hec-4 monthly streamfiow simulation · aed-a235 877 us army corps of engineers hydrologic...

AED-A235 877

US Army Corpsof EngineersHydrologic Engineering Center

GENERALIZED COMPUTER PROGRAM

HEC-4

Monthly Streamfiow Simulation

User's Manual

0 I-1

February 1971

Approved for Public Release. Distribution Unlimited. CPD-4

HEC-4

Monthly Streamflow Simulation

User's Manual

February 1971

Hydrologic Engineering CenterUS Army Corps of Engineers609 Second StreetDavis, CA 95616-4687

(916) 756-1104 CPD-4

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HEC-4

MONTHLY STREAMFLOW SIMULATION

HYDROLOGIC ENGINEERING CENTERCOMPUTER PROGRAM 723-X6-L2340

CONTENTS

Paragraph Paqe

1 ORIGIN OF PROGRAM 12 PURPOSE OF PROGRAM 13 DESCRIPTION OF EQUIPMENT 14 METHODS OF COMPUTATION 15 INPUT 76 OUTPUT 87 OPERATING INSTRUCTIONS 88 DEFINITIONS OF TERMS 89 PROPCSED FUTURE DEVELOPMENT 8

EXHIBITS

1 DETAILED EXPLANATION OF COMPUTER PROGRAM2 DESCRIPTION OF CROUT'S METHOD3 INPUT EXAMPLE4 OUTPUT EXAMPLE5 DEFINITIONS6 SOURCE PROGRAM7 INPUT DATA8 SUMMARY OF REQUIRED CARDS

1/85

HEc -4

MONTHLY STR AMFLOW SIMULATION

HYDROLOGIC ENGINEERING CBTERCOMPUTER PROGRAM 723-X6-L340

1. ORIGIN OF PROGRAM

This program was prepared in The Hydrologic Engineering Center, Corpsof Engineers. Up-to-date information and copies of source statement cardsfor various types of computers can be obtained from the Center upon requestby Government and cooperating agencies. Programs are furnished by the3cv.rament and are ac-ept!d and uzcd 'U, the recipient upon the express unaer-standing that the United States Government makes no warranties, express orimplied, concerning the accuracy, completeness, reliability, usability, orsuitability for any particular purpose of the information and data containedin the provrams or furnished in connection therewith, and the United Statesshall be under no liability whatsoever to any person by reason of any usemade thereof.

The programs belong to the Government. Therefore, the recipient furtheragrees not to assert any proprietary rights therein or to represent theprograms to anyone as other than a Government program.

2. PURPOSE OF PROGRAM

: -ThiR program will analyze monthly streamflows at a number of inter-related stations to determine their statistical characteristics and willg7enerate a sequence of hypothetical streamflows of any desired length havinr.those characteristics. It will reconstitute missing streamflows on thebasis of concurrent flows observed at other locations and will obtain maxi-mum and minimum quantities for each month and for specified durations inthe recorded, reconstituted and generated flows. It will also use the-eneralized simulation model for generating monthly streamflows at ungagedlocations based on regional studies. There are many options of using theprogram for various related purposes, and it can be used for other variablessuch as rainfall, evaporation, and water requirements, alone or in combination.

3. DESCRIPTION OF EQUIPMENT

This program requires a FORTRAN IV compiler, a random number generator(function RUGEN included, see exhibit 2), and a fairly large memory (64K onthe CDC 6600). Provision is made for use of three scratch tapes, 7 (forpunched output), 8 and 9.

4. METHODS OF COMPUTATION

a. In the statistical analysis portion of this program, the flowsfor each calendar month at each station are first incremented by 1 percentof their calendar-month average in order to prevent infinite negative

'! J

logarithms. This increment is later subtracted. The mean, standard deviation

and skew coefficients for each station and calendar month are then computed.

This involves the following equations:

Xim = log (qim + qi) (1)

NXi Xi,m/N (2)

m--l

S j (Xi-m )2 /(-)(3)

N

gi N I (xi~ x )3 / ((N-1)(N-2)S3) (4)1m=l i'm i

in which:

X = Logarithm of incremented monthly flowQ = Monthly recorded streamflowq = Small increment of flow used to prevent infinite logarithmns

for months of zero flow= Mean logarithm of incremented monthly flows

N = Total years of recordS = Unbiased estimate of population standard deviationg = Unbiased estimate of population skew coefficienti = Month numberm = Year number

b. For each station and month with incomplete record, a search ismade for longer records among the stations used, to find that which willcontribute most toward increasing the reliability of the statistics com-puted from the incomplete record. The mean and standard deviation arethen adjusted. Equation 5 is used to compute the equivalent record requiredto obtain statistics equally reliable to these adjusted statistics and isthe basis for selecting the best record to be used in the adjustment.Equations 6 and 7 are the adjustment equations.

N N1

1 2 ,N 1 21N2 -,-N I R2

N2

2

, = , 2 ) RS/S 2 (6)

(7)S, -S = (S' -SI) S)IS

The primes indicate the long-period values and those without primes

are based on the sane short period for both stations 1 and 2, and:

N = Length of recordR = Linear correlation coefficient

c. Each individual flow is then converted to a normalized standard

variate, using the following approximation of the Pearson Type III distribution:

tim = (X im - g4) / Si

Ki' m =6/g [ ((giti,m/2) + 1)1/3 - 1] + /6(9)

t = Pearson Type III standard deviateK = Normal standard deviate

d. After transforming the flows for all months and stations to normal,

the gross (simple) correlation coefficients R between all pairs of stationsfor each current and preceding calendar month are computed by use of thefollowing formula:

Rr -[ N x 2 N x2N 2_, ]Rii- --{l - [1 - ( Ximil z)/ x Xi ,2]n

m--l i'm=l i.mm=l i

(N-l)/(N-2) } (10)

in which:

X = X-X

e. If there are insufficient simultaneous observations of any pair of

variables to compute a required correlation coefficient, that value must be

estimated. Each missing value is estimated by examining its relationship

to related pairs of values in the current and preceding month by use

of the following formula using i, ,J, and k subscripts to indicate variables

used in the gross correlation.

Rij R4- (1 - Rk2) (1 - R )

Since, in order to be consistent with the two related correlation coefficients,the correlation coefficient must lie between the limits given by equation Li,the lowest upper limit and highest lower limit are established for all relatedpairs, and 'We average of these two limits is taken as the estimated correla-tion coefficient.

f. Monthly streamflows missing from the records of the various stationsare estimated for all stations for each month in turn. Accordingly, when-ever a missing flow is being reconstituted, there always exists a validvalue for all stations already examined that month and for all remainingstations in either the current or preceding month. For these remainingstations, the current value is selected where available; otherwise thepr-e~iin- value is used. In order to reconstitute the missing value, are-ression equation in terms of normal standard variates is computed byselecting required coefficients from the complete correlation matrix forthat month and solving by the Crout method (See exhibit 1). The missin7value is computed from this regression equation, introducing a random(-omponent equal to the nondetermination of the equation, as discussed inthe streamflow generation procedure.

7. It has been found that valid use of the regression technique requiresthat all correlation coefficients agree with the data that will be substitutedinto the equations and that the correlation coefficients be mutually con-sistent. Inconsistency in the correlation coefficients causes the dependentvariable to be over-defined and is evidenced by a determination coefficientgreater than 1.0. If this occurs (because of incomplete data), the inde-pendent variable contributing least to the correlation is dropped, and anew rerression equation is computed. This process is repeated as necessaryuntil consistency is reached (which must occur by the time that only oneindependent variable remains). In order to make the correlation matrixconsistent with the data matrix, all affected correlation coefficientsare re:omputed after each estimate oF missing data.

h. Normal standard deviates are then converted to flows by use of thefollowing equations;

I,!~

t im = (g,/6)(Km - gi/6 ) 1 3 -1 2/g (12)

i X + ti,m i (l-Xim Xt~~

O = AntilogX - qi (14)

imposing the constraint:

Q (15)

i. When the set of flows is complete, all correlation matrices shouldbe consistent except for truncation errors in the computer, since the dataarrays are complete. Any consistency of matrices obtained in this manneror of matrices read into the computer will result in determination coefficientsgreater than 1.0. If this occurs, consistency of each correlation matrix isassured by first testing all combinations of triads of correlation coef-ficients in the current and preceding month for all calendar months usingeqmation 11 and raising the lowest of the three coefficients to obtaina consistent triad. The test of consistency of each complete matrix isi-.,e by recomputing the multiple correlation coefficient. If this valueic greater than 1.0, further adjustment is required. Such further adjust-.ent is obtained b:i introducing a coefficient, successively smaller by0.', on the radical in equation 11 and repeating all triad consistencytests until all matrices are consistent. If consistency is not reached,coefficients in each inconsistent matrix are moved toward the averagevalue of all coefficients in that matrix until consistency is reached.

j. Generation of hypothetical streamflows is accomplished by computinga regression equation, by the Crout method (described in exhibit 1) foreach station and month and then computing streamflows for each station inturn for one month at a time using the following equation. This processis started with average values (zero deviation) for all stations in the'irst month and discarding the first 2 years of generated flows.

I I

K, = IK + + K . ' + + K +,J ,i ,l+2 2 " " -1 , -i -1 Ji,'

R iKl l . . . +Bn~i l K + - j zi j (16)

5

in which:

K = Monthly flow logarithm, expressed as a normal standarddeviate

= Beta coefficient computed from correlation matrix

i = Month number

j = Station number

n = Number of' interrelated stations

R = Multiple correlation coefficient

Z = Random number from normal standard population

k. Maximum, minimum and average flows are obtained for the entireperiod of flows as recorded and for specified periods of reconstitutedand generated flows by routine search technique.

1. Provision is also included in this program for use of the generalizedmodel requiring- only 4 generalized coefficients for each station (in placeof 1-) and one generalized correlation coefficient (in place of 12) for eachpair of stations, in addition to identification of wet and dry seasons foreach station. These are defined as follows:

(1) The average value of mean logarithms of flows for the wetseason (0 months). This value plus 0.2 is applied to the middle monthand the avera-e minus 0.1 is applied to the other 2 months.

(2) The average value of mean logarithms of flows for the dry7cazon , mcthz), 'Ai iz api,1:c ' t', all 3 1,ry .o-ths. !lean Iogarithrsfor months between dry and wet seasons are interpolated linearl,.

() The average standard deviation for all 12 months. This isanrlied to each of the 12 months.

() The average serial correlation zoefficient for n1l ! mon+'s.This value minus .15 (but not less than zero) is applied to each wet-seasonmonth, and the value plus .15 (but not more than .98) is applied to eachdry-season month. The average value is applied to all intermediate months.

