,, ~.151 ·.• ·8··26. • . .• .o; ... •656 .. .. · ·.04 .. . ~2,, •. ,14 ·.518 i;.06 -- .•·,·94 96 ·.157 ·. 166 ' •.. 91 -- ·.91 ,, ,•·oi, . , . ·- •,..000 ·.074 ·.176 • •· • -··6' 26 ' •. •.. 885 . .752 ' · ~"886 ,· .91, 5'.842 ,2.195 a.,oo •1~«:Zt i 15 • -=- . Adjust~ FMto-r = (l + 8~f.?j • l . ~ l•... 11 0:Z - 18 - accepted by emimmt. engineers, but it. servea to tllurtr--ate too £act that tor 8't.:F$ame f£ the peculiar nat.W"G or t.he San be used without the added pr ecautton o-f' checking l,W aome ~ mean.a. A statem-e nt made in the Unit.etlStat.es Geological Sutvey Wat.ff $Upp!y Pa.pe-T I-Jo. Tn. tuti~ee to t.he- fact that some 't'lncert.ainty tn the use ot the above process still exi:e-ts. Th& ~COtm'lendat.1on 1• made that if' a W6:ll-fttt1ng eune is not obta!ned using thit d.eri-vEul o:oef'fi4ent of skew* a new coeffic:ient of skew should be- sel;G9ted. and th& curve again conat-rue--ted., re-- pea.ting unt-11 an aeeuft:te fit is obtained. ,I, , B@ntallMJS AglUg1 Di.so.mm!! Inapectton of the p~1p.t t,at.ion and ~ - annunl dtecnarge eydro-grapho,. Figu-re 6, yielde a few interesting t'ac-ts which would pNJVe helpful in e.nlie:1-pati~ - ~ dhchlU"ge&. ~ t.o the lag 1nduced by gromtcl-uto~e, theff: le not a po-&itive 'lgreement between the fl•tua-tione f'~· rainfall .a nd annual runott. the p.r lmipl,es imrblved are obvious. For ez:ample-. thOugh t,,ne pr6'li.p1t.at.1;on ·h t t,}ttj year$ 1899 - 1900 and 1901 - 2 was~ M-ri:ne.l, the ·Ao•-• -due to previous depletion. 0£ storage, was we-tl below average#' ~-"VlbU.c~ in 1.h<l period 1904 - 7*~ree mod• e.rat-ety wet year& reJJUlted in eumuta'hiv-ely i higtwr· dtaehargetJ. . 11, _J\mual Floo4! 'I'M- annual tloods are :al-eo mff -e r los:& defin1t.-e in their - 19 - relation to. other -drolog1,eal data. Figul"e 7 illust:i-a"t&EJ the fun-ct-ion e-f .r atnf'all vs. annual flood. In. the ~-s or -a.n.nual runoff c9gaimt. ~ a l f'l®d" while toor-e is certainly a t.$&.d:ency for thee maxblum flood to oc.eur during a yr&ar- t>f high. flow. there 1a m distinct nwnerioa.1 comparieson,, and the nlat~qn- sl'd;p ffem8 ind~ended. of heig~ of .flow. fbnghiy- speakhg. the m.u tmum yee.J'l.y flood varies b'otn 9 to 48 tlm$:~ the rate of avenge allfltlel cU:eellUg•, with some 1nd1:ee.t1.-m of gra:up1ng: abottt a, &1.raight liM •p-N.B-oillg th& maximum t'l:eo:d ae. 28 times the av~nge -~ discharge,. The funct,:.on ia Mt plotted in the re.port.. Ill:. . P~ek FJ.Ol'(!: While the 24 hour flimd 1e -U.t normally used in rtood fretti-wncy lnvewtigat:1orut. in ~ c-aeee· •the r.isximum now of t.he at.ream for shori in""al·a ie the vit-a l factor 1n application of the NHmlt& ·th d:&aign. The height of thte· ~ ~ J ' peak di&pende ·upon ne-veral .faeton.; ·ithape and she -or ·dndns:ge are~ topo&raph1cal ~hal'- aeteri.st1ee,. or slope. and d1rectlon or tntve-1 :o-f atom. beeidaa, o,f eoursa, the actual 1nt.