HEC 4 UsersManual (CPD 4)

8/13/2019 HEC 4 UsersManual (CPD 4)

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US Army Corps

of EngineersHydrologic Engineering Center

HEC-4Monthly Streamflow Simulation

User's Manual

February 1971

Approved for Public Release. Distribution Unlimited. CPD-4

Generalized Computer Program


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Standard Form 298(Rev. 8/98)Prescribed by ANSI Std. Z39-18

REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searchingexisting data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding thisburden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to the Department of Defense, ExecutiveServices and Communications Directorate (0704-0188). Respondents should be aware that notwithstanding any other provision of law, no person shall besubject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ORGANIZATION.

1. REPORT DATE(DD-MM-YYYY)February 1971

2. REPORT TYPEComputer Program Documentation

3. DATES COVERED (From - To)

5a. CONTRACT NUMBER

5b. GRANT NUMBER

4. TITLE AND SUBTITLEHEC-4

Monthly Streamflow Simulation

5c. PROGRAM ELEMENT NUMBER

5d. PROJECT NUMBER

5e. TASK NUMBER

6. AUTHOR(S)CEIWR-HEC

5F. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)US Army Corps of Engineers

Institute for Water Resources

Hydrologic Engineering Center (HEC)609 Second Street

Davis, CA 95616-4687

8. PERFORMING ORGANIZATION REPORT NUMBER

CPD-4

10. SPONSOR/ MONITOR'S ACRONYM(S)9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

11. SPONSOR/ MONITOR'S REPORT NUMBER(S)

12. DISTRIBUTION / AVAILABILITY STATEMENTApproved for public release; distribution is unlimited.

13. SUPPLEMENTARY NOTES

14. ABSTRACTThis program will analyze monthly streamflows at a number of interrelated stations to determine their statistical

characteristics and will generate a sequence of hypothetical streamflows of any desired length having those characteristics.

The program will reconstitute missing streamflows on the basis of concurrent flows observed at other location and will

obtain maximum and minimum quantities for each month and for specified durations in the recorded, reconstituted andgenerated flows. HEC-4 will also use the generalized simulation model for generating monthly streamflows at ungaged

locations based on regional studies. There are many options for using the program for various related purposes, and the

program can be used for other variables such as rainfall, evaporation, and water requirements, alone or in combination.

15. SUBJECT TERMSmonthly streamflow, statistical analysis, hypothetical streamflows, durations, simulation, ungaged locations, standard

deviation, skew coefficient, Pearson Type III, normal, HEC-4

16. SECURITY CLASSIFICATION OF: 19a. NAME OF RESPONSIBLE PERSON

a. REPORT

Ub. ABSTRACT

Uc. THIS PAGE

U

17. LIMITATIONOFABSTRACT

UU

18. NUMBEROFPAGES

104 19b. TELEPHONE NUMBER


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HEC-4Monthly Streamflow Simulation

Users Manual

February 1971

US Army Corps of Engineers

Institute for Water ResourcesHydrologic Engineering Center609 Second StreetDavis, CA 95616

(530) 756-1104(530) 756-8250 FAXwww.hec.usace.army.mil CPD-4


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10 December 1984

Conditions of Use

The following conditions regulate the use of computer programs developed by the Hydrologic

Engineering Center (HEC), Corps of Engineers, Department of the Army.

1. The computer programs are furnished by the Government and are accepted and used by therecipient individual or group entity with the express understanding that the United States

Government makes no warranties, expressed or implied, concerning the accuracy, completeness,

reliability, usability, or suitability for any particular purpose of the information or data contained

in the programs, or furnished in connection therewith, and that the United States Governmentshall be under no liability whatsoever to any individual or group entity by reason of any use

made thereof.

2. The programs belong to the United States Government. Therefore, the recipient agrees

neither to assert any proprietary rights thereto nor to represent the programs to anyone as otherthan Government programs.

3. The recipient may impose fees on clients only for ordinary charges for applying and

modifying these programs.

4. Should the recipient make any modifications to the program(s), the HEC must be informed

as to the nature and extent of those modifications. Recipients who modify HEC computer

programs assume all responsibility for problems arising from, or related to, those modifications.User support from the HEC to third part recipients will only be provided after the second party

demonstrates that program difficulties were not caused by their modifications.

5. This "Conditions of Use" statement shall be furnished to all third parties that receive copies

of HEC programs from the recipient. Third party recipients must be notified that they will not

receive routine program updates, correction notices, and other program services from the HECunless they obtain the program(s) directly from the HEC.

6. All documents and reports conveying information obtained as a result of the use of the

program(s) by the recipient, or others, will acknowledge the Hydrologic Engineering Center,Corps of Engineers, Department of the Army, as the origin of the program(s).


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ParagraphORLGSB OF PBOd Wmapom OF PROGR MDESCRIPTIOE OFMETHODS OF C TIOXO mOPERATING INSTPIUCTIO~SI 1 E F r n I O H S OF xmlsPROPOSED FUTWlE DEVELB

DE'I AHLED EmMIhT] m O CQBiDPUTER PROGRAIUIDESCUE'TIQN OF CROW S METHODo m m mDEFIXEIONSso RamI lPJePT mm

OF REQlJlXED c RDS


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HYDROLOGIC ENGn\rmmG CENTEROMPUrER PROGRAM 723 X6 L23 40

1 . ORIGm OF PROGRAMThis program was ?re pared i n The Hydro1.ogi.c Engineer ing Center, Corpsof Engineers. Up-to-date inform ation and copies of source statement cardsf o r variou s types of computers can be obtained from th e Cen ter upon re qu es tby Government and cooperating agencies. Programs are furnished by theGovernment and are ac ce ~t ed nd used by th e rec ipi ent upon t he express under-staad.ing t h a t t he United St at es Government makes no war ran ti es, ex pre ss. orimplied, concerning th e accuracy, completeness re3.iabi l i t y , us ab il it y, o rs ui ta bi i t y f o r any particular purpose of the in rmati on ar ~d at a containedi n t he programs or furnished i n connection herewith, and th e United S ta t e sshall. be under no li a b i l i t y whatsoever t o any person by reason of any usemade thereof.The programs belong t o t he Government. 'Therefore, he re ci pi en t fu rt he ragrees not to ass er t any progr ie tary r ights there in o r t o represent theprograms to anyone as other than a Government program.

2 . PURPOSE OF PROGRAMThis program t r i l . 1 analyz e monthly streamflows a t a number of' inter-r e la t e d st a t io n s t o de te rn in e t h e i r s t a t i s t i c a l c h a r a c t e r i s t l i . ~ ~nd w i l 1gen erat e a sequence of hypo 'theti cal, streamflaws of any de sir ed l.ength havi.ngthose characteris ' t ics It w i l l recons iLute miss:ing streamf1.m~ n thebas i s of concurrent; flows observed a t o ther location s and w i l l obtain,miu and a i n im um quantl.'t;ies f o r each month and, f o r spec i f ied dura t ions i nth e recorded, reco nsti tute d and generated P lows It w i l l a l s o use th egeneral.i.zed simul. ation model f o r gen erat ing monthly streamf laws a t ungagedloca tion s based on region al st ud ie s. There ar e many options o using .theprogran fo r various r el at ed purposes, and i.t can be used f o r othe r vari able ssuch as r a i n f a l l , evapor ation , and wa.ter requir ements , alo ne o r 3.n comblinati.on

Th3.s program requires a FORTRAN N compi.l.er, a random number generator(function RbJGm included, see exh ibit 2 , and a f a i r l y large memory 6 1 i ~ nthe CDC 6600). Provision s mad,e f o r use of th ree sc ra tch tapes , 7 ( f o rpunched output), 8 and 9 ,a In , the s t a t is t i ca l ana lys is por t ion of t h i s program, the lowsfor each calendar month at ezch s ta t io n a re f5.rs-t increnented by 1 percextof ,th eir calendar-month average i n order ,to prevent i n f i n i t e ne3ati.ve


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logarithms. This increnent i s la ter subtrac , ted . The mean, stand.ard dev ia tf onand ska? coef ficien ts f o r each s ,t at io n and calend ar month a re the n computed.This involves the Pol lcx~ing quations

i.n whichLogarithm of i.ncremented monthly l o wMonthly .recorded streamfl.owSmal.1 increment of f1 m used ,to prevent i n f i n i t e logani.thmsf o r montl~sof zero flowMean logarithm of incremented monthly flowsTotal. yea rs of recordUnbiased, es ti ma te of pop ula tio n stan dard dev.iati.onUnbiased estimate of population skew coefficientMonth nuniberYear ri er

b, For each s ta t io n and month with incomplete record, a s ea rc h i smade fo r longer records among t he st at io ns used, t o find t h a t which w i l lcontr ibute most toward increasing the r e l i ab i l i t y of the s t a t i s t i c s com-puted from th e incomplete record. The mean and standard de viat io n a r ethen adjust ed. Equation i s used t o compute th e equivalent record requiredt o o b t ain s t a t i s t i c s e q ua l ly r e l i a b l e t o t h e s e ad ju st ed s t a t i s t i c s a nd sth e basi.s or sel ecti ng the b est record t o be used i n the adjustment.Equations 6 and are th e ad ju sh en t equat ions .


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The primes indicate the long-period values and those without primesare based on th e same sh or t period fo r both stat i. on s and 2 , and:

N = Length of recordR = Linear correlat.i.on coef f i .cient

c . Each indiv idua l.. flow i s then converted t o a normalized standardvaria te, using t h e foll.owing approximation of the Pearson Type dis t r ibut ion:

t = Pearsorr Type SII standard deviateK = Noma1 standard d.e,viate

d. After transforming the flows for a l l months and stations t nornal,the gross (simFle) corre3ation coeffici.ents R between a l l p e i r s of s t a t i onsPOP each current and preceding calendar nonth are computed hy use of thef01.3owing formula

Ni-1 / z xl m L-l. mm = l i m C xm = l i-1 mn=lN-1/ R-2) } lc

i n which -= X - X


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e . IF ,the re ar e in su f 2'i.cient s~mul.'taneousobservations of any pa1.r ofv ~ ~ i7 l-l.es o cornpute a reo_:~l.red or re la ti on cae.ffici.ent, t h a t v alue must bee s ' t : i ~ a t ed . Each d.ssi.n,y ,value s est j..mated by. examining i t s r e l a t ionsh ip%c re:Lated pai.rs or va lu es I n th e curr en t and preced3.n.g moa?.thby useof t h e fol:l.uwi.rAgPo-mu1.a us in g f., 5 and k subscrl .pts t o in di ca te arariab:lesused 2.n .t'rle gross cc;rrel.a'tion,

k'i

Since, in o rd er t o e consistent with the two rel.ated correla-tion coez"r"icients,the correl.ati.ori coeff ici.en.t rnus t 1i.e be.hhreen th e l.:f.mitsgiven by equation Ut he l cwes t qger 3. i .d. t and. hig hes t lower 1i.mi.t ar e esta blis hed f o r all. r e l a t edpa,i.rs, and the average of th ese %wo 1 i ~ G t ~s taken as the estl.mated corre1.a-t ion coefPi. ci en t .