(5) The average interstation correlation coefficient for all 12months is applied to each month for that pair of stations.

m. Because of limitations in computer memory size and because ofincreasing change of computational instability with larger matrices, thenumber of stations usable simultaneously in this program has been limitedto 10. However, the program can reconstitute and generate streamflows for

6

any number of stations in groups of 10 or less. It will ordinarily bedesirable to include one or more stations from earlier groups in eachsuccessive group in order to preserve important correlations. In.addition to providing flow data for all stations, it is necessary tolesignate NPASS and to follow each group of flow data with a standard-,orrmat card with NSTX (number of stations in next pass that were alsouned in preceding passes) and station identification numbers for thosestations. These numbers must be listed in the same sequence as theirlata were arranged in earlier passes. Data for the new stations for thenew pass should then be read. None of these flows can occur in a yearlater than the latest year for which flow data occurred in the first pass.

I. As soon as flows are reronstituted for any pass, they are readonto the flow tape. After statistics are computed from transformedreconstituted flows, they are read onto the statistics tape (afterilentification of stations in the nass for future reference). Finalregression equation data for each pass are read onto the same tape at thesame time (for use in -eneration later). For each new pass, the flowand statistics tapes are searched separately for data for those stationsalready used that also occur in the new pass. In order to read and writeintermittentlv and alternatively on the same tapes, it is necessary to

'een traf-! of tape records so as to assure that any read statement doesnot read beyond the record mark and so that new write statements occurat the end of all previous write statements that are to be saved.

o. Once that statistics are put on tape, they are retained throughoutthe reconstitution and generation processes. Flows, however, are savedonly for the set of data in which they were reconstituted or generated,:mntil the last pass for that set is completed. In the generation process,it is necessary to save the last flow generated for each station in oneset for ,,se as the antecedent flow in starting generation in the nextset. These are saved in the QSTAP array with subscript ISTAP.

INPUT

Intput is summarized in exhibits 7 and 8. Data are entered consecu-tively- on each card using a simple variety of formats to simplify punchingand handling cards. Computed and generated flows cannot be 1,000,000 unitsor larger, and consequently must be expressed in units that cannot exceedthis magnitude. Units should be indicated on one of the 3 header cards.Column 1 of each card is reserved for card identification. These are icnoredby the "omputer except for the A in column 1 of the first header card, whichis used to identify the first data card. An example of input is given inexhibit 3. Certain inadequacies of data will abort the job and waste inputcards until the next card with A in column 1 is reached. A card with Ain column 1 followed by 4 blank cards causes the computer to stop.

7

6. O(JTPUT

Printed output includes key input information for job identificationand all results of computations. Generated flows are put on magnetictape, and computed statistics are punched on cards in the format usablelater b the program. An example of printed output is given in exhibit h.

7. OPERATING INSTRUCTIONS

Standard FORTRAN IV instructions and random number generator arerequired. No sense switches are used.

8. DEFINITIONS CF TERM;

Terms used ti the program are defined in exhibit 5

a* ?ROPOSE.D 'VITLURE DIXELOTPMENT

There are cases where the model used herein does not reproduce histori-aI]drou,-:hts with reasonable frequency. Consequently, the model is underSontinuous study and development. It is requested that any user who findsen inadequacy or desirable addition or modification notify The HydrologicEn oieering Center.

EXHIBIT 1

DETAILED EXPLANATIONOF

COMPUTER PROGRAM

GENERAL

Much of the program is explained by comment cards and definitionsof variables. Supplementary explanation follows, referring to sectionsidentified with the indicated letter in column 2 of a comment card.

SECTION A

Correlation coefficients, R, and beta coefficients, B, are in doublenrecision for matrix inversion computation, in order to minimize computa-tional instability. Correlation coefficient, RA, as originally computedand stored, may be defined in single precision. For computers with worlen:-,th smaller than ? bits, many other variables in this program shouldbe in double precision.

When dimensions are chaned, the corresponding variable (startingwith K) should be changed accordingly, as these are used to preventexneedence of dimensions. If an excessive subscript is used, the jobwill be dumped until a card with A in column 1 is encountered, at whichtime a new job is automatically started. If 5 blank cards (with an Ain column 1 of the first) are encountered, the run will be terminated.Job specification cards are read in this section.

SECTION B

NSTAX is number of columns in correlation matrix. These consist of,13TA columns for the current-month values and a similar number for ante-cedent-month values. NSTAA is initial column number for antecedent-monthcoefficients. These are computed from NSTA, which is read in if statisticsare to be provided, rather than computed from raw data. If raw data areto be used, NSTA is defined in the program later and NSTAA and NSTA must bealso. Data for each new pass are processed after transferring back tostatement 42. In the multipass operation, NSTX is the number of stationsused from previous passes and NSTXX is the subscript of the first newstation for the current pass. Station identification for the NSTX stationsmust be in the order in which data for those stations were originally used,because search of data and statistics on tape is made in this order. Flowsfor these stations are read from tape IQTAP, and corresponding statisticsfrom tape ISTAT. Variables LQTAP and LSTAT are used to keep track of tapeposition for subsequent writing.

*Provided through the cooperation of the Texas Water Development Board.

IXHhBIT 1

Months are identified consecutively by the variable M starting withthe month preceeding the first year of data. Some quantities to beaccumulated are initialized. Station combination data are stored forthe purpose of obtaining maximums and minimum (section D) of weightedflow values later. Tandem stations are identified for cases where acheck on consistency of generated quantities is deemed appropriate.Station identification numbers are set to a large number so they willnot be undefined. The flow array is filled with -1 values to indicatemissing values. For each station and calendar month, the total flow andnumber of recorded values are computed for computing a flow incrementand other statistics later. The minimum flow for each station monthis also computed in order to avoid negative logarithms later.

SECTION C

Station data can be read in random order. Stations are identifiedby subscript in the order in which data for each station are first read.The year subscript is computed. Negative subscripts will occur if dataare for years earlier than the starting year indicated on B card, anddata for these are rejected, with diagnostic printout. The stationsare counted and the flows for each month at each station are counted forthe purpose of computing frequency statistics later. If the number ofstations or years exceeds its dimension limit, the job is aborted. Thenumber of stations is permanently stored in the NSTNP array for lateridentification in multipass operations. The remainder of this sectionis self explanatory, except to state that permanent identificationstation numbers are given for stations in combination, for tandem stations,and for consistency-test stations, and subscripts are identified for rapidcomputation later.

SECTION D

In this section, maximum and minimum recorded flows for each calendarmonth , the water year and for durations of 1, 6, and 54 months, and averageflows are computed for each station and combination. Durations do notspan a break in any record. Quantities are rounded off and printed infixed-point format.

SECTION E

The logarithm transform of flows is accomplished here. Missingvalues are indicated by an impossibly large numb,.r (the -1 used formissing flows is a reasonable logarithm and therefore cannot be usedfor missing logarithms). Before the log transform, the average flowfor each calendar month at each station is computed and one (costaziedto a minimum of 0.1 flow unit) is added to each flow. If the minimumobserved flow for that station month is negative, that absolute value

2 IXEISIT 1

is also added before the transform. After the logarithm transform,freq:.ency statistics for each calendar month and station are computed.

An increment needed to convert the logarithws to an approximately normaldistribution is also computed as an alternative future transform. Log-

arithms to the base 10 are used so that statistics are comparable to

other commonly used statistics. A variable IRCON is set to 1 if anymissing values are encountered, so that the flow reconstitution routinewill be called later. A variable INDC is set to 1 if the first approxi-mation of increments causes any one of the skew coefficients to besmaller than 0.1 or larger than 0.1. In an optional routine that follows,the increment for each station and calendar month is adjusted individually

and iteratively (up to 14 trials) until skew is within 0.1 of zero.

Stations with less than three years of data for any calendar monthare deleted, since skew and correlation computations require at leastthree items of data.

SECTION f

Correlation matrices are computed here for the purpose of adjustingfrequency statistics for short-record stations. All correlation coef-ficients are first set to -4.0 in order to identify those not computedlater for lack of sufficient observed data. Then accumulations of thevarious quantities required are computed for all items above the maindiagonal in the correlation matrix for each month, using all data commonto the two stations involved. If mor-e than two items of data are avail-able, the correlation coefficients are computed. Coefficients for themain diagonal are set to 1.0, and those below the main diagonal are setequal to their symmetrical element. Coefficients between the currentand preceding month's values are similarly computed. These items con-stitute an extension of the matrix to the right, which doubles its size,and the new portion is not necessarily symmetrical. Similar completearrays of average values and root-mean-square values for only those log-arithms common to each pair of stations are found for later use inadjusting statistics.

A search is then made to determine the station that would be mostuseful in adjusting statistics for station months with incomplete record,and the means and standard deviations are adjusted in accordance with thefollowing equations:

s = S I (S' -s ) R2S /S1 1 2 2 1 2

-X' X. + ( - ) Rl/S2

where primes indicate long-period values, subscripts are 1 for the short-record station and 2 for the long-record station and,

3 EXHIBIT 1

X = mean logarithm

S = standard (leviation or' the logarithms

R = correlation coefficient.

An optional check of consistency of standard deviations betweenadjacent stations for the same month is next made. This is to assurethat frequency curves do not cross within three standard deviationsfrom the mean. If there is a conflict, the standard deviation of thatstation designated in the input data as the dependent variable is modi-fied accordingly. All frequency statistics are then printed out.

SECTION G

All flows are next standardized by subtracting the mean and dividingby the standard deviation for the month and station. An approximatePearson Type III transform is then applied as follows:

K = qt +tl) 1/3-

where:K = normal standard deviatet = Pearson Type III standard deviate

g = skew coefficient

New correlation matrices are then computed, based on the normalizedvariates and using the same standard procedures previously employed forcorrelating logarithms. The sign of the correlation coefficient ispreserved, since the coefficient will be used to establish regressionequations. Correlation coefficients are set to zero if the varianceof either variable approximates zero, since the computation of the coef-ficient is highly unstable and since its use would be of little value.

SECTION H

For Jobs where -orrelation data are given, the portion of thecorrelation matrix above the main diagonal for all months and theentire correlation matrix relating current and preceding month'svalues are read, with a different card for each pair of stations.Values for all 12 months are contained on one card, and the two stationsinvolved are identified on the same card. An automatic check is madeto assure that cards are in the required order of columns and rowsin the correlation matrix. When generalized statistics are used, onlyone correlation coefficient for the entire year is read, but card orderis the same. Symmetrical elements below the main diagonal are thenfilled in and values af 1.0 are placed in the main diagonal.

4EXHIBIT I

Frequency statistics are then read, 4 cards per station, with 12monthly values and station identifications on each card. A check ismade of the station order, to assure proper subscripting. When gen-eralized statistics are used, only one card per station is read, andthis contains the maximum and minimum mean logarithms and the averagestandard deviation for the year. The months of maximum and minimum

mean logarithms are also read and converted to corresponding subscripts.These subscripts will differ from the calendar month number if the yearused in the study does not begin with January.