~nsity of the pree:ipcitation. In general the rdla.tive height d the peek fl°'! v-artee inversely ·ao the area of' ·t be· stre1:1.-n-b-asin... A-ttempt.s oon made to determtm. in the ease of the San Gabriel_. ·some relation bet.ween he1g'ht of average discharge and: height of: PQ«k.~ and al.ao bet.v:een height o~ penk end ti.11lCt of' oo- currance. vtithout succe.sa~ dependt>nt e.b'mente., These are apparently entirely in- From available dat4,, it waa ,dot.endned that the moioomary p-ee.k,, on t.he average,, was 2.1; t.imes the ti.ow - 20 - averaged over the oon-eo:ponding 24 hour· intenal. mine a.ot.ual f'low records fJere not available previous to 1906. it was pouible from two or three aou1tes to diseove.r eat1matea of the highest peaks- occurring en t,he C-'a."t Gabriel. There ie eme controversy as to ~her the ftood of 1884 OJ' 1889 was the largest.. In the Report of the Board of imgi.n eers nocd Oant.-r ol to t..he Board o.f Supervi&0:rs,. J.,oa Angeles County,. in the gocU.<>:n prepared by- M. Haw~ est.ima1.ee wer-e given vary!ng between lK>,.000 and ·ro.,000 e. f .s. Lo11 F. ahapin, 1n his mm.uom,. tt'fhirly Yea.re in P.aaod.ena" desc,r ibes 'the fiood• end tho~& incurred.. All evidence point.a to the o:oncltmi¢n that. theao tloud:a wer& the rdg;heat of 'Which ew 4uant..itative ncori he been kept;.. thought the,y t1e:re ol:oo&ly a p p ~ by the pealt of lto,ooo o.f.a. in 1916. A p&ak of 50,000 e. f.. &. ~ cot'l'Gsponding to .a bout 2;,.000 c.£'.a. av8r4ge 24 hour flow, ia Been f%'0lll the frequency ourv•B to .repl'SDent. .a pproxbnately t.het om hundred year, or one percent e hence flood. :IV'. Atter1vte at F'.t#ec«ati?\fi Fl®d:1,i .. m:mtoroue attropt.s hav-e been l'!lQ.d.e t.o detel'mine somo ac- eurnte nea."'la a!' foreeasttng tlood8,,, 1~ e. anticipating the flood f'low for a partiei.tlar yea.1",. or oouree •. pred1et.ion over a patiod of years 1~ impo0ttible, but noms hope 1b still enter- tained e-r being able to toroo-ast. a, flood a f~ months or~ 1&nr in advance.. So far lit,t.le ffilCoaas hat,· ken at't..ained, and i t is imp.rob~ble 'that with t.:ru\l prGSent limi't-ed knowledge .o ,f meteorolog:r and allied oubjeot.e wq pruot.toaI.,. oertain 118art8 in a llU!t&Jer of Oal.i:fernie aii,;ree.."llG,, tfflin;g a record fift.y-t,WQ, yoors in length,.. a N>aiJOna.bly close co-rmla-tion ~ ohtai1~.~ : '6 time& of tlle f'l.£'¼1'--~wo-:, ·t M• t,{.ovemhe~ l"t.dneall ap-proximat.ely indleate4 th& ~ t of' the next ,:,e'lal'lec p~tpitation. n, was ilOped. 