f . Monthly streamfl.ows &.s sin g from th e re co rds of thev a ri o us s t a t i o n sa r e e s ' t r i ~ at ed 0 r al.3. s t a t i o n s f o r each month i.n tu rn . Accordingl.y, when-ever a missi.;lg fl ar i s b ei ng ~ ec o n s t i t u t e d , h e re a l vays exis ts a valid.val.:xe f o r all. sta."ci.ons a.l.ready examined t h a t month and, f o r a1.l remain ingsta tLons i.n e i t h e r Vie curre nt o r ?receding month. For the se remainings a.t ons he current value sel .ected where availabl e otherwise theprecedinz value i.s used. In orde r t o reccnsti . tute the missing value, a.re,yess.ion egua'tion i n term of no& standard va ri at es i.s computed byselec-ting requ ired co eff ici .en ts .from th e compl.e.t;e co rr el at io n matrix f o rt h a t morrth and solvl.mg by the Crout method (See exhibit 1 , The ERissinzva.l.ue i s compu"ced f o n t h i s repess: l .on aqua.trion, introducling a randomc~omponentequal, t o ' the ~or?d.e. ier~i.ilationthe eqtaati..on, as d.i.scus ed 2 nth e atreanf'lm? genera.tion procedure.

q It has been found t h a t v a l id use or the regression technique requirest h a t all co r r e l a ti o n co e f f i c i en t s agree wi th th e da ta tha t w i l l be subs t i tu tedi i l to th e equat ions and t h at t h e cor rel a t i on coe ff ic ie nts be mutual l j con-s i s t e r i t . Inconsis tency i n the cor rel a t i on co eff ic i ents causes the dependentvar iab le to be over-define6 and i s evideacad by determi.nation coefficient~ r e a t e r han 1,0, f th i s occurs (because of incomplete da ta ), th e inde-pendent variable contr ibuting least to t he cor re la t ion i s dropped, and an a , ~egression equation i s comyuted, This process i s r ep ea ted a s n ec e s sc qun t i l cons i s t ency i s reached (which must occur by the time that only onei n d ep en d en t v a r i ~ b l eemains ) . rder t o make the c orr ela t io n matrixconsi s e n t w itl? t he da ta mat r ix, a l l affected correla t ion coeffi i en t sa r e recomputed a f t e r each est imate of rn tss ins data .

h. Kormal, standard deviates are then converted t o flows by use of theP o l l a ~ i n , y quations


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i.mpos.ing th e cons,tra .int

i . When the s e t of flows i s coqpl.ete, all. correl.a.tion matrices shouldbe con sist ent except ,for - crur?czti.on er ro rs i n th e conputer, si.nce the da taarrays are ~0rnpl.etp. Any consislency of matri .ces obtained i n thi s m m e ro r of matrices read i n t o th e coqputer wi 11 resu:l:t i n det;errmi.natfon coe ff :i ci en tss e a t e r than 1.0. I f .this occurs, corlsistency of each cor rela t ion m t r i x i sa.s ured by Pl.rs t te st i n g a-1.1 combi.nations of t r i 2 d . s of co rre la ti. on coe:ffi c ie n ts i n th e cu rren t a.nd preceding month f o r a l l calendar months usinge q u ~ t f o n11 and. r a i s ing the I m ~ e s t f the three c0ef f ic i . en . t~ o 0bte i.na consis.tent trliad. The , te st of consistency of each compl.ete na tr i. :~ ismade by recomputi.ng ,the mu1tip.le correl.at:ion coeffi.ciezt. If thi .s valse:is greater .than 1.O further ad,jus.tment i s required. Such fur.ther ad ju st-merit i s obtained by introciuci.ng e coeffi.ci.ent, success:ivel.y smaller by0.2, on the radical i .n equation 11. and repeating a l i ,-briar?. onsis,tencyt e s t s u n t i l d l ma:tr:i.ces a r e consistent. If consistency i s not reached,coef f icients i n each incons: i.stent m a t ~ i x re moved t a ~ a r dhe aversgevalue of d 1 oef f: i ci en ts i n th a t matr ix u nt i l cons is tency i s reached.

j. Generation of hypothetical strearnflmrs .is accomplished by cozputi.nga regression equation, by th e Crout method (described i n e xhi bit 1 f o reach s tat ion and month en then cowut ing s t r ea nf lm ~s o r each s t zt i.on i nturn for one month a t a t ime using the follcwing equation. This srocessi s sta rte d with average values (zero devis ,t i.on) f o r all s t a t i ons i ? Ynef i r s t month and discarding the f i r s t 2 years of generated flaws.


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fK = Monthly s logarithm, expressed as a normal standarddevia tep = Beta coefficient computed from correlation matrixi = Month number3 = Station numbern = Number of' :int er rel ate d sta ti on sR = Mul, tiple corre la t ion coeff ic ie ntZ = Randon number from normal. stand,ard po pu la ti on

k. P/iaximm, minimum and averase fl.ows are obtained for the en t i r eperiod of fl.ows as recorded and f o r specified periods of recon stit utedand generated flows by routine search technique.1 Provis:ion i s al so :included i n t h i s program f o r use of t he generalizedmodel requiring only 4 enera1;ized coeffic ients f o r each st at io n ( i n placeof 48) and one general.ized corre1,ation coef fici ent ( i n place of 1.2) f o r eachp .r of s ta t; i.ons, i n addi tion t o iden t i f i ca t i on of w e t and dry seasons f o reach st at io n. These are defined as follows:

I.) The average va lue of mean 1ogari.thms of flows f o r t he we tseason (3 months). This value plus 0 .2 i s a ~ p g i e d o th e middle monthand the averaze minus 0.1. i s appl ied t o the o the r 2 months.2 ) The average value of mean logarith ms of flows f o r th e dryseason 3 months). This i s appl.i.ed t o all 3 dry months. Mean logarithmf o r months between dr y and w e t seasons are interpolated I . inearly.3 The a.verage standard deviation f o r a l l 12 months. This i sappl.i.ed 'to each of the 12 months.4) The average se r i a l co rre la t ion co eff ic ient f o r a1.l 12 months.This val.ue Illlinus 015 (but not less than zero) i s applied t o each wet-seasonaonth, and the value plus .15 (but not more than .98 i s applied t o eachdry-season month. The average value i s applied t o a l l intermediate months.5 ) The average in te mt a t io n co 'melz t ion coeff ic ient fo r lmonths i s appl ied t o each month f o r t ha t : p a i r of s ta t ions ,

m. Because of 1imi-tati.ons i n computer memory s iz e and because ofinc reas ing change of comp.xtat5onal i n st a b il i ty with la rg er matrices, thenumber of stat i.on s usable simultaneousSy i n t h i s program has been limitedt o 1.0. However the progrm can reconst i tute and g en erate s t r e d l o w s f o r


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any number o.f s ta ti on s i n groups of 10 or l e s s . :It w i l l ord:i.nari.ly bedes irab le t o inc1ud.e one or more st at io ns from e a r l i e r groups i n ea.chsucce ssive group I.n or de r t o preserve important correl.at i.ons. I nad di tio n t o provid:i.ng f ar d at a f o r a l l s , tat ions , it i s necessary t odesI.gnate NPASS and t o fo llow each group of f l a r da ta with a standard-format card with NSTX (number of s ta t io ns i n next a s s t h a t were al..soused i n preced.ing pas ses ) and, ta t i on id ent if cat i .on numbers f o r thosest at io ns . These numbers must be li s t e d i n the same sequence a s the:i.rd.ata were arranged i.n ea r l i e r passes. Data, for th e new stati.ons f o r thenew pass should then b.e read. None of the se fl . a ~ scan occur i n a ye3-rl a t e r than the la te s t year fo r which flow d at a o c c m e a i n t he f i r s t pass.

n. s soon as flows are reconstitu ted f o r any pass, the y ar e readonto the flow tape. f t e r s t a t i s t i c s a re computed from transformedr econst i tu t ed flows, t hey a r e r ead on to the s t a t i s t i c s t ape ( a ~ t e ri den t i f i ca t ion of s t a t i ons i n t h e pass f or future reference) . F ina lregression equation data for each pass m read onto the samf t ape at t h esane t i m e ( for use i n genera tion l a t e r ) . For each new pass, the flowand s t a t i s t i c s tapes a r e searched separa te ly fo r da ta fo r those s t a t ionsal ready used th at a lso occ w i n the n a r pass. In order to read and wri teinte rmit tent ly and alt er na ti ve ly on th e same tapes, it i s necessary tokeep tr ac k of tape records so as t o assure khat read statement doesnot read beyond the record mark and so that new vrite statements occura t the end of a l l previous write s tatements that are t o be saved.

o. Once tha t s tati .sti cs are put on tape, they ar e reta ine d throughoutthe recons t i t ~ t i 0 ~zld generat on processes, Floirs ~ ~ ~ e v e r ,re savedonly fo r the se t of da ta i n which they were rec onsti tut ed o r generated,u n t i l t he last pass f o r t h a t s e t i s completed. Tn t h e gen era tion proce ss,it i s necessary t o save bhe las t f l o w generated fo r each s ta t i on i n onese t f o r use as the an tecedent f law in s t a r t i ng genera tion i n the ~ l ex tset . These ar e saved i n the QST P arra y with subscrip t ISTAP,

Input is summarized .in exhi bi ts 7 and 8. Data are entered consecu-ti v e ly on each card using a simple var ie ty of formats t o sim plif y punchingand handl.i.ng car ds. Computed and generated f l ms cannot b e 1,000,000 unitso r l ar ge r, and consequently must be expressed i.n uni ts th a t cannot exceedth i s magnitude. Uni ts should be indi ca ted on one of th e 3 header cards.Column of each card i s reserved f o r card i.d en tif ic ati on . These a r e 2:ynoredby .the computer except f o r th e i.n column of th e f i r s t header card, whichi s used t o i den t i f y t he f i r s t da t a car d. n example of input i s given inexh i b i t 3, Certain inadequacies of da ta w i l l abo rt t h e job and was te in pu tcar ds unti.1. th e next; card with i n c o l i m .s reached.. card withi n column olla red by bl cards causes th e computer t o s top .


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Pr-i nted output includes key Snprxt info rma tio n f o r job identif cationand al l. r e s u l t s of computations. Generated flows are put on magnetictape, and computed s t a t i s t i c s ar e punched on cards i n t he f o m t usablel a t e r by th e program. An example s printed output i s given i n exhibit

Standard FORTRAN IY ins'tructions and random number generator arerequired. No sense switches are used.

Terms used i n the program a re defined i .n ex hibi t 59 PEOPOSE FIJTLJ1.W DEVELOP1\,lEUI

There are cases where the model used her ein does not reproduce historicaldroughts wi th rea sona ble frequency. Consequently, th e model i s undercontinuous study and devel.opment, t i s request ed t h a t any user who fi nd sa n inadequacy o r desirabl e addi t ion or modif icat ion not i fy The EydrologicEngineerin3 Center


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DETA I I 3D EXPLANATIOI\TOF

O M W T E R PROGRAM

Much of t h e program i s exylained by comment, cards and derinit-ionsof variables. Supplementary explanat ion f o l l m s ref er r ing t o seet i onsiden t i f i ed wi th the ind ica ted l e t t e r i n column 2 of a comment card-

Cor re l a t ion coef f i c i en t s , R, and beta coefr icients, B, a re i n 3 0 ~ b l eprecis ion fo r matr ix inve rsion camputation, i n ord er t o minimize computa-t i o n a l i n s t a b i l i t y . C o rr e la t io n c o e f f i c i e n t , RA, as ori inally computedand stored, may be defined in s in gl e -orecision. For computers with worcllength smaller than 3 b i ts many ot her v ar ia bl es i n t h i s proTra?l shouldbe i n double precis ion .