SECTION I

This section searches for each calendar month the entire correlationmatrix to be the right of the main diagonal for misiing correlation coef-

ficients due to the nonexistence of at least three years of simultaneousdata for the month. As soon as a coefficient between two variables is

identified as missing, a search of the correlation matrix is made to findestablished correlation coefficients between each of these variables (iand j) and any other variable (k). The range within which correlationbetween the two variables must lie in order to be mathematically consis-tent with the correlation with the third variable is established by useof the following equati ,n:

Rij = Rki RkJ J(l'Rki2) (l-Rk)2

As each successive third variable with established correlation coefficientsis found, the upper limit of Ri1 is constrained to the lowest of all upperlimits computed, and the lower limit is constrained to the highest of all

such lover limits computed. When the entire matrix has been searched thecorrelation coefficient is estimated as the average of these two constrainedlimits. If this element is above the main diagonal, the value is alsoentered for the element symmetrically across the main diagonal. Thesearch for further missing correlation coefficients is then continued.

SECTION J

Where a correlation matrix is not to be used for reconstituting data

but might be inconsistent, a triad consistency test can be made in thissection. This is done by examining all groups of three related correlationcoefficients, and testing the lowest one to determine whether it is aboveminimum constraint established by the equation in the preceding station.If not, it is raised to that minimum. When this is done, it is possiblethat the adjusted coefficient had already been used in another triad test,and consequently that previous test would need to be repeated. In orderto do this properly, the entire matrix is searched up to 12 NSTA times,where NSTA is the number of stations, until a complete search reveals noinconsistent triad (INDC = 0).

EXHIBIT 1

A coefficient 'A'.' of the radical in the equation is used in orderto obtain complete matrix consisten-y in difficult cases, wheneverpossible by this means. A test for overall consistency is made insection K, and if this fails. FAC is saccessively reduced by 0.2until overall consistency is reached.

SFTION K

The test for overall consistency oi the correlation matrix foreach month is made by constructing foi each station the correlationmatrix that would be used in flow generation for that station and com-puting the multiple determination coefficient. If the determinationcoefficient of the matrix for any station and any month exceeds 1.0. allcorrelation matrices must be reexamined, since some coefficients arecommon to two or more matrices. This is done by reducing PAC in thetriad test (section J) by 0.2 and repeating all triad tests. If FAC isreduced to zero and consistency is not obtained, an index of NCB is setto 1 and an averaiin routine is .sed For each inconsistent matrix. Aquantity SUM is computed as the average of all correlation coefficientsin that matrix, and each element is modified by multiplying SUM by theexcess of determination coefficient and adding this product to theuroduct of the complement of this multiplier and the value of the ele-ment in the inconsistent matrix. The averaged or smoothed values arererlaced in the complete matrix for the month, and this requires somecareful manipulation of subscripts. A new computation of determinationcoefficient is made and the smoothinc, process is repeated up to ninetimes until consistency prevails. If this does not occur, the job isterminated. When consistency is established all complete matricesare .irinted out and essential elements are punched if desired.

SECTION L

In reconstititing missing data, a search is made for each month ofrecord starting with the first for stations that have no record duringthat month (Q=T). When one is found, a search of all other stations ismade to determine whether recorded or previously reconstituted flows existfor the current month or, if not, for the preceding month. If one isfound, it will constitute an independent variable for estimating themissing value, and its value and pertinent correlation coefficients arestored in new arrays for computation purposes. The correlation coeffi-cients with the dependent variable is temporarily stored in the NVAR(NSTA*I) column to assure that coefficients relating independent vari-ables which have sufficient array space (they cannot exceed NSTA innumber). A variable ITEMP counts the number of independent variables(stations for which recorded or reconstituted data are available). Itis incremented after its set of correlation coefficients are stored inthe R array, and is finally used to relocate the correlation coefficientsinvolving the dependent variable. If no independent variables with data

6 EXHIBIT 1

are found, as can happen in the first month of record, a correlation ismade with the preceding vaiue for the same station and that precedingvalue is arbitrarily set at the average for the month. The regressi6nequation and deLermination coefficient are then computed using subroutineCROUT. The variable having the lowest absolute value of correlation withthe dependent variable is identified, and beta coefficients are searchedIn order to eliminate all unreasonable coefficients. In the usual casewhere the simple correlation coefficient between any variable and thedependent variable is positive, unreasonable coefficients are assumed tobe those larger than 1.5 or smaller than -.5. In the case where thevariable correlates negatively with the dependent variable, the reason-able range is -1.5 to 0.'. If an unacceptable coefficient is found, INDCis set to 1. If this happens or if the determination coefficient doesnot lie between 0 and 1.0, the variable with the smallest correlationcoefficient is eliminated, the correlation array reconstructed accordingly,and the regression equation recomputed. This process is repeated untilall required conditions exist. The missing value is then computed byuse of the regression equation and adding a random component normallydistributed with zero mean and with variance equal to the error varianceof the regression equation.

As soon as the missing value is estimated a search is made for allestablished values in the current and preceding month with which it isto be correlated, ad sums of logarithms, squares, and cross productsare incremented in preparation for recomputing all affected correlationcoefficients. After checking for sufficient (three years) record andnonzero variance, the correlation coefficient is recomputed. If thestandard deviation of either variable is very small, the correlationcoefficient is set to zero. If the coefficient is above the main dia-gonal of the correlation matrix, its value is also assigned to sym-metrical element. Since estimation of a missing value affects correla-tion coefficients between variables in the current and following month,which coefficients are stored in a different matrix, this process ofadjusting the correlation coefficient is applied to those values next.

SECTION M

After all flows are reconstituted, the flow tape is read until theproper position for writing the newly computed flow data on that tape isreached, and headings are printed for writing flows on the printer later.Then the standard deviates are converted to flows by reversing the Pearsontype III transform, multiplying by the standard deviation, adding to themean and taking the antilogarithm. The increment is then subtracted andif the resulting value is negative for a variable with zero lower limit,it is set to zero. In the case of reconstituted flows, the Pearson TypeIII transform is constrained so that the excess of the standard deviateover and above 2.0 is multiplied by a maximum of 0.2 (if the standard

7 EXHIBIT 1

|* _

diviation exceeds 0.). This simply prevents obtaining unreasonablyextreme values due to sampling errors. It is a moderat'on of theextrapolation rather than an abrupt truncation.

The test for tandem station consistency is next made. and incon-sistent flows are identified for printout and changed to the limit ofconsistency. The downstream flow is aacie consistent witb the swm ofupstream flows. Flows are punched on cards, if desired, printed out,and written on the flow tape for use in future passes. NQTAP is incre-mented and represents the total number of" records on the tape.

SECTION N

After convertinri deviates to flows, the frequency statistics arerecomputed in order to aree a: eurately with observed and reconstituteddata. If a consistency, test is rcalled tor, the variable ITRN3 is setto I and computation is transferred to near the end of section F, wherethe test is made ancl the transfer index -auses a return to this portionof the protrarm. Aj!stel statistics are printed, and the consistentcorrelation matrix is rrinted (and, if desired. also punched) by transferto section K, usi-in- ITPN., as a return indicator again. The statisticsare then punched. i" desired. P'lows for the snecified station combina-tions are then comouted.

SECfTION 0

Maximum and minimum recorded flows are computed by transfer tosection S, usin,- ITRN.-=l as a return indicator. The variable ITMP

keeps a record of the remaining years whose maximum and minimum flowshave not been searched -et.

Next, generalized statistics are -omputed, if desired, (if IGNRLequals two). As indicated, straight averag-es of all 12 monthly correla-tion coefficients in every category are taken. Means are averaged forthe three wettest consecutive months and the three driest consecutivemonths and the seasonal timinc, noted. Standard deviations for all 12months are averaged. Generalized statistics ac'e then printed out.

Next, generalized statistics read in section H are used to computereouired arrays oi statistics. Skew and increments are set to zero.The mean for the middle month of the wet season is .2 higher than thewet season averare and means for the other two months are .1 lower.Means for the dry seasons are uniform, and means for the transitionseasons are interpolated linearly. Correlation coefficients for thedry season are .1' higher (constrained below .98) than the annualaverage, and those for the wet season are .15 low (constrained abovezero). All of these operations are in accord with the generalizedmodel developed in HEC.

8EXHIBIT 1

SECTION P

After obtainih- monthly statistics and correlation matrices, re-i'ression equations for ehch station and calendar month are computed.Flows are generated in the station order in which data or statisticsare read and are generated for each month at all stations beforeproceeding to the next month. Flcws at each station are correlatedwith flows of the antecedent month at that station and at all stationsfor which the current month's flows have not yet been generated. Forother stations, fl1ows for the current month are used.

Regression equations are comouted in subroutine CROUT. If anycorrelation matrix 'orned is inconsistent (which should not occur atthis stage, except for truncation of computated intermediate variables),a transfer to section J is effected, and consistency operations performedon all correlation matri.ces. After such a transfer, all regressionequations must be recomputed, since any correlation coefficient mighthave changed. After this, only the beta and alienation coefficientsneed be retained, in addition to the freqoency statistics. Tn +.he -,,ti-pass operation, these are all written on tape I3TST at this point.

3iXTION{.

A routine for nro'ect-i_: histori,.al seruences into the future isemployed here. Values o- ,J RE"V (previous month's deviate) "or eachstation is determined as the trans'orm of the flow for the month pre-ceding the first month specified (by input data) to be generated. Thevar-'ele M.1A is comnutel f'or the subscript o" ; that conforms to the'irst month of uroj ected "'lows. If the Droiected flow routine is not

to '-e usedl the computer is next set up to yenerate two years of flows,at the end of whirh synthetic sequences will have a virtually randomstart.

In the multipass operation, stations are identified and all neces-sar : statistics are rontained in the order needed on. tape ISTAT. In an.--ass after the first. "lows -,enerated in earlier passes for the samenernV (the same sec-en-e o" J]ata) must be read from tape I-TAP, and thistsne nust he rewornd before each pass in order to permit a completesear .i.. In any seqtience after the first, the preceding flow for the'irst month to !e generated is the last flow in the preceding sequenceur that station, and these are saved in the QTAP array for multipass

operation. If' the multipass feature is not used, all necessary statisticsand 'Jows for -eneratin are in memoryr.

C]rTIO 1

In startin' to renerate flows, a variable JXTMW is used to identifyhe ,rear n,,unber o' the "irst -ear of each sequence in the multipass

0 EXHIBIT I

6o .mmmm-m mmmmm im ii m m

operation. Variab1les AVG and SDV are used to ,-omoute the mean andstandard deviation oF' the deviates "or ear-h flow sequence. These arelater used to 8djiust all deviates so that the means and standarddeviations in ever, -generated sequenc'e will be the same as those ofthe historical sequence.

Variables JA and NJ are set up to correspond to the first andlast year of !eneration in each suctessive sequence, depending onthe type of operation. MA has alrea,1. been set up as the subscriptof' ' correspondin- to the first month of flows to be Tenerated (foruse in projecting7 historical flmws re.orded to the current time).<PR3EN jor each station has 7teen identified as the previous month'sflow for that station. Plows are then enerated for each station,using stored re'ression equations and a rnndom component. Each generatedflow is immrediatel' entered into the QPRV array, because its precedingfl.-ow will never a-ain ")c used in that pass.