1-n vt-aw of too d,ependenee of the sip o'f fiootl on rainfall;,. that a relation hwolrtng Novmoor t"ainfall pl etely. ~ ently Dr,.. Oarpenter·• s relation doea not hold in Pf,.l-sa;iemt a.rut Vi"Cini't.y. a?W e,f furl. toward an a-etUEtl qtiantitaUve prediction would be ua:oloo$ and dnngeroua. 'the· annual f'lood hydrogru_ph on Flgu,re e t ~- ,and rt.rnctff. W:S:thoot definite: knowledge: o:t·- the·- hab:U.:a <Yf the part;i'Cttlar ,s\rt·.,a,t,.,. a f'fisign ~ b.e mo.do tmiiat'a undff aidie •0£ ~ to an un®ooomle. eKten1... ftth a zsc:o-l'd af ,_ele length., and the •aittta.."lOe '6f t.he ft.<Jod f'reqt~.1 dffi~ee~ i~ fa J)()a:sible to e·t minate uncertainty t-o a great. en.en~ !n deigning on tm b.turis of' ~et.ad floods, there are two conditioo:r; to be .eon»1:d.ered1- that of maxi.~ ~t.aiQ pea.Jt,, -and tha-t ot fl.~duni.ttou. !br hr-Ugea, high~&.:,- le~a eulvffts,. a.ptllwli\tft, -a te., it. la the heiwrt, of the flood o~t mtieh ~ t be anttaip.at'Eid and provid'Sfl for. the d.a,"'?t.. The ·momentary tlt~t,~ s. and pro-party lying above the ptiiteetive h1tluano:e ot oon\fflle:~ stol'Eige are .S:af'& only as l .on,& -LW theyreraain shove the high,-wat('J-r m:.nge of the stream. ln allo-r'J.n,z f'-ol' Gpeet,ed flood&:,,. an arbit.rery expocte:d .d amge looe is a.ellign&d to ·a :t100'd at~d.ing the desi01ed ~ . ~den>t. ~•. .and ms.v range h-m o»e.~ d: ~lbt• 4► &t ruet1on ~ · t.lw f l t ~ to a $lQ;ll pe~i:.age a£ !t.J.J etta't... lt" ·~ life d o ~ ·~ · tht, atifSty of tiw ·s ~ t ~ undEfr wrg· c.iMtWetames., tt ts d & ~ for the met - ~· cotid1i'.i<>n W!rl::oh m• r ~na:bly be -¾'J~t:Od during its t 1ft"tit~. · la not end~~i"ed by it1! f'ailuf'~.,, lf t he life of human ~ then ,some design is coo~ baaed. upon tho jP.dgement of tlte· ~ln&el' 1n ohtu·ge, and upon a v,a.Uable· fundo., miah 1t. 1• hoped wlll ·n ot be· subj~ >oo un extr:~ flood mt,\:il 1-t ie paid for.. ll- , ~ e t J,ca.1 ~ , . i ; ~i! ln vi:e• of f.M. ,f.ntetUJivo reaeal'l)ll. on the subject,. .o f f'.lcod- frequeneies" tt ~ j:uatttiablo to carry 'tho e:ause of refine- mam. aa ater ~ r . . •i nt.o· ·t.he f5.old of eeonomlo dest:gn. Af.t A t'leod e.uteedtng th& ~$.«:ti'ty sf a 1rt1"UCt ure, oauaes -damage~ and finanobd loss; and- 19t U> build a .etruo:tttn) enti-r,oly f'reo ~ da.ttg&r <.ft ut:rG• t.lood&~ent«U:~ ~!:t.tv.e coet.., there aheUld je some happy ao'dium,~ .at, mieh ·t he 1ee.'f'~Y oost OS: upke€Jp. reit1n,... ment. . and !'&patr ~ d be a m!n.immt,. - t$ttatt<l':G 1 I it.Ile i-ntt.ial cost o.f ' the .m.:1,ic't<u:r.