When dimensions ar e changed, th e corresponding va ria bl e (s ta rt in gwith K should be chan,ged acco rdingly , as t h e s e are used t o preventexceedence of di.mensions. If a.n exce ssive subsc ri,pt i s used, the ;jobwi l 1 be dumped, u n t i l a card wit h A i n c o l m i s encountered, a t ~ h i c htime a new job i s au.tonati.cal.ly sta.rted f 5 blank cards (with an Ai n columri of th e f1.rs.t) a re encountered, t he run w i l l be terminated.Job speci f ica t io n cards are read i.n th is sec t ion .SECTION B

NSTAX i s number of columns I n cor re la ti on matrix. These co ns is t ofNSTA co'lumns f o r th e current-month val ues and a s im il a r number f o r ant e-ced.ent-month values. NSTAA I.s i n i t i a l col.umn number f o r anteced.ent-nonthc o e f f i c i e n t s . These a r e computed from NSTA, which i s read i n i f s t a t i s t i c sar e t o be provided, ra th er than compxted from r a w da ta . If raw data a r et o be used, NSTA i s de fin ed i n th e program l a t e r and NSTAA and NSTA nus t beal so . Data f o r each new pass are processed a f te r t rz nsfer r i .n g back ' tostetement k2 :In t h e mu lti pa ss operat;i.on, NSm i s the nillnber of stat;:ionsused from previous passes ~ n 3 .STXX 5,s th e st iosc r ipt of t h e f i r s t newsta t io n fo r the cur rent pass . S ta t io n Tden ' t if ica tion f o r the NST4 s t a t io nsmust be i n the order i n which d ata fo r ' those s t a t io ns w e r e or ig inal ly used ,became search of da ta and s ta t i st . ic s on .ta?e i s made i.n t h l s ord er . Fl.arsf o r ' these sta t io ns ar e read from tap e IQTAP, and corresponding s ta ,t is % ic sfrom t ape ISTAT Va ria bles LQTAP and LSTAT a r e used t o keep t r a c k of 'tapeposit ion for subsequent wpit ing.*Provided throug h t h e c oop era tio n of th e Texas Water Development Board.


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Months are i.d.entifZed consecutively by ,the var ia ble 4 s ta r t i ng wi ththe month preceeding ' the f i r s t yeaT of dat a. Some quan tit ies t o beaccumulated a r e i.ni.tia1ized. St at io n combination data are stor ed fo rthe purpose of obt aini ng maximums and minimums (sec, tion D of wei t;edlow va3.ues :Late r. Tandem s ta t io ns are 1denti:fied fo r cases where acheck on c0nsi.s en cy of generated q ua nt it f es i s deemed appropri ate.S ta t io n id ent i f i ca t ion numbers are set t o a l.arge number s o the y w i l 1not be undefined. The f l a z array i s f i l l e d w i t 1. values .to in6i.cat emissing values. For each st at io n and ca lend ar month, th e to tal f l o w andnumber of recorded values are computed fo r computing a .fl.aw incrementa n d o th e r s t a t i s t i c s la ter . The -mi.ni.mm l o w f o r each s ta ti on month

i.s d . s o computed i .n order t o avoid negative logarithms l at er .SECTION C

S ta t i o n d a t a can be read i n random ord er. St ati ons re i d e n t i f i e dby subsc r ip t i n the order in which data for each s t a t i o n a r e f i r s t r e ad .The year subsc r ip t i s computed. Negative su bs cr ip ts w i l l occur i f dataare f o r y ea rs ear l ier than the st ar ti ng year indicated on B card, andd a t a fo r t h e s e are reje cted , with diagnosti c printout . The sta ti onsare counted and the flows f o r each month a t each sta ti on are counted f o rth e purpose of computing frequency s ta ti st i . cs la te r . If the number ofst at io ns or years exceeds i t s dimension limit, the job i s aborted. Thenumber of s t a t i o n s i s permanently stored i n t he N S W a r r ay fo r la teride nt i f ic a t i on i n multipass opera tions . me remainder of t hi s sec tio ni s s e l f e x p l a n ~ t or y ,except t o s ta te th a t permanent ident i f ic a t io ns t a t i o n numbers ar e given for st at io ns in co .i.nation, f o r tandem st at io ns ,and for consistency-tes t stat ions , and subsc ript s ar e id enti f i.ed f OP rapidcomputation la ter .

I n t h i s se ct io n, maximum and minimm recorded flows fo r each calendarmonth he w a t e r year and f o r durati.ons of 1 6 and 54 months, and averageflows a r e computed f o r each st at io n and cominat ion . Durations do notspan a break i n any record. Quan tit ies ar e rounded off and printed i nf ixed-point format.

The logarit hm transform of fluws I.s accomplished here. Hss i .ngvalues are indicated by an fmpossfily large number (the -1 used formissi,ng fl.ows s a reasonab le logarithm a.nd th er ef or e cannot be usedfo r missing logarithms Before the l o g transform, t he average f1.mfor each calendar month a t each station i s computed and one constrainedt o a. minimum of 0.1 flow u n i t ) i s added t o each f l a w f the ninimumdbserved flow f o r ' that station month i s negative, th at absolute value


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i s al so added befo re . the trans:form. Af'ter th e logarithm trans.fo m ,.frequency s ta t i. st i c s f o r each calend.ar month and s'tat:ion a re computed.An increment needed 't o convert t he I.ogarithms to an approxi.mately normaldis'tri 'bution i s also computed as an al ternative future transform. Log-ari thms t o the base 1.0 a.re used so th a t s t a t : i s t i c s re comparable 'toot he r common1.y used s t a t i s t i c s . var iable n C O N 3.s set t o 1 i:f anymissing val.ues are encountered, so t h a t t h e :flow reconstLtuf;j.on ro ut inew i l l be ca l led l a t e r . A var iable LND i s s e t t o f ,the f i r s t approxi.-mation of increments c m e s any one 04 the skew coefficients t o besmaller than 0.1 or l a rg er than 0 .1 . In an opt ional roa t ine th a t fol lows,the increment f o r each ,station nlh calendar nonth i s adjus ted individual lyand i , t e ra t iv e ly (up , to 14 t r i a l s ) until skew i s withi.n 0.1 of zero.

Sta t ions w i t h le s s than thre e year s of dat a fo r any calendar monthre deleted, s ince skew and cor rela t ion computations re quire a t l e a s tthr ee i tems of da ta,

Correla,tion ri.ces ar e computed he re f o r the purpose of adj ust ingfrequency s'tat:i.st.i.cs :for s ho rt -rec ord s a t i ons o A l 1 correlati.on coeff i c i en t s a re f i r s t s e t t o -4.0 i n order t o ident i fy those not computedl a t e r f o r la ck of ssf i c i e n t observed da ta. Then accumulations of .thevarious qu an tit ie s required a re computed f o r al l. i ,tems above ,the maindi.agonal i n t h e corre lati.o n matrix f o r each month, using a l l d a ta commont the two stat ions involved. Tf more th an two items of da ta, are a vz i l -able, th e co rrel .at ion coeff ici.en'ts are computed. Coe:ff ci en ts f o r themain di.agona1 are s e t t o 1 .0 , and those below ,the main d iagonal are s e tequal t o t h e i r symmet:rical. element . C0eE.f i c i e n t s 'between 'the cu rr en tand preceding month s ,values axe si . a i la rl y computed. These items con-s tl . tu t e an excensi.on of 'the mat;ri.x 'to ,the ri g h t , which doubles i ts s ize ,and the new portion i s not ne ce ss a~ i l y yrmnetr ical . Simi l.ar completear ra ys of average v alu es and root-mean-square values f o r on1.y 'thos e log -ar i thms common t o each p a ir of st a ti o n s are found for later use i nadj ust .in g stat;'i.s'ti.cs.

A search i s then made .to determi.ne th e s'tati.on t h a t would be mostuseful :in ad j us ' t ing s t a t i t i e s f o r s ' ta t ion months with incomplete record.,nd the means and standard. de via tio ns a r e adju sted :in accordance with thePol lwin g equat ions

where primes :indic ate l.ong-period, va lue s, s ubsc r ip t s a r e o r t h e s ho rt -recora s t t i t ion and 2 f o r the l.ong-record st at io n and.,


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X mean logarithmS standard devia tion of the logari thmsR corre l a t ion coef f i c i en t .

An op tio na l check of cons istenc y of standard devi atio ns betweenadjacent st at io ns f o r the same month I s next made. This i s t o a ssu rethat frequency curves do not cross within three standard deviat ionsfrom the mean. 117 t h e r e i s a conf l ic t , the s tandard deviation of t ha ts ta t i .on designated i n th e input data as the dependent variable i s modi-fied accordi.ngly. All frequency s t a t i s t ic s ar e then prfnted out .

A1 I f lms ar e next s tandw dized, by sub tra ctin g the mean and d ivid ingby th e s tandard d.evi.a tlion f o r th e month and st at io n. n approxi.matePearson Type IIL transf orm 1.s ,then apgli.ed as follo ws:

whereK normdl s tmdard d ev ia tet Pearson Type I standard, deviateskew coefl:icient

New co rr el at io n matric es a re th en computed, based on the normalizedvariates and using the same standard procedures previously employed forcorrelat ing logari thms. The sign of th e corre lat ion co eff icie nt i spreserved, sinc e the coe ffi cien t w i l l be used t o esta bl i sh regressionequat ions Correl.ation coeff ici.en ts are s e t t o z er o i.f the varianceof e i t h e r var iab le approximates zero, sLnce th e computation of t h e coef-f i c i e n t i s highly unstable and since I t s use would be of l i t t l e vd u e .

For jobs where correlation data are given, th e portion ~ t h ecorrelation matrix above the main diagonal for a l l months and theent i re cor re l a t ion mat r ix re l a t ing cur ren t n preceding month svalues are read, with a di f fe re n t card fo r each pa i r of s t a t ions .Values for a l l 12 months are contained on one card, and th e two stat ion si ~ v o l v e d re identified on the s card. An automatic check i s madet o assure t ha t ca rds re i n th e requ ired order of columns and rmsin the co rre lat io n matrix. When generalized s t a t i s t i c s a re used, onlyone cor r e l a t ion coef f i c i en t f o r the en t i re year i s read, but card orderi s the same. S-metr ical e lements below th e m.5-n diag on al are thenf i l l e d i n and values af 1. 0 ar e placed I n the main diagonal.


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Frequency st at is t i .c s are then read, cards per sta t io n, w i t h 12mon'th1.y values and stakion identi.ficat;i.ons on each card. checlr. i smade of th e s ta ,t io n ord er, to assure proper subscri.,pting. When gen-era l i zed s ' t a t i s ' t i cs a re used, ordy one card per s ta t i on i.s read, andthis contains the max:imum and mini .mum mean I.ogar:ithms and 'the averzzestand.ard deviat io n f o r the year. The months of maxim1.m and rmirlimummean logari,thms ar e a l s o read and, converked ,to corresponding su bs cr ip ts .These subscripts will d.iffer from the callendar month number if t he y e wused i n 'the s'tudy does not begin wi'th Jmwry.