Tn t'-e multipass routine, flows (as deviates) are written on tapeat the end of ear.h nass, and the last f'low for each station is storedin the :"STAP arra, 'or use in the next sentuence.

. more than 1 _Gears (an arbitrarili selected length) of flow

are beinf generatel in any! sequen!-e, deviates are adjusted so that theirnean is zero and variance 1.0. Their unadusted mean and standarddeviation a-e printed. Then the,, are transformed to flows, and, ifc.alled. for, consisten"- tests between stations are made. For variableswith zero natural limit, a rheck lor ne-ative values is then made. Flowsare then printed and. if desired, punche(]. Plow combinations are thencornputed.

SBCTIO 3

Before comptinj meximum anr riinimum values of 7enerated flows,a nositive value of JX is looked for to assure that flows generatedare not to be discarded (the first two years generated for a randomstart). Also, at least NYMG years must have been generated beforemaximum and miniium values are -om-pnted (this applies only when thenumber of years remaining for 7eneration in the last seauence doesnot equal I7%Y(G). Ma9ximum sums are initiated at an extremely largenegative number and minimum sums as an extremely large positive number(T). Then a routine search of flow stuns Por the snecified durationsat each station is made for the sequence, and results are printed out.Since this routine is used for reconstituted flows as well as forgenerated flows, a transter indicator is used to determine whether thenext step is bac'- to the reconstitution routine or the generation routine.If the latter, a check is made for the multipass routine. If all passesare not completed, a transfer to section t, is made. If all passes arecompleted for this sequence or if the multipass routine is not being

10 EXHIBIT I

used, a ,he: is -nade o" remai . ii, errs to e 'eerated. I; *resterthan zero, a transfer to section 4r mnade Pf'ter ad.lustin, :-ears yjetto > e generated . Othei.ie the 'oh is e-ided and a new lob. if an,,,. isstarted.

RANDOM NUMBER FUNCTION RNGLN

This random number function is for a binary m;chinv ;and the constants must becomputed according to the number of biLts in an inteoer ,7ord. The numbersgenerated are uniformly distributed in the interval 0 to 1.

The function is called from the main program by a statement similar to the

following:

A R Ci., (I.:)

Wherc A is some floati ;,,inL variable name and TX is som, integer variable

name. The argumenL name IX need not be te .T%,, in thie main program and thefunction. The argument must be initiol Hoed to zero in the main progra . Thelocation of the initializing statement is important and depends on tho resultsdesired. If it is desired to have differejt sets of random numbers for eachof several different sets of computations (jobs) thait are run sequentially onthe same progran, then the argument must be initial ized at the very beginningof the program and never reinitialized. IT it is permissible to use the samesequence of random num'ers for each job, tie argument must be initialized at

the beginning of each job. The advanta'o of this latter option occurs when oneof the jobs must be re-run for some minor reason as the same random numberswill be used and the results will be comparable.

Three constants must be computed by the following equatior.s:

Constant one (Cl) 2 ( + l ) /2 3

Constant two (C2) = 2" -1

Constant three (C3) = l./2.

Where: B - number of bits in an integer word

The constants for some of the common computers are listed In the following table:

INT J:GER CONSNATSCOPU'fER WORI) Cl C2 C3

GE 200 Series 19 1027 52/4287 0.1907348631-05GE 400 Series 23 4099 8389607 0.1192092901.-06IBM 360 Series 31 65539 2147433647 0.465661287E-09IBK-I 7040 and 35 262147 34359738367 0.2910383046E-10

7090 SeriesUNIVAC 1108 if

CDC 6000 Series 48 16777219 281474976710655 0.355271367811-14

11 L(HIBIT l

April 1960

EXHIBIT 2

Crout's Method

One of the best methods for solving systems of linear equationson desk calculating maohines was developed by P. D. Crout in 1941.This method is based on the elimination method, with the oalculationsarrasged in systematio order so as to facilitate their scoomplisbaenton a desk oaloulator. In this method the ooeffiolents and oonstanttoes of the equations are written in the form of a "matrix," vhioh isa recatogular arna of quantities arreae in rows and coluns,

The method is best explained by an example. Suppose that in amultiple oorrelation analysis it is required to solve tLe followingsystem of linear equations to obtain the unknown values of b 2 , b 3 , b 4

snd b5 .2 b 2 + E,2 x b .,- b 4 + -2x5 5 - x ix

22 b £xxb b5 1 2 +2x +b2 E 2 b + Ex b + Exx

X2 2 3 3 314 4 3t5 5 1 l3

ZY b2 + LExx b3 + 14 b + lxx b 5- EX 1'

Lix5b a3x 3 xx b4 + Ex2 b Lx2 + 5i b ' E4.

For si plioity lot us replace the ooeffioie-'q of the b'e by the lettersp, q, r and a, and the constant terms by t etter t, using subscripts1, 2, 3 and 4 to denote the respective equa. onss.

p, b2 + q b 3 + rl b4 + 1 b 5 ti

P2 b2 + q2 b3 + r2 b4 + s 2 b5 5 t 2

p3 b2 + q3 b3 + r 3 b + 83 b5 - t3

p 4 b2 + q4 b3 + r4 b4 + % b5 - t4

A continuous cheok on the ooputations as they progress may be obtainedby adding to the matrix of the above system a oolmn of u's, such thatu - p + q + r + a + t. The matrix and oheok oolumn are written asfollows#

EXEMBlT 2

I

p1 q, 1 ~ 3

P2 q2 r2 2 t2 U2

P3 q3 sr 3 3 t3

p4 q4 4 %4 t 4 %2

The elements pl, q2, r3 and e4 form the "principal diagonal" ofthe matrix. Ekamination of the original equatlons shows that the oo-effioients are symetrioal about the prinaipal diagonl, i.e., q, - P2rl -p, 'r2 - q, 1, - p4l 2 " q% and 63 - r4e.This in oheracteristi of the system of equations to be solved in anymultiple oorrelation analysis. Because of this symmetry, the oompute-tions are considerably simplified. While the Crout method my be usedto solve any system of liner equations, the oomputational steps givenhere are applioable only to those with symetrical coeffioents.

The solution oonsists of two parts, viz., the *amputation of a"derived matrix" and the "baok solution." Let the derived matrix bedenoted as follows;

INN

3 K 3 5 3 3

P4 Q4 R4 S4 T4 U4

2

E)XIIT' 2

The elements of the derived matrix are computed an follows

P1 a Pi P2 = P2 P3, P3 P4 -P 4

QR _r,_S T Ui = 11 p1 1 Pi 1 " u

Q - q2 - P2Ql Q3 "q3- P3Q1 R 2

St 2-T 12 u2-lP2S4 " - l S2 - 2 2 2 " "

R r3 -QR -PR R4 r R2-P, S Lt433 3 2 3 1 3 r 4 'RRP 3

T ' t 3 -T 2 Q 3 -T1 P IU 3-U 21-U 1.

33 3R

S 4 -s84 - 4 3 - Q 4 S2 - PSl44

t-TR-T2Q.-TIP u3-U2R- U F

5 R 4 U 4 " R 4.U 1

s -s4 - 4 - s - p s

The general pattern of the above computations, which my be appliedto a system containing any number of equations, is as follows&

(1) The first column of the derived matrix is copied from the firstcolumn of the given matrix.

(2) The remaining elements in the first row of the derived matrixare computed by dividing the corresponding elements in the first row ofthe given matrix by the first element in that row.

(3) After completing the W th row, the remaining elements in the (n+l)

th

oolumn ere oomputed. Such an element (X) equale the corresponding elementof the given matrix minus the product of the element imediately to the leftof (X) by the element immediately above the rinzipal diagonal in the samecolu as (X), minus the product of the second element to the left of (X)by the second element above the principal diagonal in the sam column a (X),eto. After each element below the principal diagonal is recorded, and whilethat element is still in the oaloulator, it is divided by the element ofthe principal diagonal which is in the earn colum. The quotient in theelement whose location is symetrioal to () with respect to the principaldiagonal.

3tEXIB IT 2

(4) When the elements in the (n+l>- column and their symmetricalcounterparts have been recorded, the (n+l) t h row will be complete exceptfor the last two elements, which are next computed. Such an element (x)equals the corresponding element of the given matrix mimis the produaotof the element immediately above (X) by the element immediately to theleft of the principal diagonal in the sam row as (X), minus the productof the second eiement above (X) by the second element to the left of theprincipal diagonal in the same row as (X), etc., all divide, by theelmnt of the principal diagmal in the 1 row as (X).

The check column (U) of the derived matrix serves as a continuousoheck on the computations in that each element in the column equalsone plus the sum of the elements in the same row to the right of theprincipal diagonal. That is,

U 1 1 + R 1 + S + T

U2 1 I + R2 + S2 + T2

U - 1 + S + T5

U4" 1+ T4

This cheek should be inAe after completing each row.

The elements of the derived matrix to the right of the principaldiagonal form a system of equations which may now be used to computethe unknown values of b2 , b V b4 and b5 by successive substitution.

This is known as the "back solution." The computatios are as follows:

b 5 = T4

b4 - T3 -S3b 5

b T Sb - R b.3 -2 2b5 - It

b2 T S1b5 - Rlb4 - Qlb3

It is very important that the computations be carried to a suffi-cient number of digits, both in computing the coefficients and onstantterms of the original equations, and in computing the elements of thederived matrix. It is possible for relatively smal errors in thecoefficients and constant texias of the original equations to result inrelatively large errors in the computed solutions of the umkznna. The

4

MXIBIT 2

greatest souroe of error in computing the elements of the derived matrixarises from the loss of leading signifioant digits by subtraction. Thismust be gmrded against and can be done by carrying the computations tomore figures than the data. As a general rule, it is reoommendod Vkatthe coeffioients and constant terms of the original equations be carriedto a sufficient number of decimals to produce at least five significantdigits in the smallest quantity, and that the elements of the derivedmatrix be carried to one more decimal than this, but to not less thansix significant digits.