$~ r the l"e;t.,e ~ lntereet. and A the annuity mee-ess~ t.o C·t >ftte a replacing QU!l1 «t th~· •o nd ·G'~ ·~ · 11~•, of the Ettrueture... A ·~ an. m,· writ.ten ~ A = l'r :~iji1 _ l. in ~,_._o.t t at :r1 « ~ t ~ -of' 11tft.- 'Then :tl"l ··.· • ~ ... Ir(! + - l S .-., ·• l (r + l ii - 1 *~in r> • , ..~t. •. , 1r'rtt \' .. :,' +'1 0 - • M + tr + ( a ,r + t n - 1 · Ge i - ,, :tn prac.uce. ~er. th& l ~ of lt~ of a at.Nett~.,,. or :d leut- the length of•t.ho tnt~al bet.~ d ~ "- .d ther6,fOM ~ b ' a ,. floods. ts dependent upon the e&paottq of .~ ' the- atmetutYf., S : ~ with tho si~ of the ~rtJ'tlOtun•. As I tmd· -d the l n ~ n also 1nareae:es tdth -the ei®-, l b ~ an inilnas1t.Ig funet:f:<m o,r n ·and ~ be- writ-ten in tnoe fa~ of tle p81"'tteu.tar t.--ypo a£· :et.ructU2'9. Form.tt.1 (lJ ~ - thm btt r&-~rltt.en .( 2." i 1 Q • M + (A + nnC) r{~ +- l} :, . . !8', · 1\r + 1'!1. • J -; 1 (2) ~ •a 1Y11nimua pcint f'Gi- ~ •aluo of n. - ?JOtu.d be ffl) complex. and the derivation of too ot.her relati;on- $hipe. mat.hetafti-eally so tedious that a g r-aphical or tahulur aethod.,- Ulu:&tb'ted bYJ Figure 8., would aec,omplieh the same r&-· llUl;t vtith le&s etto:r-t. - 25 - Figure 8 th& initial coat~ In f is a .9 0rtes <t£- cost -~ ; .. plO!tted trom eq:J$tion (2) for veriou e<mstmit values, ot t~ Th'$ the .a beci,rsa in g ,and. the o:rd!nate.e ¥or 04 ·a l$ e~locted from 1? at- t.."te point ·» =- l-00 p • l. • J,.. . ·( From .e ). V 'rhs.t. g - ~ ha~ a rd.ni?tUm po:int lo readily ~ On co.s t curve#- "1~1 outff :and t4!tlts :fall on higher ~tte-e of' t 1. .f'e9mt.ing in a "ralelng~ 0£ the- e?-Jtve. The eo&t-t:requency o.f the variable ~ n to tw c ~ , and CO.Jnb~ the ten1e corresponding to that eliminated in a llel? re;la,tiot1$hi;l'J.. The Sw:r GurtelRtvel'" has a fairly wo1l-d-et1ned flood-frequency :f' r&latl~p. ?t plctB eq_ua,\ly well and is e-qwdly uaabl~ on ' eithe'r logarithmic -or probability paper.. The ·ue. &f.' Rt\:z e.nts eoef"fie.iettt.a 1e ~rid-n ~ euoh. '1tN6mB) ~ J.Jnottld not ba relied upt.m w.t ~hon't some form ot Cheek. tt. itt ~se-ible to tbree-aet 11!:t:h -.-«r eertldnty the sl~ t>r t ~ o,r oecv.rranee ot f1t\V particular fiood ev:mtt. 1.'he~tn obt.41Md 'through ft-ood fl-equency ~ho@ tUl&· exprettBio?Uf o~ ·t11e mt~rage ·~ <lea-ired 1'>\ft"p'~,- b'i.tt ean not ha :~ 11ed upon to hold f'or an,- individua). defligtt. It U3 posotblti t.o d etennlne tJio·e eonomtcal percent ®.a.'"l.CO n .ood for which t;o. dOtifit.;n. but this p.~ u-re el.so is worth 'li't1Ue- 0:nly wh.en applied ovei- a 8Uf'fici-0nt num:be-r or investigaUom w al low the: 1,eli1 of a,,erag-e.e to ~pens.ate John WU ey and Sons. M. Y. - 19,0 •StOl"age to b.e Pl'cnided in I~unding Roeorv<>ire- f'o:r !lm'1- "SUnepota, 0yd es, ant St,ru:tonal Rainfall n Or. Ford A.