This se ct io n s earches f o r each ca,lendar month t h e e n t i r e c:orrelat:onmat r ix to be t h e r i z h t of the main diagonal for misi ing correlat ion coef-f ic ie n ts due t o the nonexistence of a t fe as t th ree years of sia1.fitz.neousdata f o r th e month. A s soon as a coefficient between xqo variables i si d e n t i f i e d as missing, a search of the cor rel atio n matrix i s made LO findestablis hed cor rela t ion co eff icie nts between each of these variabl-es ( iand j ) and any other variable I.;), The range within which correlationbetween the two variables must l i e i n o rder t o be mzthematicall:~consis-t e n t with th e cor re l a t ion with the th i rd var iab le i s established by useof the fol lowing euuation:Rij

A s each successive thi rd variable with establi shed c orr elat i on coeff ic ie ntsi s found, th e upper l i m i t of R i j i s constrained t o the lowest of' a l l upperl i mi ts computed, and the l m e r l imi t i s constrained t o th e highest of llsuch lo ve r li m i t s computed. 'When he e n t i r e matrix has been searched theco r re l a t i on coe f f i c i en t i s estimated as the average of these two constrained'Limits. If Lhis element i.s above th e main diagonal, the v alue i s a l s oentere d f o r th e element syn-metrically across t h e main dianonal . Thesearch fo r fu r th er missing correla t ion coefEicients i s then conti.llu;?cl,

Where a cor rela t ion matrix i s not t o be used f o r reconst.i .tut5ng da tabut might be inconsis tent , a Lriad consis tency t e s t can be made i.n thissec,tion. This i s done by examini.ng ll poups of thre e re la ted co rrelat io ncoeff ici.ents , and t e s ti n g the lowest one t o determine -whether it i s a'boveminimum cons%rai .nt es tabl ishe d by the equat ion i n the preceding s ta t io n.If not , i t .s raised, t o t h a t minimum. When t h i s i s done, it i s ,possfblt h a t the ad.justed cw ff ici enk had already been used i n another t ri ad ' test,and consequently that previ.ous t es t would need, t o 'be rep eat ed. In ordert o d.o hi.s properly, t h e enti .re matrix i s searched up t o 12 NSTA Limes,where NSTA i s th e number of st at io ns , unt i l a complete search revea1.s no:incons: istent t r ia d INK = 0 ) .


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coeff ' irrent F P-C or th e radical in the e u tlox i s used i n ortierto cir :+a in cornnlete matrix con sistency i n di ff i cu lt ; ca ses, whenevernnqs i h l e by thSs r?ea.ns, A t e s t fo r ove ral l coiisi s ten cp i s made i ns.>::Li.osi K, and i f t h i s f a i l s , FAC i s successfvely reduced by 0.2un i5.1 ove-ra? cons i s ,eac;y i s reached

The t e s t f o r overal l . consi s tency of the cor re lab ion mat r ix fo reach rnont ? i s ma3e by co n s t r u c t i ng f o r e ach s t a t i o n , th e co r r e l a t i o nmatr'ix th a' t wou:ld be used i n f . o ~ ene.ra.ti.on f o r t h a t s t a t i o n and com-puti .ng the m1~1tipl.eetermination coeff icien'k . If ' the determinat ioncoeFfi.c:ient of 'che m3tri.x f o r any s t a t i o n and anx month exceeds 1 .0 , a l lcor rel ati .on ma.trices mist be reexanined., si.rrce some co ef f. ic ie nt s are(:emon ,.ti:, two or more matr ices . This i s done by reducing FA6 i .n theirri.a.d t e s t ( s ec t i o n J ) by 0.2 and repeating a l l t r i a d t e s t s . f FAC i sreduced t o zero and consistenc y i s not; obtained, index of MCB i s sett o 1. and a.n averagri.ng ro ut in e i s used f o r etch incons i s ten t mat r ix . Aq u an t i t y SIR4 is computed a.s th e average of a l l cor re la ti on coef f i .c ientsi.n t h a t matrix, and each element 5s modified by m~xlti.plyi.ng UM b y t h eexcess of determi.na, tiozl coeff i .cien t and adding thi. s product t o th eproZuct of the complement of t h i s m u l t i p l i e r and the va lue of t he ele-m e n t i n th e inconslsten. i tr ix. The averazed or smoothed value s ar erepl-aced i n t h e complete ma.t;n .ix f o r t h e month, and t h i s re q u i re s somecareful. mani.pul.ation o f subscr l .p ts . A new computat;ion of det;ermi.natloncozPfi.cien i.s mile and the smoothing process i s repeated up toninet in es un t i.1 consi s tency p rev a i l s . f t h i s does not occur , the job 5 sbe-minated. When co ns is te nc y i s es tabl i .shed a l l compl .e te matr icesare xi .n te d out and e s s e a t i a l el-ements a-re punched i f d es i r ed .

I n recofisti.-Luting missin g da ta , a search i s made f o r ea ch month ofr ecor d s t a r t i n g w i th t h e f i r s t f o r s ta t i on s t'nat have no record dur ingthat month ( =T). \ henone i s found, a search sf a l l o t h e r s t a t i o n s i smade t o determine whether recorded or previously re co nst it ut ed f lows e xi stfor t ne cu-rrer~?, nonth or, i f ~ o t o r th e _areceding month. f one isTouhd, it w i l l con s t i t u te a n independent var i ab le fo r es t imat ing themiss ing va lue, and F t s va lue and per t inen t co r re la t io n coe f f ic ien t s aresto red i.n new ar ra ys f o r computation purposes. The co rr el at io n co ef ff-c i -nts wit h th e dependent var iab le i s t em po r ar i ly s t o r ed i n t h e NVARMSTA~~)olumn t o a s su r e t h a t c o e f f ic i e n t s r e l a t ing indepnden t var i

a3les 3 ~ l ? i r t l have s u f f i c i e n t array spsce ( th ey cannot exceed NSTA i nnumber) X irariable ITEMP counts the n\xlliber of independent vari. ables( s t a t ion s f o r which recorded o r r eco2s t i tu ted da ta are a v a i l a b l e ) . Iti s inc remented a f t e r i t s se t of co r r e l a t i o n co e f f i c i en t s are s to re d i nt h e R array, and i s f i n a l l y used t o r e l o c a t e t h e c o r r e l a t i o n c o e ff i ci e n tsin-aoltsing th e dependent v ar ia bl e , If no independent va ri ab le s wi.th da ta


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aye found, s can happen i.n th e f l r s t month of record, a cor re la t ion i smade with the preceding value f o r t h e same sLation nd t h a t precedinagvalue i s a r b i t r a r i l y set a t t he average fo r t he month. The regressi6nequation and determination coefficient are then computed using subroutineCROTJT. The variable having the lmest absolute value of cor rel ati on witht h e dependent va ria ble i s ident i f i ed , and be ta coe f f ic ien t s are searchedi n o rder t o e l im ina te l unreasonable co eff ici ent s . I n th e usual casewhere the sfmple co rr ela ti on coe ff ic ie nt between any var iable nd thedependent variable ts posi t ive, unreasonable co eff ic ie nt s are assumed tobe those la rg e r than 1.5 or smaller than . 5 . I n th e case where thevarftn'o1.e co rr el at es n egati vely with th e dependent va ri ab le , th e reason-ab le range i s 1.5 t o 0.5. If an unacceptable coefficient i s found, IRDi s set t o 1 I f t h i s happens o r i f the de termination coe ff ic ien t doesnot l i e between and 1.0, the var iable wfth the smallest cor re la t ioncoe f f ic ien t i s eliminated, t he co rre lati on arra y reconstructed accordingly,and t h e regre ssio n equation recomputed. This process i s repeated u nt i laHI required condi t ions exis t , The missing value i s then computed byuse d f the regression equation an6 adding a random component normallydistributed with zero mesa and with va riance equa l t o th e e r ro r va~ ian ceof t he regressio n equation.

As soon as th e missing value .is e s t f m t e d a search i s m de f o r a l lest abl ish ed values i n t h e c urren t and preceding moneh wit h which i t i st o be correlated, and sums of l o g a ~ i t b , quares, and cro ss productsare incremented i n pr epa rat ion fol- recomputing al.1 a f fec ted cor re la t ioncoef f ic i n ts . After checking fo r suf f ic ien t three record andnonzero variance, the corr ela tio n coe ffi cie nt s recomputed. Xf thes t m d m d de vi a ti on sf e i t he r va r ia b l e i s very small, t he c o r r e la t i oncoe f f ic ien t is s e t t o z ero , Lf the eoe f f fcien t i s above the main dia-gonal of t he c orr ela tfo n matrix, i t s value i s al so assigned t o sym-metrical el.ement. Since estimation of a missing value affects correla-t i o n c oef fic ien ts between var iable s f n the curre nt and fol. laain g month,which co e f f ic ien t s a re s tored i n a dfffe rent malr ix, t h i s process ofadjus t ing the cor re la t ion coe f f ic ien t i s appl ied t o those va lues next.SE TION M

After all f lows are reconst i tuted, the flow t ape i s read u n t i l t h eprop er po sit ion f o r wr it in g the newly computed flow dat a on that tape i sreached, and headings ape pr inted f o r wri t i ng flows on t h e p r i n t e r l a t e r .Then the standard deviates er e converted t o flows by reve rs ing the Peasontype transform, multiplying by the stsulda~ddevia t ion, adding t o themean and taki ng th e a n t i l o g a r i t h . The .increment is then subtrac ted mdi f th e re su l t ing value i s negative for a var iab le with zero lower limit,i t i s set t o zero, In th e case of rec onst i tute d flows, the PearsonTypeI transform i s constrained so t h at the excess of che standard deviateover and above 2 O i s mult ipl ied by m x i m u m of 0 2 i f the standard

EXHIBIT 1


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di.viation exceeds 0.3) 'Phis simply pre ven ts ob ta in in g unreasonablyextreme values due t o sampling er ro rs. It i s a moderation of theextrapolat ion rather than an abrupt trunca tion.The t e s t f o r tandem s t at io n cons istency i s next nade. and incon-

s i s t e n t f lows are i den t i f i ed f o r p ri n tou t and changed t o the l i m f t ofconsistency. The downstream f1.w i s made consis tent with the sum sfupstream f 1 m ~ F l w s ar e punched on cards, i f desired, printe d out ,and written on the flow tape for use . in future passes. NQTAP i s incre-mented and rep re se nt s t he t o t a l number of re cords on the tape.

After convertl.ng devi.ettes t o flows, the frequency s a t i s t i . c s rerecomputed i n ord er t o agree a ccu rately with observed and reco nst itut eddata. If a consistency tes t i s ca l l ed for , the var i ab le I EWS i s s e tt o 2 nd com~uta t ion s tran sfe rred t;o near th e end of sec tion F, wherethe test i s made and the transfer index causes a r e t u rn t o t h i s p or ti onof th e program. Adjusted, s't;a' tistic s are print ed, and the consi.stentcorre1,ation matrix i s printed (and, i f des ired . a l s o punched) by t r ans f e rto sec 't lon K using ITR lS as a return indicator again. The s t a t i s t i c sare ,then punched, i des i red. Flows f o r th e spe cif ied st at io n combina-t;i.ons are 'then computed,

a i r n u m n and minimum recorded flows are computed by tr a ns fe r t osect f on S using ITRNS= l as a return indicator . The variable ITM?keeps a record of th e re mi ni ng years whose ma xi mum and mini.mm flowshave not been searched yet.Next, genera l i . zed s t a t i s t i cs are compu:ted, i f d.esired, ( if IGNRLequd .s two) A s fnd,icated, s tr ai gh t averages of d l .2 nonthly comela-t i o n coefficients i n every category are taken. Means re averaged forthe th re e wet te st consecutive months and th e th ree d.r ies t consecutivemonths and t h e se aso nal timdng noted. S%andard dev iat ion s f o r l l l2months are averaged. Genera l i zed s t a t i s t i cs are then printed out .Next gener al ized s t a t i s t i c s read i n s ec ti on H a re used t o computerequired arrays o f s t a t i s t i c s . Skew and increments are set t o z ero .he mean f o r t h e ni.ddle month of th e w e t season i s 2 higher than thewet season ver ge a n d means f o r t h e o th e r k o months are l lmrerMeans f o r th e d r y seasons are wxifom, and means f o r the tra ns i t io nseasons are in te rpola ted l inear ly . Comebat ion coeff icients for thedry season are 3.5 higher (constratned b e l o w .@) t han t he annudaverage, and t ho se f o r t h e w e t season are I5 l o w (constrained abovezero). A l l of t h e se o p r a t i o n s are i n accord wi th the general izedmodel developed i n HEC.