5EXHIBIT 2

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EIIT 5

DaFIITI(S- 7235-42340

AC1 - Alienation coefficient for station 1AC2 - Alienation coefficient for station 2AC3 - Alienation coefficient for station 3ADJ - Plus sign indicates value smaller than upstream sum by

tandem testADJI - Equal sign indicates value adjusted by tandem testALCFT(IK) - Alienation coeffiient arrayALOG - Computer library function of natural logarithmANLOG - Number of logarltmANYRS - Number of years of recordAV(I,K) - Muan logarithmAVG(I,K) - Average of the generated deviatesAWG(I) - Average monthly flow for a stationAVMN(I) - Average logarithm of flow for minimum 3 consecutive monthsAVMX(I) - Average logarithm of flow for maximum 5 consecutive monthsB(L) - Beta coefficientBETA(I,KL) - Beta coefficient for generation equationBLANK - Blank spaceCROUr - Program subroutine to solve simultaneous equationsCSTAC(KXK) - Coefficient by which flows are multiplied before adding in

a combinationDABS - Computer library function of absolute value of double precision

numberDQ (IK) - Increment of flowDTRMC - Determination coefficientE - Letter E indicates estlmated valueFAC - Temporary factorI - Index for calendar monthIA - Indicator in column 1 of first card for each JobIANAL - Indicator, positive value calls for analysisIENDF - End of file indicatorIGNRL - Indicator, + 2 calls for computing generalized statistics

and + 1 or + 2 calls for using generalized statistics forgenerating flows

IMN(I) - Month sequence number of last month of 3 driest consecutivemonths

INH - Calendar month number for first month of water yearIX(I) - Month sequence number of last month of 5 wettest consecutive

monthsINDC - Transfer indicatorIP - Month number for precedin monthIPASS - Sequence number of pass (subset of stations)IPC!Q - Indicator, positive value calls for writing discharges on tapeIPCHS - Indicator, positive value calls for punching statisticsIQ(I) - Fixed-point conversion of flow values

IXIImT 5

UL -

IQYAP - Tape number for storing flownIRCON - Indicator, positive value calls for flow reconstitutionISKz - Positive. value calls for varying flow Increment (DQ) to

mw skew zero.ISr(x,L) - Sequence moer of upstream station for tandem testISTA(IC) - Station nmbterISAC(OC,K) - Station nmbter in a combination,I3I'AN - Temporary station nmbterISTAP - Statics sequence niumber for all passesISTAT - Yap. number for stor ig statisticsISTII(L) - Station nmbter of domsre tandem statics.IITri(J L) -Station number of upstream tandem stationISI'X(LS Station nmter of independent statics for consistenices testiarr(L) -Station number of dependent statics for commistences testITEMP -Temporary variableIYMP -Temporary variableITNPP -Temporary variableITP - Temporary variableITMN - Transfer indicatorIX - Temporary variation of IIlK - Argument for random number functionIYR - Number of current yearIYRA - First year of dataIYRPJ - Year of start of flow projectionJ - Index for yearJA - Sequence number of projection yearJTT4P(L) - Matrix column numberJTP - Matrix column number.11 - Temporary variation of JJ)XI'P - Temporary variation of JK - Index for stationKM - Dimension limit for number of consecutive monthsKPASS - Dimension limit for numiber of passesKSA - Dimension limit for total number of stationsKSTAC(KX,K) - Index number of station In a combinationKDI'AP - Dimension limit for total number of sations1(1 - Temporary variation of K or combination sequenceKYR - Dimension limit for number of consecutive yearsL - Index for related stationLA - Temporary variation of LW1'AP - 1.imber of records up to present position on tape IQiTAPLSlA! - lumber of records up to present position on tap. IODATLTJ4P(L) - Matrix row numberLYP - Matrix row numberLTRA - Letter ALX - Temporary variation of LLYRPJ - last year of each projectionM - Serial number of monthMA - Sequence number of month of projected flow

2

uMWIiT5

MO(I) - Calendar month numberMPASS - Temporary counter for number of passesMTHPJ - Calendar month of start of each projectionMXRCS - Number of years in each period for which maximum and minimum

recorded and reconstituted flows are desiredN - Serial number of period of flowsNC - Counter to prevent continuous loopingNCA - Counter to prevent continuous loopingNCAB(I,K,L) - Number of values and cross products used to compute correlation

coefficientsNCB - Transfer indicatorNCOMB - Number of combinations of stations max. and min. quantities

are to be computedNCSTY - Number of consistency testsNINDP - Number of independent variables in regression studyNJ - Number of years in computation sequenceNLOG(I,K) - Number of logarithms used to compute frequency statisticsNMNMX - Number of months following dry season and preceding wet seasonhnMfXN - Number of months following wet season and preceding dry seasonNPASS - Total number of passes in jobNPROJ - Number of projections of future flows from present conditionsNQ - Counter for number of flowsNQTAP - Total number of records saved on tape IQTAPNSMX(L) - Number of upstream stations in tandem testNSTA - Number of stations in analysisNSTAA - NSTA + 1NSrAC(KX) - Number of stations in a combinationNSTAT - Total number of records saved on tape ISrATNSTAX - NSTA + NSTANSTNP(I) - Number of stations in a particular passNSTX - Number of stations in current pass that occurred in preceding

passesNSTXX - NSTX + 1NSUM(K) - Number of stations upstream from a station for tandem testNTNDM - Number of tandem testsNVAR - Total number of variable in regression studyNYMXG - Number of years of generated flows in each period for which

maximum and minimum flows are desiredNYRG - Total number of years of generated flowsNYRS - Number of years of recorded flowsQ(M,K) - Monthly flowQM(I) - Monthly flowQYIN(I,K) - Minimum flowQPREV(I) - Flow for previous monthQR(M,K) - Identification symbolQSTAP(I) - Temporary storage of QPREVR(K,L) - Correlation coefficient in a given matrixRA(IK,L) - Correlation coefficientRAV(K,L) - Average correlation coefficient for 12 calendar months

3

EXHIBIT 5

.. .... ..

RMAX - Maximum consistent correlation coefficientRMIN - Minimum consistent correlation coefficientRNGEN(IXX) - Program random number functionRi - Correlation coefficient being testedR2 - Correlation coefficient being testedR3 - Correlation coefficient being testedSD(I,K) - Standard devaition of logarithms for calendar monthSDAV(K) - Average standard deviation for 12 consecutive monthsSDV(I,K) - Standard deviation of the generated deviatesSKEW(I,K) - Skew coefficient of logarithms for calendar monthSMQ(J,K) - Maximum or minimum flow for month or durationSQA(I,K,L) - Sum of squares of first variableSQB(I,K,L) - Sum of squares of second variableSUm - Average correlation coefficient of matrixSUMA(I,K,L) - Sum of first variableSUMB(I,K,L) - Sum of second variableT - Large positive constantTEMP - Temporary variableTMP - Temporary variableTMPA - Temporary variableTMPB - Temporary variableTMPP - Temporary variableTP - Temporary variableX(I) - Value of independent variable in regression equationXINCR(I) - Iteration value for flow incrementXPAB(I,K,L) - Sum of cross products of first and second variables

4

EXIBIT 5

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C WASTE CARDS UNTIL AN' A IN COLUPN It FIN$T TITLE CARO 1043C to CARO A to 1044

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140 WOTE (6,*1701 hYNSN3TAptKCflV4N.PAS3 1060ITO FOMAT (119i4 rIIMEWNO ENCECEt #5%g4WNYNSI4*1X$4"mNTA9I3pSX. 1061000

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IF (LYIPJ.IYRA.GIE.KYMI 60 TO' 160 1069cq * * * SET CONSTANTS 1070

tws**1071t4SIAA6'.ITA01 107?NSTAI"T'1A4005A 1073

Tmeqqqqqq 0 1075

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NTNON(J)80

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c . CARD J *4 10l1

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220 RFnIOVAP)TTNP,(0CNK).Pu1,ITP) 1108L4YAPLO!AP+1 1107IF .fT4TA(K).NE.IT"~P1 go TO 220 W

230 IWPPN£TPPP.1 1109IF0"Pt-T1E:P 7"n To240 1110

LSA3LST?*11113IF (!11P.EQ.!STA(X)) 60 to 250 111*Gn Tol 230 1115

240 REA"CTSTAT) 1116LATATULSTAT#1 1117HPASS84PA38+1 1118tTEMP32J8TNPp (PA33) M19JV.PRO 1120Go Tr 23fl 111

250 CflPKTtk'iE 1122On ?60 XmI.NsTN 1113

On P60 ?vist2 11es260 fLOq(I.E)uNVRS 1128270 IF(!AN'AL.6T90) WSTAWNSTI 1127

0n 24f0 TwIP12 11e64o0(1)3J1PNTH* 1119IF(PO(I.LT.t3)G#0 TO 100 1130HM ane)~?(!)*12 1131

260 CONTINUE 1138I7(NCPMR.Lf.0) go1 TO 320 1133

C IOE4.TIFY STATION COPRZNATIO4S 1134On 300 NXlOCOMA 1135

14 CARD 0 ** 1138R!*D5.3)ITP CItAC(.L)LSI.TPI1137

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MTN04 CrP1AS)?'TNDN00 540 Ly1-1.NTNDM 1 146

gE00 3) YSTN (LW) .11~'P.(ISTTCLXL1,L.1,1TMPI it&&WQITEC6.33()) iXaISTN(LIO, (JSTTLLX,L),LSI, yyhpJ 1149

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C 7Ij1TJATE -1, NO RECIRO FOR ALL FLOW6 117')a 360 Mhl.KM 1156

AfI(MOK)U.-10 1159am 370 1.1,12 1160

00 IN 11. 1163

37C CONTINLIE 116434C Cr'NTIt~IE 1165

YF(NCSTyLE.0) 60 TO 420 1166~4R!TE(6p. 1 1167

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4"0 IqlTT(b.JII01 ~ L#TT(L)oI.1TYCL) 1173

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C A;INSUf3SC41PT TO YEAR I 14044"C JaXYqvYP4 I 191

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C S~fl.E FLOWS Ji~ 3TAT1C'N AND MO.;ITM ARRAY 1197Ma "Jo,11.1 1 1194rfI 490) ?21.12 t 199

~ 1 1200SGO ril. 490 1201

1203

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SIC CO'KTINUf 1225S2C CMNTINUE JIM2

C REDUC~E STATIONS To THOSE IDENTIFIABLE 1227N4YhCCKV, IPA3S)2LX

530 CON~TINUE 1229C IDENTIFY STA?IOCS IN TANDEM 1230

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9;!C Cnh?rNIJE 1235SAC TSINCLX)xK 1236

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570 CO~NTINUE 1242SAC IATfK.LsIPASs)zKX59C CnN!TINUE 1244

C 10E~irIFY PAIRS CF STATIONS FOR CON31STENCY TESTS 124560C IP(NCSTY.LE.0) GO TO 630 1246

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610 !ITX(L)uRc t252GM O 7 30 1253

62C ZATY(L)XK 12S4630 CiINT!NUE 1255bac cf"xTINuE 1256690 ITMp3NSTA~jCtPM 1257

CD A A 0 1 4AXC AND MIN RECOiNDEn VOLUMES 0 tOt*0f t0f t001258

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EXH4IIT 6 4

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C STAwiT NEW ACCUMULATIONS WHEN F40W MISSING 1369oJso 1290TmpmO. 1211YMPASO, 129ZGO To 770 1293

?10 TEMPX0(fl.K) 1294C I-MONTH FLOWS Iq

tVCSMOL28,K) .rT.TEMP)SMC(28,K)uTCMP 1299C b.MflNTM FLOWS 1300

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770 CONTINUE ISISr~0 nrINUE 1316TFlMhUNO 1311AV~tl K2A VG (k) /TED4P 1318

7 CnNYz'.uE 1319XTE(6 800)1320

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Ble FOnmAT ($H AT&#12I7,3SH S1MO b.MO 54*NO AV 140) 1323000I TPPz'N3yA*NCflmo 1324.)r 431) Kz'iITwX,rTHP 13a5lTPAvrfl(X)*.5 I £26

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400 Cn~fINUE 1361942 al~~ 1362

On 970 j.1,WY4S 1363On 960 1.1,12 1364Hmmm I 1365tF(0CM#K).E0."le) GO TO 950 1366

C REPLACE FLOW ARRAY WITH LOG ARRAY 1361TFMPAOG(gC(i.)*fl(I))/2.3025I51 1368r(0,KuEMP 1369IF(K.LE.NSTX) GO To 960 1369-2

C SUM, SnUARES, Ahn CUBES 1370Lv (1*K 3uAV CT K) .TEMP 1371$fA(r,K)2sfl(I,K)+TEiP*TEPP 1372SxEA(rN)3SXEW(1,K)TEMP*TE4P*FMP 1373GmTO 960 1374

C MITSSING FLOWS EQ2UATED TO T 137595C ji(m.K)=T 1376

9Lc CnklTINUE 1378970 C"n.YINUE 1379

!~W.E. Gfl ~ TO 1180 1379o2!wTW~nO1380

n~l lono 121,12 1361T7PL0G(DK) 1302

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T~w~SO C. ()1387

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toic Fn;."AT CI'.t5,8i4 mcL&F.12FO.3) t40100O

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iA'1C "IU-47 ($l%,h~IoCuT.F7.2,ltF8.2) 1407000

1 f,' p61C~C~,Q!11)1010AC lr(N.AT (q.514 1, TO 18 14100

JF(?n0C.LE.nj f;- 7 1180 1411C T'E FLLl;1dNq ACUjTPkE WILL ADJL3T THE INCREM4ENT TC 1412C TRY Tn CdTATIN ZERC SKEW 1413C CHAI%C~E THE FCLLC'wTmW. 3747 T9 I8'CZs To ACTIVATE 1414

IF(TAKZ.LE.0) GO TO 1180 1416lyps-11 1411,n ti10 t31.1 14111421 ?* I 1419on 1080 JaloonYs 1420

E VH6T

6*6

YV~f(f),I().1O#T) Go To 1070 1422T",Fxrl (pip ) 1423J (M.K)UlO."*TMP nfo(I*K) t424Goi Tn 10ao 1425

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C QEfluCE 311~8SCRIPT9 OF SU03SEOUENT 3?ATTON8 1443On 1170 KXSK.N3yA 14441.sTA(Kx)mISTACXWa1) 1445imj 144ban 1130 JV1,NYHS 1414An 1100 1M1 1 12 1446

r~i ~6A TjV214159

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WIC c'".rpUE 1456nnfl 910 1457

110Ccn CntNiIF 1436

TFCTsjCP?.LE.d)) GO TO 1370 14160CF* * * * * A~jtjqlmENT Of FRECUENCY STATISTICS TO LIP4G TE41N 11 * *a 0

Or 1 191) KaltiSTA 1463oA 1190 Lml,NSTAX t6NC44N(1 * K,L) cA 14653tk&!1.KL)MO. 1416bS1.I"IC!,I(,)0O* 1467SrA tT.K.L0. 1460S1,;rT#9,L)V0. (469wP An~(I,, L.) =A 1470af!(*,K *1)Z . t 171

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,(Vcx~l1474'11 1 1473nn 12PQ jaiol'iS 1476D00 1210 141012 14177

TI MP05 (P* ) 14791FrFrP.Er).T) Gil to 1210 14810(3n 1200) LUM)(,NTAW 1461

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St)4CI.4L)~ll.JqCTNeL)Tpp1486

IF(L.GT.NiTA) GO TO taoo 14qa

ova EVMTIYST 6

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.Sr'AI (I# ,1*K 313 A I #)(L) 1495SI A F(I #* .,K) 23) K i 1 K L) 149

l2~C Cfl~I~uE1498

1210 CnKTINUE 1499I220 CnNTpIJUE 1500

t2CcIN'C 1501[In 2K4 K*IvN3TA 1502

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I (T'PP-LT.O.) TlIPP0O. 1514ma (TK.L)T~lP...51515

T -Pf'z TP.T0P4i.*/TEmP) /TEMP 1516kF (TMPPp.LT.O ) TmPP3Q, 151751C!,KL)Tm4PP**.5 Is19

(FeT'4P.LE.(i.) G;1 TO 123M 1511! 0 %32WP1nf(I.L)TPAT)IPf/TFMP 1522r 1523

tF('4ALT3)Tmpau.Tmps 1520T'fP.':y 'PA AT 'PA / 1 -P Isas

IfP(TmPA .1 T.0.) T44PA:0* 1527.A(f,K,L)TH4PI*T~lPA**.5 12

L A =I.

tf (L.ILE.N9TA) GO TOJ 1233

fr(' P.Lr.1) -ATP212t. -A -

1235 rF(Io(I.K).LT..0001.OR.SOCZTP,L&).LT..0001) GO TO 1230". T 1240 1529

1530

15341?M. I'.TTNUF 1535

ITh 1~AK=1,0TA 153?

1539

L 1540154a1(L.K.ACKL~.~J)GO TO 1270 1502

'k~'GfT*L).L..PLUG(IX)) Gr Tn 1270 1543T'IrI2t.CAPC?,K,LJ 1544

"'r'=LPGTL)1545fV(TP.Lt.TE'4P) GO TO 127?0 1547Lva t. 1344

re~varp159127'C CM' T!4UP 1551

I )I .LE.0)) rO To 1280 19f'oiCri 15,13T" 0!AA(KL)/SnR(3I,K,LX) 1550r"'AgSII'4A C? K#LW) TMPF 1355

Evp~T8Trr 6 .8.

T"FuSup4Iq CIKpLX) /T'4P0 15As ,K.):TMPA4+(AV(TLX).TINPI.1aQA(1,KLx)aymp M3r C To K)8OA (I vK LX) +(SO(1 tLXf) 3(l1S (I# K.L0 ) *AI#CK,L U *a2*1iP 1598

C LOJUST SYAND&II OEVTATON3 FOR COJNSISTENCI 1560C (NC.E0 TO; 340 5

KCISTY CLX) t564LUXISTY cLir) 156500 1321 t1112 1566TFHP=PUAVCT,9).AYCJ,L))'3. 1567IFCAVCIX).rTAYCX,L)) GC TO 1300 1568TFPzTEM0+SflCIN) 15691F(1,0C1.L).LTflmP) Gt, TO 1310 1570

IFCInCXDL) - TEmP) t120,1320.1310 157e1300 TFmpzyEmp~gnCI,1C) 1573CF(5n(IL).GT.TEmP) GO TO 1310 15741Fv~a:5nC,K)a2. - TEMiP 1575

IF(qfftL.rE*TEPP) GO 701320 15761310 3'C,L)RTEMP 1577t3PC C,.,TINUE 157a133c C0m.INuF 1579JF1FTR4~S.f5y.) GM TO 28e0 1 sma134C 1F(TkOC.LF.n.AKfl.NC3T'Y.LE.O) GO TO 137 1501-1) 1TF (b. 1350) 1542t3SC rnrATC/39H FRE9iiENCY STATITIC3 AFTER AOJU3TMENTS I 1583

(,n 1360 Xm1IoNSTA 1585dIQIl'EU,.1OIO)ISTACK),CAVCTK),Zu1l,12) t586

1589136C COPKTINuE jgqOCG * * * * * TOsAIS~FlP To. STANOI)DIZE0 WARIATES we* a aa aa13 7 C '1' 1420 Kvl1iSTA 1592'Is1

1593On 11410 Jxu14YR3 59.0~ 3,12 m+It~

OR(Hx~zSANK15961F(n(NK).EQ).T)GO TO 1400 19IFUqnTK).Erj.O.)Gtj TO 1390 1600

CEAANTYPE III TRANSPORM lOIFCSkEW(.K7.FG.O.)G0 TO tiOO 60TF P.5*KEl(I#K)JaOCMsK)+1 1604*yvx 160SIF(TENP.E.n.2GO TO 1380 1606TV 'PM-TEP 1607

* 16041 3PC 1609G1i TO 14lO0 1610I.ICr~.Tu

161111cC CfII.TTNF 1IEIGICCnKYNUE1613

C It a * * * Ci'~tIT SUMS3 OF srtJANES AND CR03S PRI1OICIS a ai a a1100' l4Ob kU1.-STA 1616

rn 1030 L3t.NSTAX 1618.IHA C!K,L):o 1620

3"'A low* )ZO,1620in~~f(TKPL)M0* 162210£ '( T * K.1)0.

1624

IU4C (.Ko)mO, 162!

4&(Toxx~sl,1626145C CO'.?IvuE

1628

-9- EvHRIT 6

)Iri 1540 KZI,NSY4 1629KVZK~t,630,-*1 1631

nfl '460 J:1.NYHS 163a

n 1470 IC10i2 1633va . 1 1634

yrmpacnM#K) 1635IF(TENPsE0.T)GC TO 1470 163bDO 14160 LzWXNSTAX 1637

c SUBSC$41PT3 EXCEED1ING p.574 RELATE TO PRECEDINGl MONTH 1638

LY*L.NSTA 1639IF(LXLT.1) TmPxQC'4pLl 1640

IFCTHP.En.T)Gl) To 146i! 1612

c Cr~i'iT A"O JiI5 ChLY REC04floD PAIRS I64l~A (I XK t.) auvAI (1 ,Kpt) 41 Ib44

IIA( I PKA )300 A(Is K 1) 4TD'P teas31 ~ fi(7,K, L 'i I~4 (T ,I ,I)4 ' p1646

3rJAu*i:7A (T,K,L)*YEIPPTENP 1647

IF(L.rIT.N5TA) GO TO Id4bC 1610

JJ (TK,L,K)=J.14Aj (1,KaL) 1654SmA (K.L,K):Sjn (r,kPL) 1654

wq(I .L. K) cxPAlCIe( Kl ,LJ1651460 CnTINUF Wy~14~7C rmNTTYNE tb58141AC CflA.TTNIUE 1659

C . * * a CuMPUTE CUH4EL4TIAlN COEFFICIENT3 a * * aa1660~

On 1530 T = tI I 16bl'10 1520 LZKX,NSTAX 16012

LV=LNsTA 1663C EL14INATE PAIRS OITP' LE3S TpiAN 3 yR3 UATA 1664

IvCvCAB(!,A,L).LE.2) GO TO 1510 1665TFNPZNCAPT.I(.L) 16405

TMP~(.ljA (,K,).5JMACK.~a5UACIKLrEM)*C(IKL)SJ t 67

p K ~L) *SU43 I PK L) /TE~lP) 1668i

C ELTrITNATE PA1;45 WITH ZEkO VARIAN~CE PRODUCT 1669)