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SECTION PAfter obtaining monthl.y s ta t i s t ic s and co rre lat i on matrices, re-gre ssio n equ ati ons f o r each staf;hon and cale nda r month a re computed.Flows a re generated i n th e s t at io n order i.n which da ta or s t a t i s t ic s

are read and are generated f o r each month a t a l l s ta t ion s beforeproceeding to th e next month. Fl ms a t each s ta t i on are correlatedwith f lows of the antecedent month a t that s ta t io n and a t a l l s tat io nsf o r which the curren t monthss f l m s have not y et been generated. Forother s t a t ions , fl.nws f,or the current month are used.Regressfon equations we csmp ted i n subrouti.ne CROUT If anycorrelation matrix formed i s inconsistent (which should not occur a tth is s tage, except f o r trunca tion of computated intermediate varia bles )a t r ans fe r t o s ec t i on J i s effected, and consistency operations gerformedon a l l cor re la t ion matrices. After such a transfer , a l l regressionequations must be reconpted, s ince any corre lat ion coeff icient might

have changed, After t h i s , only the beta and al ie na tion coeff icie ntsneed be r e ta ined , i n addi t ion t o the frequency s t a t i s t i cs . n the mul ti -pass operation, these are l wr itt en on tape ISTST a t t h i s po in t .SECTION Q

A r ou ti ne f o r p r o j ec t i ng h i s t o r i ca l sequences i n t o t he f u t u re i semployed her e. Values of Q P W (previous month s dev iate f o r eachs t a t i on i determined as the transform of the low for the month pre -ceding the first; month specified by input data) t be generated. Thevariable N i s computed for the subscript of 'J that conforms t o thef i r s t month of projec ted flows. I f the projected f . L a ~ rout ine i s nott o be used, the computer i s next set ilp t o generate k?o years of flows,a t the end of which synthetic sequences w l l have a virtually randoms t a r t .

In the multi:pas s operation, st a t i03s ar e i.d.extif ed and d.1. neces -sary s t a t i s t i cs a re conta ined i.n the order needed on tape ISTAT. I:n anypass a f t e r the f i r s t f1 a~~enerated. i.n e gr l i er passes f o r th e saqeperiod (t he same sequence of dat a) must be read from ta pe IQTA-I and thistape must be rewound, bef ore ea.ch pass i n ord er t o p e r ~ i t compl.eteseerch. In any sequence after the f i r s t the preced:ing E 3 a ~ o r t hefi . rs t month t o be generated i s the l a s t fl.ow i .n ,the >receding sequence,for t h a t s tat ion, and the se ar e saved i.n the @TAF array Por mu.t.tipassoperation. f he mult;ipass feature i.s not u s e d . a l l necessary s tat i .s t icsand Elms :for generzit-ing are i.n memory.

I n s t a r t i n g t o g en era te flaws a var iable m1W i s used t o identi.?;the year number of t h e f i x s t year ol each sequence i n the multipass


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operation. Var ia l~ les VG m d SDV a r e used t o compute t h e mean andstandard deviat ion of the deviates f o r each flow sequence. These a r el a t e r used t o ad Jus t all devlates s o th a t th e neans and s tandarddevi.atTons i n ev ery qenerated sequence will be the same as those orthe h i s t o r i ca l sequence.

Variables 3.A and NJ are se t up t o co,rrespond -to t h e f i . r s . t andl a s t year of generati.on i n each succ es siv e sequence, dependi.ng onth e t ~ ~ ef operat ion. l/IA has alrea dy been set up as the subscr ig tof Q correspondi.ng , t o th e . f i r s t month of fl.ows t o be generated (f oruse I n proj ect ing 1ii.stor:ical Plor?s recorded t o th e c ur re nt t i m e.LpREV fo r each s t a t io n has been iden t i f i e d as the previous month'sflow f o r t h a t s t a t i o n . Fl.ows ar e then genera ted fo r each s t a t io n ,trsing s to re d r e - ~ e sio n equati.ons and a random component. Each generated_flm7i s immedia.te1.y' ent ere d i n t o ,the QPm array, because i. ts precedingflow wi.11. never a ga in be used 2.n t h a t p ass.Trl the ~ u l t i p a s s o utin e, f o~rs(as devia,tes) m wr i t t en on tape

a t the end of each pass , =d th e la s t f low fo r each s t a t io n i s storedi n t h e GTAF a r r ay f o r use in t h e next sequence.I f more than 9 year s ( an a r b i t r a r i l y se lec ted l eng th ) o f f la?a r e bein2 generate6 i r r any sequence, dev ia tes a ad j us t ed so t h a t theirm e a n i s zero and varlance 1.0 heir unadjusted mean and standarddevizt ion e.re printed. Therl they a re trarrsformed t o flows, and, i fc a l l e d for , co-nsis t ency t e s t s between s t a t ion s are made. For ~rariableswith zero nat ura i l i m i t , a check for negative values i s then made. l w sare then printed and, i f desi red, punched. F l w conibinations are thencomputed.

Before computing maxix~unanrd mi.nimwc val.ues of ge ne ra te d .E lm s,a posit ive value of JX i s l.ooked fo r t o as sure t h at flows generatedar e not t o be discarded. ( the f i r s t two years generated for a randoms t a r t ) . Also, at . eas t ? M G years must have been senerated beforexaxinm and mi.nimua values are com~uted this appll.es only when thenufiber oP years remaining for generation i .9, the last sequence doesnot equal IYM;CG). 1 , k s ~ i . mums a r e i n i t i a t e d a t an extremely largenegative number and minimum sums as an extremely :larg e po sit i.v e numberT ) Then a routine search of flow su m f o r the specif i .ed dura, tionsa t each s t a t i o n i s m d e f o r t h e sequence and . results tir pr in ted ou t .S i nce t h i s r o u t i n e i s used, f o r recons.ti:tuted flows a s w e l l as orgenerated. ~ ~ O T T S ~t r an s f e r I n d i ca t o r i s used .to determine whether t h enext ste,p i.s back to t h e yecons t i tu t ion rou ti .ne o r th e genera t ion rou t ine .f t h e l a . t t e r , a check i s made f o r t h e md.t;ipa.ss ro ut. ine . If all passesare nbt completed, e t ra ns fer , to sec .t ion Q i.s made. f all.Passes arecomgleted f o r t h i s sequence or i f t h e rrU:ltipass rou.t:i.ne 1.s not being


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used, a check i s made of remain in^ years t o be generated. f g r e a t e rth n zero, transfer t s e c t i o n Q i s made a f t e r adjusting years yetto be generated. Nherwise the Job is ended and a new ,job. i .P any i ss czrted .

This random number function i s f o r a b i n a ry maclline and t h e co ns ta nt s milst: becomputed according t o th e number of b i t s i n an i n t e g e r word. The numbersg en er at ed a r e u ni fo rm ly d i s t r i b u t e d i n t h e i n t e r v a l t o 1The f u n c t i o n i s c a l l e d from t h e main program by a s t a t e m e n t similar t o t h efollowing:

= R N G N IX)Where i s some f l o a t i ng po in t va r i ab le name and I X i s some inr g r v a r i a b l ename. The argument name I X need not be tile same n t h e main program and t h efunc tio n. The argument must be i n i t i a l i z e d t o z e r o i n the main program. Thel o c a t i o n o f t h e i n i t i a l i z i n g s t a te m en t i s im por ta n t a nd de pe nds on the r e s u l t sd e s i r e d . I f i t i s desired t o h ve d i f f e r e n t s e t s o f random numbers f o r eachof s e v e r a l d i f f e r e n t s e t s of c om pu t at i on s j o b s ) t h a t are r u n s e q u e n t i a l l y onth e same program, the n th o argument muse be i n i t i a l i z e d a t t h e v e r y besinningof the pr ogr a m a nd ne ve r r e in i t i a l i z e d . I f i t i s p e r m is s i b le t o u s e t h e s a n esequence of random numbers f o r eac h j o b , the argumcrlt n i i l s t be i n i t i a l i z e d a tth e beginning of each job . Tke advantage of this l a t t e r o p t i o n o c c u r s when oneof th e jobs must be re-run f o r some minor reason as t h e same random numbersw i l l be used and t h e r e s u l t s w i l l be comparable.Three co ns tan ts must be computed by t he foll .owi.ng equa tio ns:

Const ant one CI) = 2

Constant tw ~ 2 ) 2 -1C ons ta n t th r e e C3) = 1./2.

\ f i e r e : B = number o f 5 1 t s i n a n i n t e ~ e r ordThe c o n s t a n t s f o r some of th e common computers a r e l i s t e d i n t he fo l l owi ng table:

---SIZE OFINTEGER .OI\I STALJTS

COIPUTER ORD C1 CP. C3 .---GE 200 S e r ie s 19 1027 52[+287 0 .1907348631: 05GE 400 S e r i e s 2 4 99 8388607 0 11320929011-06IBM 360 S e r i e s 3 65539 2147453647 O.4G 566128713-09IBX 7840 and 35 262147 34359738367 0.29L0383046E-107098 S e r i e sUMIVAC 1108

CDC 6000 S e r i e s 48 16777219 281474976710655 0.3552713678E-14


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April H*

h e of th best -methods fo r solving sy~tems f l inear equationson desk calculating machines w s developed by P, D Crout fn l l,T h i s method is based on the elimination method, w i h the ~18blaulatiozmamsagedl in ep amtAs order ~o a8 to fac i l i tate theimp s tcem pl i~kenton a b e g ealcuh%or, In tWe me.%;hodhe owff io im%aand e c m ~ b tterns of' the equations are written n the Porn of ga ~~atpl%sr,'~wPoh Pa8 f ql-Mtk ~ EZ i WS ma 43

The method is besf explabedl 'ag an exmaple, Suppose ktn amultiple correlatio n analysis it i s regdred to solve the fo1lcwh.gsyetem of linear eqtzatio& to obtain ths unknown values of b2, b -b5* 3 4

For simpli ity let us rql-e the o ~ ~ f f P a I e n sf the b t e by tkm lle% emP e q p a and s, and. the canstant t e r n by h t ter , wfwg e;lub~orip @1 2, 3 and b a demta the ressgectim qwaticxm~

A oomtlnu~laaaheek on the comp~7~tatioraas they pmgress m y bo ob%ahedby add* to the matrix of he above system a aolmm of u fs , snob ha%a = p q r s t. The pat and oheak oolwm s written aef llows


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th(4) the elenents in the (n+l)-- column aml their tr iaale ~ ~ ~ ~ & ~am been rrecorded, the (n+l)th row w i l l be o e except20 %ha h ~ W O 1 - @ ~ 2 8 9 XW -.la& 0 0 ~ t a * d , Bbol ~ i 3 i W ~x)@QU S %he 00 s1m-t of %he TeE TEBtTiX B D ~b m B h ~of -&a ~ 1 ybove (x) the elies-ea% ita&Piely 0 thela % 02 %he p h o i p a . l d i agon a l in %he ), mb-ma p m k o tof the s e a a d e1wmnt a w e x) by the t to - ha e f t o f $he

of * xd.X keilpenl die&T b &eak eohmm (u) f the derived makrix %-a a 0 0 ~ 1 t ; h f p o ~ahok am %he eompu-batisns in b ach el@mmt131 the oolum fp~m3.sone g1m %he sum sf th el%mentreh~he e r a w t o the right 02 %he

~ & B ~ ~~~~~e b 3%

The e%emn$@f he de-a m a w to* ight 0% th p r f n ~ i p ~ ldiagana.1 o m qy-s%emof equations whf eh nay now be used to ao18lputeti10 own values of bp, b3, b4 d b by sucoessive rrubstih%ion.5

It is v e q hpor lan-t that the comp%a%iome oarrded t o a suffi-oi@n% umbm of digf t 8 bo%hin oomputfng eosffieient s and sons- t@EBB of or% quatioas and in eomputhg the elements ~f thed@X'f~@d$ E k e It i k p ~ s s i b l e o r ~ . 4 91 8 t i~ e lrINLUXTOZ?S t hcoeff&oiesa s and eomtant terns of the azdginal equations to result in

F ~ = Z & ~ V @ &%I?@ 3 8ELW9P8 bl the -p Zhd S O ~ U ~ ~ @ I $f t b W l k l Q W l 3 S e


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m a t e s t soum of -x? ~60-e- f& eQ@z ea ~f he r - ..va t r b carises tb 108s of P ~ d w~ i@ i f i ~m tI . ~ %Smb tm~ t d o ~ ~ ehisn wt be gwaded a g c b a t andl o n ozw .P;olistthe gQ@ffi~i@r&sdl e m t tto a&ffeien number of dtB~imabto pmhae st;least fiw si@if'icumU t e r 9n the m l le~s tqteatiw, am3 t h t the elemants of th derive&ma%rjlebe oamied to one more deaimal him hi@, but to not Pees th nsix signffi-t ai& s,


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DEFINITIONS - 723 X6 I2540AC1 - Alienat ion coef f ic ien t fo r s ta t i onAC2 Alienation coe ffi cie nt fo r st at io n 2A C 3 - Alienat ion coef f ic ien t fo r s ta t io nAD - Plus sig n in di ca te s value smalle r than upstream sum bytandem t e s tA D J l Equal si gn i nd ic at es value adjusted by tandem te s tALCFT I,K) -A l ie na t ionc oe f f i c l . e n ta r ra gALOG Computer l i b r a r y funct ion of n at ur al logm-ithmANLCG - Number of logarithmsANYRS Number of years of recordAV I,K) - Mean logarithmAVG I,K) - Average of the generated deviatesAVGQ I 1 - Average monthly flow f o r a s t a t i o nAW I - Average logar ithm of flow fo r minimum con secut ive monthsAW I Average log ar it hm of flow f o r maximum 3 consecutive monthsB L) - Beta coeff ic ientBETA I,K,I.) - Beta coefficient for generation equationBLANK - Blank spaceCROUT - Program subroutine t o solve s im lta neo us equationsCSTAC K)[ ,K) Coefficien t by which flows a r e multi.plied before adding i na combinationDABS - Computer l i b r a r y functi on of abso lute value of double prec isi onnumberDQ I,K) - Increment of flowDTRMC - Determination ccxff ic LentE - Letter E indicates estimated valueFAC - Temporary factorI - Index for calendar monthIA - Indicator i n column of f i r s t card fo r each jobIANAL - Indicator , pos i t ive value ca l l s for ana lys i sIENDF - End of f i l e indicatorIGNRL - Indicator, + 2 ca l l s fo r computing general ized s t a t i s t i c sand + o r t 2 ca l l s f o r u s ing gene ra li zed s t a t i s t i c s fo rgenerating flowsI ~ I ) - Month sequence number of l a s t morrth of d r i e s t consecu tivemonthsI W H Calendar month number f o r f i r s t month of water yearIMX I - Month sequence number of l a s t month of 3 wettest consecutivemonthsINDC - Transfer indicatorI P Month number f o r preceding monthIPASS Sequence number of pass su bs et of s t a t i o ns )IPCHQ - Indicator, posi t ive value c a l ls fo r wri t ing discharges on tap?IPCHS - Indicator, pos iti ve value ca l l s f o r punching st=i;ist icsIQ I 1 - Fixed-point conversion of flow M u e s


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IQTAYIilCO JISKZ

ISI P(LITEMPITMPITWPITPIT RSI XKXYRIYRAIYRPJJJ AJ T ~ ( LJTPKmMP

KmKPASSXs'rAKSTAC a,r n A PaKYRLLLQTAPLSI'ATLTMF(L)LTPLTRaXLYRPJMMA

T a p number f o r st or in g flowsIndicator, posi t ive value ca l l s for f low recon st i tut ionPosit ive value cal ls fo r v rying flow increment (DQ) omake skew zero.Sequence number of upstream s t a t i o n f o r tandem t e s tStation numberSt at io n nuinber i n a combinationTemporary station numberStatl.on sequence number f o r a l l p s s e sTape number fo r storin g s t a t i s t i c sSt a ti on nuniber of downstream tandem s t a t i o nSt at lo n number of upstream tandem st a t i o nStat ion number of inde~ ende nt ta t i on f or consis tences t e s tStati on number of dependent st at to n fo r consistences t e s tTemporary variableTemporary variableTemporary v ar ia bl eTemporasy var ia bl eTransfer indicatorTemporary variation ofArgument f o r random number fun ct io nNumber of c m en - t yeapF i r s t ye r of dataYew of s ta r t of f low pro j e c t i ~ nIndex for yearSequence number of p ro Je ct io n yea rMatrix column numberMatrix column numberTemporary w i a t on of JTemporary variation of JIndex for s ta t ionDimension l i m i t fo r number of con sec utive monthsDimension l i m i t f o r number of pass esDimension l i m i t fo r to t& number of st at io nsIndex number of s t a t i o n in a combinationDimension l i m i t fo r t o t a l number of st at io nsTempx-ary variation of K or combination sequenceDimension l i m i t f o r number of c onse cutive yearsIndex for re l a ted s t a t io nTemporary variation of' LMmber of records up t o present p ositi on on t a p IQTAPNumber of records up t o present posi t ion on t p ISTATMatrix row numberM t r f x r w numberLet ter ATemporary variation of LLast year of each projectionS e r i a l number of monthSequence number of month sf projected flow


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MO(I) - Calendar month numberMPASS - Temporary coun ter f o r number of p s s e sMTHFJ - Calendar month of s t a r t of each pro jec tio nMXRCS - Number of ye ars i n each per icd fo r which m ximum and minimumrecorded and reconstituted flows are desiredN - S er i a l number of per iod of flowsNC - Counter t o prevent continuous loopingNCA - Counter t o prevent continuous loopingNCAB(I,K,L) - Number of va lues and cro ss products used t o compute c o r r e l a t i oncoeff ic ientsNCB - Transfer indicatorNCCMB - Number of combina tions of s ta t ions max. and min. qu an t i t i e sa re t o be computedNCSI Y - Number of c onsis ten cy t e s t sNINDP - Number of independent va ri ab le s in reg re ss io n studyNJ - Number of yea rs i n computation sequenceNLOG(I,K) - Number of logarithms used t o compte frequency s t a t i s t i c sN N X - Number of months fol lowing dr y season and preceding wet se as onN X N - Number of months fo ll owin g wet season and preceding dry seasonNPASS - Total, number of pas ses i n jobNPROJ - Number of projections of f'uture flows from present conditionsNQ - Counter fo r number of flowsNQTAP - Total number of records saved on tape IQTAPN~MX L) - Number of upstream s ta ti on s i n tandem t e s tNSTA - Number of s ta ti o ns i n an aly sisI s T A A - NSTA N D A C IM - Number of s t a t i ons i n a cm-binationNSTAT - Total number of records saved on tape ISTATNSTAX - NSTA + RSTANSTNP I ) - Number of stations i n a part iculas passNSrX - Number of st at io ns i n current pass th a t occurred i n precedingpas sesNSrXX - NSTX +N ~ ( K - Number of s ta t ions upstream from a st g t i on fo r tandem t e s tNTNDM - Number of tandem t e s t sW R - Tota l number of v ari abl e i n regression studyNYMXG - Number of yea rs of gene rated flows i n each perio d f o r whichmaximum and minimum flows are desiredNYR - To ta l number of ye ar s of genera ted flowsNYRS - Number of y e a s of recorded flowsQ(M,K) - Monthly flow~ 1 - Monthly flowWN(I ,K) - Minimum flowQPREV I - Flow for previous monthR(M,K) - Identification symbolQ ~ A PI - Temporary storage of QFREVR (K,L) - Correlation coe ffi cie nt i n a given matrixRA(I,K,L) - Correlation coefficientR V K,L) - Average cor rel ati on coeffici ent fo r 1 2 calenzar months


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C 7 2 3 - ~ 6 - L 2 3 4 6 M PN?WLV * T 4 tA p f2 ~ ? , , ~ I ~ ~ ; L & s I U ~~ t ~OF F r U S E : 9 7 0h * * t * * * L IR P A E Y F t Y C f lc h s A L Q ~ , D k 4 3 , * * h s a * * * * * * i O d 2C PPDGPAM SUE@CJLlTl l C R t ~ 7 ~ R h ~ f r ; S E E CnnnEN7S 13 R N G E N 1003C I N D E X E S ISCALENDAR Y O b t Y J I J Y E A P #o3TA L B W E C A T E D STA H ~ s u c c E S S I ~ E O k T B 1 0 0 8c 1 0 0 5D I P F N S I f l N 1006. o r l o ) , w t i o I l 1 ) , I O O ~ O O Q. A L C F t ( l 2 , 1 6 ) I A y t l 2 1 1 O ) P ~ G ( l z , 1 0 ) I ~ ~ ~ ~ ( ~ o ) , a v ~ ~ ~ l O ~~ ' d ~ x ( ~ O ~ 8~ ~ E T ~ ( ~ ~ I ~ ~ I ~ F ~ ~ ~ ~ ~ ~ ~ ~ ~ I ~ ~ I I I ~ N ~ ~* I ~ T A ~ ~ ~ ~ , . J T ~ ~ P ( ~ ) , L T H P ~ I I ) # P O [ I ~ )h C h R ( I ~ # l ~ t ~ ~ ) *. N ~ O s ( 1 2 ~ 1 ~ 1 1 0 C 1 2 0 1 ~ 1 0 ~6 ~ 1 i ] ) c r ~ h l ~ o )~ ~ ~ ~ v ~ 1 0 1 1 ~ ~ ~ 1