!F(TF'P.LE.O.) CS1 TO 1500 1670TmP01231 * 167T"IPAXXPAf3C!,K ,L) .5IJ~'A (1,K.LIaSUI4ICIKL)/TEMP 1672

C '4FTA1N ALG~t1qA1C SIGN 16737F(T 'PA.LT.0.)Tmr~z.TmPP 1674T' -P A: =TMP A * T45, A / Tf!~P 1675:;'(VI4,LET!)*TMc'Aaa.5 1676

yp~i! 1677L AL 1676

IL C *.i.TA) rfl TO 149 16801 1 -1

IFCtTP'.LT.1) ITPc1a 1641LAI X 16ma

( ?fl 1910 1684

i S 0C 4 A( T KL) a(. 1665

SilC :rfI..0T.K'TA) GO TO le I~ 16fl* 1., K) UR4A(Tv ,KL) 1697

15?C ClIPYINIIE 16p8I 53C C? TIN iJZ 189154C nKTINIJJ Ith90

inr TMl 2170 1691

156C FfRMATC/ISN DATA OUT CF CgROEq) 1693r,0, TO 190 1694

C;4 * a * - o at PE40 C0U'Rt'LATir% COEFICIENTS 16951SCOm 163o KUIMSTA 1696

19 (i(.EG,1)Gf TO 1800 1697

ITONK1t 1690On 1590 L21-1TP 1699

C CuRRI4CT IMfNTh CCOPELAYXON 1700

EV~rUI?*t.1

C A* CARD L *01701

;AO(5.7o)iT'4PITE4P. (R&(TKL).zul12) 1701*" Vf(iL) 378(1 *K. LI 1703IFCTCNWL.FQ.I11TAY(K)ITVP 1704IF(TTMP.NEI~sTA(K)IO TV! 1550 1705Ic(1TEMP.?JE.ISTA(L))GC TO 1350 170*C-i 15AO 71112 1707

1380 flA (T.L K)NRA (!,K,L) 170a1590 CflhINUE 1709

C PRECEDOING MONTH CORRELATION 17101600 LV:'k-S7AA 1711

IF fIGNPL.EO.1) LXQNSTA*K 1712LAMNSTX1713

IF UIGNRL.EJ.I) LAgLX 1714rr1 1610 LGLX,LA 1715I!P21.-ISTA 171b

c a CARD K( OR M A* 1717

M79IF(k.EQ*1fl8TA(ITP)=ITE0P 1720IF (IGPJRL.Efg.l) PAYCKpX)9QA Cl ,'L) IM2

XF(ITMP.NE.IA(K))f',O TI! 1550 1?72JFI9PN.-9AIP); TO' 1550 1723

1610 CrNITTNUE 1724011 16?0 71.12 1725

103C CrM\TINUE 1727C a * * * READ FREQUENCY aTATTSTICq A Aaaaaa aaaaaaaa 1728

01h 1640 XK:1,NiTA 1729

C ARO84 N C4 0 A* 1730

rP(TTP.NF.TSqTA(K))Cfl TO 1550 1732

C GENF'WALIZEO STATISTICS ON ON~E CARO PER 3TATInN 1733AV44V K)ZAV (1.K) 1734A Vtlk~(K)Z3A V(2, K) 1735

S~~Av(K:AVCK)1737

1739.2

IF (IXK) L.)i1X(X)m:PYC),12 1740IF (1M')tc) .LT.X) I~iw1(K):IpN(K)+%2 1741

C aaCARD P 1a 743

?F(TTP.PJE.XSTA(K))t;(J TO 1550 1745C aaCARD 0 aa1746

qEAf(,Sf)Tp(.qF~K(.).1l.12) 1747rF(TTP.NE.I'iTA(K)).o Yf 1550 1748

C aaCAkO 4 1749

1F(TTP.NE.15TA(K~))flA TO 1550 1751thao C?, TINUE 1752

Cy EFITIMATFJ M1351KG V.'WIELATION CtI!FFICIENTS 17331650 IFfI'1NPL.F,, 1lG(I Tf 3'2e 17,54

tF(NT4.LF.IGO. TO 2311) t755

00), 1720 rm1,12 1756zI:-'I. 173?TF(TM.LT.I)101I2 Il5801 1710 K1.&N9TA 1799

ITP~l(+l1760

It' It)O LUTS 1761C L A~n K ClOR4ELATII!N POSSIBLY m17ds7NG 1768

!F4A!K,).F.(G) O TO 1700 1763~i'*Au1 *17644M1N.1 *1765

C iw SEARCHES ALL QELATEO CORRELATIONS EXCEPT FOLLChING mTm 176*

Or 1640 LXN1.NSTAV 1767Irt ~ TO.) o 1b90 1768

IF(L.FO.LV)Gn 70I 1690 1769TFNPPACIXPLX) 1770IF(L.LE.NATA)GC TO IbbO 1771

.11, EV),rsyy *

IF(LK.LE.NSTA)Gn1 TO 1670 1772

c SOT10 L AND LX P~rSethr PIECINGI NOW 11

T11E4PNLXftN8TA 1775Tt'P*RA TP#EIV1PIT(Npq) 177Gn TO 1680 1778

c L REPRESEPITS CLRMFNT 14O*4YT I 778

Gil T0 1680 t170

c LX AND NOT L NEPOFIENT8 COJRRFNt MONTH 17821610 T&4P~q4(1.LX#0 7)

t6AC IF (Tm0.TEMP.L7..2.0) Gc rr b 1783T4pAU(..TE.P*TEmp)*(..TP~Pe7,P)) F8IF (TM0A-LT.0.) T4PAm* %IRSTb.PAvy"PA*.5 174bTbPP TN P.TEN P.7 $PA 17871'rCTfiPR.Lr.RiiAx) mAxmThPB 188Tep4%TmPRTM*A.TfMPA. 1791IF T490TRisRm~~~ 1190

169C Cfl\IINUE 1791

c AVER~AGE 11HALLEST P~AY AND LARGE31 MEN C0NS1STENT VALUE 1792

IF CL.LE.NSTA)PACJLJ()MOAC!,KL) 1794tVIC CribTINuE t793

tIC CflNTtN,1E 1796172C C'ip.rTNUE 1757

G1 Tn 2311~ 1798Cj * a TEST Fr~f1 TRIAb CC?4JS7TENCY a * * S* 1719

173C NC300 1800174C FAC=I. 1801

~ ~ ~411802I-;UNCA.LTNATA*1Z) Go Te 1790 1803

In TO LS0 1805I75C NCIX 180b

t 7 4 C 1"no180707E' 1b0 111 18019

tPIT-1 1810

C Ko Li AND 0X SEARChb ALL 9ELATfn TRIUS OF COMPEL CCEFS l8121F~Q !A2o mioNTA, Ms1

IT "PD M .1 1814m ISIO LZDTPONSTAX 1813

V (L.Et2.-4STA)G TO 1611D 1816LA41.LNSIA tat?,4I ib.A(IoK.) 1il18

I~wcL~l A19nr 1400 LY.2!TP,?3TAX 1820

I 1~ 2LXN9 TA1821

(L.L.H5T)RS~(ILLW11823

C 5lT~4 L AND LV RFPPESEN? PRECEOINto MOMN 1424t(L.0,T.NSTA)q3:RaCIP.LAeIT~t4P) 1825

C RAI~k Lni'VST CCEF21C!ET47 IF tNC%)N313TENT 1826

Le t(1 ..- aR* 1829

IF(41.GT.02) GC TO t770 1830

I-.1 PZ*p3.ACP.ACJ*FAC 1632

IVfb~4b.L.1*I NZ-1 1633I~W.GMP1Gn Tn 1800 1834

I' nrt 11133P~ t~EL)QNIN1836

IF (I.LE.NSTA) RA(1,L.K)IURPIN 1831Gn TO 1800 tills

1770 IFI1?,.GT.03) GIn TO 1780 1839kmpIbmaj*3wAC1*AC3OFAC 1640

ININS01- 1653

EW,4?PIPIN 6P TO*010as

;A CTt,LX)uRti!N 1044IF' (LI.1-E.NSTA) 181.41O5MP(;n TO 1600 1646

t7A~ IJ~c~1.2.AC*AC~FAC1847

1FC03.G9.R11J) GO TO 1660 149tNOr*1 log0IF (L.GT.NSTA) GO TO 1790 18s1

IF (LY.LE.NSYA) RAClLX#L)DRMINi 1853(fl To 1p00 1814

1790 PA(PLA.IT6MP)21Rm1 1855RA (!PITE0PPLA)24mIN 186

I1IPC CnTINUE 185371510 CrnhfImue 1451tA~r COnTINIJE 1659la3c COnTINUE 1860

IF(NC.LE.N3TA*I?) GO TO 1850 1862,ItTE(6.18a01 1863

1~an FnRiI&T324 CtRRELATTON FATRIX ?NCOP.SISrENT) 1864

18 On r(rNMC.Ef).1) GO TO 1760 18046r * * * * * TEIT FORJ OVEP-ALL CMNSISTVICY a * a 1867

IfEMPSO 186C"1 TM 1870 180§9

i36C tTEMPSI 1870C WHFP1 ITEMPU1D CUPFNT MIONTH uSFD FOR~ ALL %'DFPE4CFNT 3TAS 1571C nTHE,7'I5E. PRCC MTH USED FOR CUeAENT AND SUBSEQUENT ATAS 187

1J70 J4TOfPZNSA 1573.vAQZNINDP,1 1874

?m;160o 0.1.12 1875Tv=Tr.1 1876

C CONSFR'JCY CUP'PLETE COPREL MATRIX FOR4 EACH MONTH AND 8Th 18785M 2150 Kml.p!ST4 18?9

C L IS Rflti NU,4eEq, J T3 COLUMN NUMOIR t8'0,)n P020 L=1,.JSTA 1841LYZL+NSTA 1oseInr 1900 JX10)STA 1883Jv=J+N3TA 1864TFrig *) 18l80,1920.1960 tops

I Al"cT; V(I~ 090. 0100.1900 M8bt8qf q(LJ) 2 JLECA(1,L,J)) 1847006

LTHP(L)CL load3T&PCJ)2J 1889Gr t 170 1800

1QnC IFC(fl.MP) 1910,1910,189' 1841191C O(L.J) 2 OEFiLECNA(I,L#JX)) 1892000

0T 10MXL 11193JTP' (J)Zjw 1h894

fr n 1970 19

!1 7(LJ) 2 ORLE(QA(I#J#LX)) 1047000LymP(L)NJ 1898

J1 T P~P (J) Z L 1849q~r' yO 1970 1900

t94s .tL.J) a OLE(RACPPLJ)) f96100t)LT 'P (1 )KL Me0

J7IPCJ)UjE 1403Gm' TM tqln t904

1 n!C ' T fFPP 8ir) P I ,4r0, 1930 1905194C fFCTTF4P) J9e'0#1920e1A48q 1906197C I(JL)GP(LPJJ 14071450 CMTTNUE 1913e