, ~ ~ ~ ~ P ~ ~ O O ) ~ ~ ~ ~ ~ ~ I ~ O I ~ ~ ~ I ~ A V ( ~ O ~ ~ ~p S K E u ( 1 2 , l O ) r S ~ 0 ( 3 O l l O I d C A ( 1 2 , 1 m ) , s Q P ~ ~ I I ~ ~ ~ o Is u M A ( ~ ~ I I O P Z ~ S ,p ~ l l ~ ~ ( 1 2 ~ 1 0 ~ ~ 0 ~ ~ ~ ( O ) ~ ~ 1 ~ C ~ ~ 1 2 ) I ~ P ~ 3 f 1 2 ~ ~ ~ e 2 0 ) ~~ ~ ~ ~ ~ ~ ( ~ I ~ ~ ~ ~ ~ ~ ~ J T ~ ~ ( ~ ~ ~ C ~ I ~ . T ~ (. ~ ~ T Y ~ ~ ~ ) I K T A C ( ~ ~ ~ ~ ~ ~ ) I F ~ S ~ Y ~ ~ O ) I ~ ~ ~ T S C ( Z ~ ~ )~ N S ~ V ( ~ O D S ] , M C ~ P R ( ~ ] , M T ~ C ~ J ~ ~ ) ~ I T ~ ~ ~ ) ~O,ab,S]

C OU P LF P R E C l 3 I f l N R t Y 1 0 1 6C n H H O h D T Q ~C l ~ IN D P 1 0 lo;?D A T A L T P A I l H A / , f l L B N # /1 H / , E / ~ W ~ / , A D J / ~ H + / , A O J ~ P ~ Y ~ ~ I 0 1 810 F O R M A T ( ~ H ~ ) 1 01 92 0 F OR YA T 1 ~ ~ 1 5 1 1 9 I b ) 1 02 0 00 63C F O R M ~ T I ~ X *7 1 9 1 8 ) 1 0 2 1~ ~ R M A T ( X ~ A ~ , ~ A ~ ~ O A ~ ) 1 0 2 25 0 F D R ~ A T ( ~ X , X ~ , I U I ~ ~ F ~ ~ O I 1 0 2 560 F O P H A T ( ~ Y I F ~ , @ , ~ V ~ ~ ~ ) 10247C F O R M ~ Ti X I 1 3 r I a I li?F5,3 1 0 2 5

R G FORHAT (1x1 7 r 1 2 F b . 3 ) 1 0 2 6q0 FORMAT ( 1 X I 17r12Fb .11 1 0 2 1l a c F ~ ~ ~ ~ ~ ( t ~ ~ ~ ~ ~ l b ~ i 2 1 8 ~ I 1 0 ) l 0 2 81 1 6 F ~ R P A TA l ,A 3 1 9 4 4 r lO A O) 1 0 2 91 2 0 F n r ~ a ~~ x , ~ Y , ~ F ~ . ~ , T I ~ I i a 3 0 0 o o13C FORMAT ( / 2 3 Y GENERALIZED S T A T Z S ? I C Z / / 1 3 H 3 7 1 8 1 % 4 A V ) 11131l d c FOAYAT( /38H STA I V P X A V H h SD&V H A X H U H % N ~ U ) 1 0 3 219TA7=8 1 0 3 410TAP=9 1 0 3 5KPA95SSK 9 2 A P = l O d 10x7K S ? A = i O 1038#YR: l03 39KY:KYRt12+1 1040h'STilZ3 1 0 0 2c W A S T E C A R D S UNTIL A P A I N c n ~ u r k P I H ~ P ITLE C A R D 1 0 4 3C d 6 C A R D A 6 6 1 41 5 0 2 E A @ ( 5 1 t o ) I A ~ s ~ Q H ~1, M ~ I , ~ O ) 1 0 4 5I F (TA.RE.LTRb) G O T O 1 5 0 t O 4 bWR ITE ( 6 1 1 0 ) 649R E A ~ ( S , ~ O ) ( ~ ~ Y Q ( M ~ K ) , P = ~ , ~ O ) ~ K = ~ P ~ ) 1 0 5 0

RITE f b , 4 0 ) s u Q ~ , K ) t is e 2 @ ) 1 ~ a i 1 3 ) 10 5 1C a * C a R D B C R D C * a 1052000~ ~ A ~ ( ~ , ~ ~ ) ~ V ~ A I I ~ Y ~ ~ ~ ~ dO S 3l,NCflMR,NTbIoMIYCSTYI 16hl iL , h P R n J I I Y G P J , p T b P J t L Y R P J 1 0 5 5C TERv IhATE W I T H 9 P L A N C A 4 0 8 , A N CiYL 1 CS FIR3 7 1 0 5 6P Y H P ~ I A N A L + Y Y R G '1057I F ( J T H ~ . G T . O I G G 7 6 18 1 59STOP 1 59

h S 4QITE ( 61 17 n) h Y k Z r P 3 T A t h C R ~ 8 ~P A S 1 0 6 0I f F R R H A T ( / 1 9 H D I H E 4 5 1 O h EXCEEDED ~ S ~ I Q ~ ~ ~ S F X ~ ~ ~ X V Q ~ ~ S ? A ~ I ~ ~0 6 1COOl f H N C P ~ R , I S I ~ X ~ 5 H ~ P 4 ~ s ~ I ' S ~ 1 0 6 3 0 0 0

Gf l T O 1 5 0 1 631 f l C H R IT E (S r1 9 O ) 1 0 6 419C F 0 a u b ~ ( / ~ O ~ ~v ~ 4 pth Tc I A u A L * t X P C S ~ v R G Y M x G P A S S I P G ~ Q P c H ~ 0 5 51 ~ 3 7 1 C O ~ ~ OT W ~ J Y N c S T ~ ScNDL F J P ~ JIYqPJ H T bP J L Y R P J 1 1 0 6 6

#RITE b l z O ) 1 ~ ~ 4 ~f l * l T M l ~ A ~ A L , ~ Y Q c P , ~ Y ~ G ~ P v ~ ~ ~ s . I ~ ; ~ ~ ~ ~ I1 l o b ?l N ~ T A I ~ ~ O r B I ~ ~ ~ ~ ~ I h ~ 3 T Y , 1 ~0 6 %I L V R P J - ~ Y R A ~ G E . K Y W ) G O 7 0 160 Oh9CQ * SET GCNS T A M T S r * e * r * a * e * * * fi * * * d 1070f X X t O 1 0 7 1Y S T I A = N S T A + I 1072N S TA X = N S Y A + N S TA 1 0 7 3~n99999qq9 1 0 7 4X Y R I ~ I Y R L - 1 1 0 7 5


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a C R D E a r 4


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s r ~ s ~ f E 1 5 ~ 3 l o lC ~ T A C ( K , L , ~ P P ~ ~ ]LZ , r i p )JIG F f l Q P A T 7 r L ~ ~ I ~ * A T I P I ~ X ,u ~ n . 3Ti c t F ( f J 9 N D . L E . Q I G O T O 350f l 7kF I i [ ~ P ~ S S ] : I I T Y ~ M

3 330 L U = l r N T N D H

3 b C ~ ( C I K ) = - I . 1 1 5 93 0 3 7 0 I = l , l 2 1 1 6 0p J L C G I , K ) = O 1161D d ( f I W I S G . 1 1 6 23 M f N I X I # ) = T 1 1 6 3g l ~~ K T I U L I E 1 1 6 4J P 6 CnhT IYUE 1 6 5~ F ( N C S T V . L E . O ) 6 T O ~ O 1 1 6 bJ R I T E ( ~ I39 : 1 1 6 7

J Q C F ~ ~ M A ~ ( / ~ D Y ~ B H S T A T I O Y : : / I ~ WR N S I S T E N C Y T E s T , ~ X ~ ~ ~ W / N D E P E N O N ~E I1681 Pf:'k1DENT) 1 1 6 9D O 003 L z I I N C S T Y 1 1 7 0

C r* C b R D G t 1 1 7 1E A R C5r30 I S r X C L ? , T STY [L) 1 1 7 2i n 0 4 ? T T E ( b r 9 1 0 ) L r : S T X I I . ) I I S T Y ~ L ] 1 1 7 3l i t C F ~ ~ R ~ A T C ~ ~ Y , ~ ~ ~ ~ X I~ I C J Y I X ~ ) 1 1 7 4n 2 c I F ~ I A N A L . L E . Q G Q T C i f 7 o 1175cc z a R E A D AN9 PROCES; 1 S T A 7 i O b r Y E A P O i A T A a * 1 1 7 6c r C A R D n *t 1 1 7 7d?c l ? ~ n [ 5 , 9 0 S T A M , I Y ~ , ~ w ( ~ ) ~ r = i , 1 2 ) 1 1 7 8

C ** C A K D * * 1 1 7 5C S L A M C R D I h O I C 4 f E S END CF FLSh D A T A 1 1 8 CIF(?STAN.L?.IISO T O S ~ Q t i eX G [ N ~ T A . L ~ . ~ I G UP 4 5 C 1 1 8 2C A ? , R f 4 N SUUSCGIPT 1 S T A T I O Y f 1 8 3o n a 4 0 K = H S T Y I , ~ I S T A 1 1 8 4X F ( X ~ Y A N . E ~ . I S T A ( K ) ) G O TO 4 6 0 1 1 8 5U q C C n N T I N O E 1 1 8 6030 b i S 7A= NS T A+ l 1 1 8 7I F ( N S T A . 6 T . X S T A l G D TO 1 6 8 1 a? -2*K=NSTL 1 1 8 8I 9 T A K l = ? 3 T A b J t i 3 9C A S 9 l C N S U R S C ; q I P T T U Y E A R 1190hC J : I Y A- I Y f i 4 V 191I~ NyQ3.~?,J.AhD,IP35~O~r;,l)~YR~aJ 1 1 9 2I F [ J . G T . o , ~ v D . J . L E . ~ J Y ~ S ) O T O 080 1193

RIT ( 6 , ~ 7 0 1 I Y R 1 1 9 4470 F nkFc4T ( / l h H U I . i4 C tk P TB F ,L E Y E b R o I S 1 1 ~ 5 0 0 0

G O T O 1 5 0C S T O P E f t O N S 1 V S T C t l D & AND M ?;+TH A R R A Y


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73/104

e n r s obfiC n t H , K ) - l .h 9 C C t lh 'TTk U E7 0' 2 X F ( n ( N * K ) . k E . - l r ) G o 10 710c s ~ i a T EN A C C U PU L A T I O N S U H E ~ ~L O W n 1 3 3 1 ~ eN = oTPIPZO,I U P h a O .G f l TO 7 7 07 1 0 T E w p s ( J F ~ I K )

C l o H n N T H FLflW8: F ( S N O ( I ~ K ~ ~ L T . T E P ) S ~ ~ ( I I K ~ ~ Y E F I PI F ( S M R ( I + l f I K I r G T . T E ~ ? ~ ] 3 F S ( I + 1 S l K ) = 7 E ~ PI F q M Q ( 1 3. K ) . L T . T E t ~ P] , 9 W G [ i 3 p K ) % l E t J PX F C S M Q ( ~ ~ ~ K )G T r T E H P ) S Y t ( ~ R I K ~ I T E H Pc 6-MONTH F L 0 N STHP:fHP+fE 4PT r P L n T n P A + T E h P1 ~ ( ~ - 6 ) 7 h n , 7 3 0 , 7 2 072C TuP=TVP-Q r - b r K l

7 3 C I F TMP,LT.S"f? l29,K) 18Cf l 2 9 # K ] a T M PI i ~ r u P . G t . s ~ i ~ ( l ~ , K l l 5 ~ ~ 1 ~ 1 4 , K ) ~ ~ U Pc S U - ~ ~ R T HL O N S1 ~ ( ~ - 3 ' J ) 7 6 0 1 7 5 0 r 7 4 07 PC T ~ F A ~ T Y P A - Q [ M - ~ O , K )7SO : (TMP&.LT,9HQ ( 3 C r K ) 9 ;b [~CIK) :THPA~ F ( T M P A s G T . 8 ~ O ( 1 f l K ) ) ) . R [ 1 5 ~ K ) t i M P AC ~ ~ I E P A G E L O W7 6 0 ~ v G ~ ~ C K ] ~ A V G B ( K ) + T E H PN n = w a + l7 7 0 C O N T I N U E7 R C C n t i ? l N U E

T F . U Q = N QA v G ~K ] 1 b V G O K ) I T E H P7 9 0 C Q h T I U l J E

hC I ~ ( I ) = S ~ G ( I + I S ~ K ) + . ~6 7 C ~ * ~ I T E ( b r 0 ~ 0 1 1 S f A ( K l r1 Q I I l p X = ~ 1 ~ ~C E * C3 w PUT E F R E O U E ~ C Y T A T I S T I C S * * *r a I T E ( 6 , R 9 0 )R P O F n E M A ? ( / 2 l H FR EQ U EN C Y S T A T X S T I C S )

i < P I T E [ 6 , 8 S O ) h f O C l ) = r I ;89 F U K r A T (/14R S T A I T E M , L ~ I 1 1 1 8 )C H I S S I h C FLOW P F E t F B L N G FIRST H E C O R D M O N T Hon ~ O O S ~ I S T Y Y NSTI90C O l l p K ) = T

P N = OXTFf4P N 3 T AD n 118 K = ~ ~ I T E * PI F I J TE n P ,G T ,N S TA ) G O TC l i eI F ( K , C E . N 3 T x ] G O TO 9 5 2

9 i c nn 920 1=1 1aT E M P = K L O G I ~ X ~D n ( f K ) = D ~ C I , ~ ) * . O I / ~ E H PIF(nQ(ir


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Nod930 nn Q UO YR , iA V ( I , K ) 3 f l a: n ( I , K ) = ? 1 .S tE 4 ( I lK )=0 .

T H 9 l NX ~ ~ C Q ~ ~ ) ~ ( O ~ ( ~ ~ X ) + O ~ ~ X ~ I ~ K I : / ( ~ ~ ~ ~ T ~ ~ P )sao C ~ K P ~ N U E9 z=1On 9 7 0 J n t , N y R 3O i l 9 6 0 Isl,12: r = r r 1I F ( f l ( M , K ) . E 9 a = I a l 6 T O 9 3 5

C 2Ef'LACE FL04 A R R A Y WITH L O G A H R A YT E W P = ~ L ~ C ( ~ ~ ~ ~ ~ K ~ * ~ ~ C I ~ I ~ ~ ~ ~ ~ ' J O ~ S ~ ~ ~R I M I K I Z T E H PI F ( K . L E . N S T X ) G O 70 9 6 0C 5 U H , SnUARE3, AhO C U B E 34 V ( 7 , K ) Z A V ( 1 0 K ) + T E f l P

S D ( I , K ) = F ~ C T , X I + T E ~ ~ P * T E I * PS K E ~ ~ I ~ ~ I = ~ K E ~ ( I , X ) ~ T E Y P * ~ E ~ P * ~ E ~ PG O 4 0 900C *iX33IhG FLOW E G U I P E O TO T

fC 2 t N . K l a TI?COY=l9 b C C ~ ~ ~ T I Y U E970 C Q h T I f f U EI e ( K , L E . h 3 T : O q 1 118I N D C Z OO i l l o n o ? = l l i ?Y E u ~ = ~ L O ~ ( I , K )f F ( P E Y P . i T . 3 . 1 G O 1 1 1 2 0T 1 ' P + A V t T a K

I F C $ D ( X , < ) ,LE.O.I GO TD 4 P QS D I T I K ) = S l l C I s ~ ) * * . SI F [ s ~ ( I , K ; ~ ~ . , 0 3 f l S ) G U T 9 9 0s u ~ r ( ~ , x ) = ( T i ; ~ ? * ~ E ~ t P ~ S ~ E ~ ( x , % l ~ . 3 . ~ ?l I T E N P , ( T E ? f J ~ 1 w ( T . L t F * 2 . ) 2 9 o ( I , i 0 * * 3 1I F ( s K E M ( ~ ~ ~ ~ JLi,[:,l)aOQ.S~EU(I,K)aG3.aL INOC=II F . ?x E ,4 ( 1 1 K ) . G T . 3 . ] S K E & ( I , K ) = 3 a

I F ( ~ ~ x E I J I I ~ x Il.T.-'3*] 9 X f b ( I , o = m 3 .G O ? r l 15009a0 40CT,K)=Oe9 4 C SrEw(r,Kl=O.

1 O n G C n K T I N U EN = h + iI ~ . G T . 1 1 G o TQ 1 6d ~ ~ ~ ~ ( b e l ~ l ~ ]s ? ~ ( K ) , A ~ ( l a O ~ ~ = l , i z ]i o i c F ~ R M A T / l ~ , ~ ~ , a t r V E S ~ ,% ~ 6 , 3 1d ~ l y E [ b e b a O ] ( $ f l ( I ,K ) r I =1 12 )1 0 2 C FnriqAT (79,7;1,9Tl D E v , 1 2 F P s 3: ~ a l r ~ r ~ , t e 3 0 1s x ~ c ( ? , ~ ) , 1 = 1 , i 2 11 0 3 0 F 7 R H i T ( l b ~ r J ~ S ~ E % ~ l 2 P A . 3 1r a I T E ( 6 , I O C O ) D P ( I , W ) , I = l 1 1 2 )l n O c F w M 4 T b ~ , h ~ X k C ~ ~ ? , F 7 . 2 , 1 1 F B . t )+ a r : ~ r s , a s n l ;hLcc(I,x) , 1 = 1 , 1 2 11 O S C F n HP d T ( 7 Y , 5 H Y E A R 9 , 1 2 1 8 )

lob ' IF(N.GE.Ia) G f l 7 1 1 8 0r r t I m c . L , ~ . o j G O 7 2 1 1 8 ~C THE F C L L f l i q I N G R C c T I k E H I L L A D J c S T T H E ~ S C U E ~ ~ E ~ TCc 7 9 ~ O O d T l f N Z E S O KENC CHANGE W E P C L L W I N G 3 1 A T TO ISJ (Z=l T O ACTIVATETSK720IF (TSKZ.LZ .0 ) G O T O 1 1 8 0

I T P ~ 1b n 1 1 1 0 I a l t l i ?i4ZTTP+XD P l o e a j = l t ? ~ Y ? 3


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' l sH+ \ ? i u z iZ F ( ~ ~ ( N , K ) . E O . T ) 0 TO 1 0 7 8 422f t4:xn(bl , l0 1 4 2 311 ( H # ) x IO . * *T M P r n f J Q (1 1 K ) 1 4 2 4~n ~n 1 0 8 0 1 4 2 5107C G l V , K ) n - 1 . 1 4 2 6

O A O C ~ ~ T I K L J E 1 4 2 7T F W P S S K E ~1 , ~ ) 1 4 2 8iF (T EM P.C T. ( - 9 1 ) a A ~ f l . T E M P ~ L T . ~ l lO T O 1 4 2 9I F ( T F M P ) 1 0 9 0 ~ 1 1 1 0 ~ 1 1 0 0 1 4 3 0

lOqC ~ ~ o [ ~ , x ) a f ~ O ( I , K ) * 2 , 1 31cn T O i i r o 1 4 3 2l l O C b ? ( I l ~ ) = u O ( t l K ) ~ ~ I f ~ ~ C H ( X ) 1 4 3 31 1 1 0 C n h r ~ ~ u E 1434GP To 9 3 0 1 U35C * D E L E T E STATICY3 WITH L E S S T H A h 3 Y E A R S OF D A T A * 1 4 3 61 1 2 0 * d u l T E ( b t 1 1 3 0 ) T S TA ( K1 3 7113C FPRWAT ( / UY 3 T A , I B , 2 8 R DELETED, I N S U F ~ X C S E N T O A T & ) 1438h l q T A r R g T 4 = 1 4 3 9N S T A A S V ~ T A + I 4 6 0N S T & X = ; J $ T A + N S T A 1 4 4 1I F ( K . G t . Y S T A l G G T 0 1180 1 4 4 2C PEDIJCE SUHSCRIPTS OF S U B S E Q U E N T TATI IONS 1 4 4 3o 1 1 7 0 K X = K , N S T A 1 4 4 4I d T n ( K X ) = X S T A K X + ~ I 1 4 4 sti J i a a 6Dn 1 1 5 0 J ' l r f J Y R 9 1 4 4 7

1 1 4 0 131 i a 1 4 4 8'1=Fc+i 1s4qi i f i c n r n , ~ x ) = g c ~ , u % + l ) 1 45 0i l S c C P b Y L C U E 1 4 5 1

Q O 1 1 6 0 3 = l r 1 1 ? 1 4 5 2J v f N : T I K x ) = f l * 4 I h J , K x + 1 ) 1 4 5 3? I O G ( T , K : O = ~ ~ L O G ( I I K W ~ ) 1 4 5 0116C O 0 ( T r K ~ ) = D i 3 l I r K X + i ) 1 4 5 5117C Cnh.TtNUE 1 4 5 6fl r n 9 1 1 4 5 71 l P C I E ' T I N I I C 1 4 5 8I T Q b J S t 0 1a 9IF(TPCD~.LE.O) G D 10 1 3 7 0 1 4 6 0CF* a AUJUSTfAENT OF FREGUENCY 3 T A T I 3 T J C S 7 0 L O N G TERM 1 4 6 1on i lso 1 = 1 , 1 2 1 u 5 2nn I S J ~ = ~ , N S T A 1 4 6 3

Dn 119 L = l c N S T A X 1 4 6 4xcn~ : , ~ , i . ) =n l a i s$ i t r i d (I,K,L] O. 1 4 b bS I ; f ' 4 1 1 , K 1 L l ~ O e 1 4 6 7on ( I , K ~ L I = O . 1 UCBsot3 ~ ~ , K I L I ~ O . 1 4 6 9X P A n ( T I K , L ) = O . 1 4 7 0R 4 ( l I K , L ) = - 4 , l G 7 11190 C P h T l N t J E 1 4 7 2D O 1 2 2 0 N = ~ , N S T A 1 4 7 3X Y = L + ~ 1 4 7 4I= t 1 4 7 5DP 1 2 ? 0 J = l , N Y h 3 1 4 9 6D O 1 2 0 I = i r 1 2 I 4 7 71 1 r + 1 1478T F M O z Q U r K ) 1 4 7 9I F ( T S r ~ P . E Q . T l G O T O I 2 1 0 1 5 8 0~ f l 2 0 0 L = K X , ~ S T A Z i u a i~ w : ~ - k s T s 1 4 82I F L x , L T . I ) T ~ ~ = I J : ~ , L ) 1 4 8 3I F ( L Y . G T . O ) T H P = O O ~ = ~ , L X I i ~ e u~ F ( T M P , E ~ ~ . Y ) 0 Y @ 1 2 C O 1 4 8 5scrn(I,KIL)=NChH(1,K,I.)+~ 1 9 8 8S I ~ * A ( I I K I L I = ~ ~ J ~ A ( I , K ~ I . ) + ~ E M P 14e?S ~ ~ ~ R ( X , K : L ) = O U ~ ~ ~ ( I , K ~ I ) + T P P 1 4 8 6~ ~ ~ ~ ~ K ~ L ) = S O ~ ( I I K , L ) * ~ E K P * T E M P 1489S ~ E ~ I ~ K , L ) ~ S ~ ~ ~ ( I , K , L ) + T ~ P * T

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