L11'PL~xX1909C iPECIAL SIJSSCRIPI FOR DEPENDENT VARZADLE 1910

IF (L-0) 144M,23iC.2000 1911194C R(L.,NqTSA) a nPLECA(#x#L)) 1912000

Gm Tn Rojo 1914,fIF (1TEMPGT*0) no TO 1990 1915

-13o Ey"IftI? 6

?olCRfINSAA)* O1LECA(IM.Lt))1916000JTAO(NJTAA):LX 1917

20iC CAANTNUP 1918c tNATRIX COJSI3TINT IF CORREL DOES NOT EXCEen t~o 1919

NoO 1920N. C2 ft1921

P03c CALL. OVYCR) 1923c *==uCZuuau 1924

1FfiATR11C.LE.l.) GO TO 2130 iqq.,WRI (6,0f405 K, I#KOtYRMC 1926

P04C Fn9MAT (/36H4 IN~CONSISTENT CnRREL MATRIX AOJUSTEI),314,p12.3) 19V700c NITH~DRAW 1928v1931

FACuFAC..2 193aIFCFAC.Gr...12GO TO 1750 1933

,0' (%a 1934tnE N* 1935IFCN.nT.10) GO TO 150 19303tImmo. t1137On ?nAO' LCIPtl!NOP 1938On ?o70 LXxt,NVAR 1939IF(L.E').LX) GO TA 2070 1940

TM~a4 CL.LX)1941# ~5U*TM Pp 1942

207C CnKTIUE 19432PC COSTN~pUf 1944TFMP=N1NDP*NtNOP 3965611' S U /TEM P 1946TE 4 PSI)TQP- 1947Ir(T~!mP.nT..1) TENP2.1 1948TmiPm1.-TEMP 19'49On P120 LM1,NlNnp t950JT,-I b 1 1951On P110 LX41TPNVAR 95qCL-LY) a 0LF.CTMPP*TP StJm*TEMP) 193300IP(LY.L-E.NXNOP) P('.v#L)-:4 CL#LX) 1954LTPZLTPI'fL) lsJTP=JTtlP (LX) 15!Vr(.TI.LE.NSTA) GM TO 2100 1957IF(lTP.Lt*NSTA) GO TO 2090 1958LTFtLTP-N3TA 1939J'I'=JTP.NSTA

1960WA(T0,t.TP, JTP) = L ,LX) 1961R4&(lPJTPpLTP!=P(LLX) 1962

?O9C ITM~5LTP 1964L7PZ,51P 1965JT~'aTTmP 1966

TF C.TP.LF.NarA) kA(1,.JT0L7P)=R(L.,Lx) 19#18Plic CnN T I :tiE 1 41,921pc CrNTINUS 1970;nr Tn 2fl30 1971;)13C I;CnTL;,C.GE.O.) GO TO 2140 1972

-Q ITYF (,S 71) 1 , K, 0T~t!C tq73r)T'- "C20, 1974

Pl)jC 1F(oNCA.GT.fl) GO TO 1740 197!;). I Im7NTtiJe 5970?16c Cfl%TINiJE MY7Ir fYTF'4P.El.O) GO TO 1860 3 978

TFITTRNS.EQ.2) Go TA 31CO 1979217C .ep1TyEt, 103 1900C * * a PRINT CORRELATION MATRIX aa ****aa**a*aa 19o~i

IF (TYTA,.L! *n) wGITE (6,24O)PO~) t9p]?1AC FIRNAT (11394 RAN. C"lNRELATflnw COFFFICIENS F0R MAN?N,13) 1984000

IF(CTTROJS.GT.0) 14t.ITE(6#?1903 Mori5) 19#k!P19C Fni "AT (//404 Cfl'jSZSTFNT CVQAELATTON MAThIX FOR ?4ONTH.13) 598,000"Q1TkU6,2?f0O) CI9V(K),1c11.M8TA) 19P7

pIoo ~Fnl~hAT (/3X,3H3TA,18I7) 1948000ow~1T8C6,a21) 5949

2210 !AWkATC201,19H '4174 CURiOEWI "OI)1910

EvWMTIT 6 14a

flo n.ao xu,,4 1 qq j401'"9(60223n) M~&~ SAtKtIPSA ,2

P230 Fnpm47 tt,5~73 q93 000

,; 0T~F6.2I~) 1990

224C iFl-,OA7 (20%,3iITH411 PkECEDTING g4ON7 AT A8OVE STATION) 1999000IP3'157A,: 1996On ;250 K23I143TA 1997

P250 '-:DTClS,1A(K)(RA1,(.L),LUITPDNaTAX) 199SA2AC crWTI1UE l9q9

ZF(TANAL.LF.O) r' To 3tnC 20001F(TIRNS*AF*Q) or TO lbsfl Pool

IF(IPCHNI.LE.nl Gos To 2870 2002C PU'ICH f5E~.rNTAL ELEmENTS OF MATRIX 2003

t'f P30o xwj,)* 7& 2004

IF 70EQt rU o8C 2005

P2C "I1 A2 90 LU*NSTAA,0.TAX 2009

1fF 4PzL.NSTA M010

P2C Qlikfor O 2011

rn rn 2850 2013CL * 0 * * * * ECIk~TjTUTE MTS31N. QATA II It II II IN **UU 2(114P310 F(TANAL.LE.0) GO TO 31PC 2015

19 (TQCSK.LE.6) rO To 2610 2016,:VAP2N3TA*1 P017"421 2016D', pb00 32184YRS P019

2021

2023

01 PSAO 1K31,WqTA 2024IFCGC(m.N).IF.T) Un To 2580 ?025

c FL3wo r(.;4F.LA?irh oi&TRiv FOR EACH MISSING FLO% 202b

Ntkpso Lt4T 202V

LYZI*NSTA 2029TIvCOML).Nk.?) 6n TO 2320 2030

117(n M-IL).F'I.T) GO To 2 39f) 2031Nn7NflNnOp* 2032

lyc"P~yhop2033x( rnv~q~m-vL)2034

4(PsTNOP.k.VAhi) I O1LE(RAAI,#,LV)) 203500070 T 2330 203b

232C Nr~.OPaNTP.Op*l 2037ZpIT pikP 2038

xr~ ~r')EOC.L)20392 0~ECUAI,14L))2040000

.131C (',P0TtDlP P .0 041M00IrrL.E0.NSTA) GO 10 2JqC A042

0r 23JA( LANITP,NrTA a044

JIII1114TA &1045

1F(i(m.L).fQ.r) r.O To 2.150 2006Cn.tA.~~n)ro ?C ?340 20'17

~Y9.~Pu~ff'4'*12048~e~Ifl~T~uP 2 IIL(RI(,LA))2009000

nn TO 2370 20l0

113JC 1(c1LaE.)GO TC 238n 201

,u~bplr.jI4Pt) a rI1LE(RA(IvL.JX)) 2053000Gn TO 2370 2054

P35C IF2M.&.C3T)G TC 1360 20552056

~4tN~Jfl. !E~P)* OL~fO CIL' .x))2057000Gn TO~ 2370 25

a36C 400MlL).(.~Q TC 1300 1019IT"~PIITE"P*1 2060

2(TnI1p a rB.ECA(Iv#LtLA)) .7001000c £00 SYH'PI!TRICAL ELEPEIKTS 1081

also £y"IbTT b

a37C Rf1EMPmNItJDP)2R(NINDPo, hP) 26P3AC cnh?pkuE Z064

p3qC CnN?!NUE 2065IrCN1INOP.GY.e0) GO TO 2400 2066?N0~pot 2061Y(I)S0. 2066Pria1) 8 1.000 2069000LX3S.+4STA 2070R(I-14VAfl) R D0LECQAC11KLX)) 2071000

140C TTEHOUNNOP,1 2071'(inl ?d LNl.MINDP 2073

2411C !7fL.ZTfP1=(LNvAR) 2070C 222:2X8389 207124a2C CALL CpOUT (q) 207b

C m=vu2u2077ITE04PUNINOP41 2076TF'HPu1 2079I p'nezo 2080nln P0d40 Lx1,JfNnP 2081TmPUDAAS(R(L, !TEMP)) 2082IP(T"P.GY.TEpiP) GO TO 2430 2083?FPPxTmtP 2084I ?P*L 20.S5

P43 GC To 2440 2067

Ifa CMNO 0 2086

TI:CJ1C.GT.0) GO TO 2450 2090f~rTtCL..A~..TICG.. 6o TO 2510 2091

C IF MAt~jX INCCPNS13TEN7, OiMIT VARIABLE WITH LEAST 2092c CoqIIELATION 21093

2'490 IT!'PUNINOP-1 P094

IF(TTP.GT.IT4P) GOr To 240 zqD)n 2'io LQITI'. ITMP 2096Dn P'IAO LAMI.TTEMP 2097if1-,1A)zR(L+1 ,LA) 2098

2-17C 1YtIAUY(L+1) 2099C'~ 11 ?500 L1,lT T

1'P 2100

pac(L-L.A)2R(LvLA$1) 2102P501 (.nNTINUE 2103

-1T N fl I 11p 2104

f'n TOi 2420 2105

C ADDt RANIDCM CrMPCN.VNT TO PRESERVE VARIANCE 210bp5Ir frmpml20 2107

Q, ?20 Lxtoh 2108T0~?.~IN;EN(XX)?109

21?C :Ep~NENIX 2110C C0I4;)UTE FLOW 2111

AL~f..OO~C2*.52112~ ~ :TEM, AL2113

Z!33C TPP3FMPOl(L)*X(L) 2115"I".0TEMP2116

1::1 4 t ) 2 2118

C ADD NEW VALUE TC Sumis nF SOUARES AND CROSS PRODUCTS 2119Or 4560 L81PNSTAX a22I( L.El.K) Gn TO 2560 2121

C SuflSCRIPTS EwCEEDING NSTA RELATE TO PRECEOING IIUSTH 212,2IVml,.NSTA 2123

IF C'.LT.1) ?T'OCM.L) 2124IFCLX.r?.0) YmPzrt".1,Lv) 2125!F CTMP.EO.T) GO TO 2560 212b

C C0jII1T AND Usk CpLY QECOROEO PAIRS 21a7

11~A (,ItX#L)uSUMA CIlcL)4*TP 1319

I" ACf.K,L)zt,IIpC,K,L)+4PTMP 2130

IF(LogToNSTA) GO TO 2560 2134

owI4THtT 0116

.11,4A (I. L.x)xs0PF1 (I# K#L) P136'%j' (I L. K)03tGA (TI KL) 2139

XFAtiCT.L.K)=XPA1(I,K.L) 2140c RECri1I2LITE C0ARdELATyflN COEFFICIENTS TO INCLUOE NE% DATA 2141P340 IF(Nr.A5(I.,L).LE.2) GO TO 2560 2102

TFMP8NCA9CI#KtL) 2143TMPZtSOA(IK.L)SUlA (y9KL)*SIJMACEL)iTEP)*C

5QSC!,x.L)SUmi 2144I(IX.L).SUM8C!,K,L)1TEMP) 2145

C EL1'41hATE PAIRS WITH ZERO VARIANCE PROUUCT 2t46IF(TMP.LE*O.) GO TO MO6 2147

TMPAUNPA4 C!,KeL)-3UMA(ZigpoL2.8Ufl8(I.KL)/7E"P P149C RETArp, ALGEBRAIC 1Gb' 2100

IF (T'fFA.LT.O.) TmPvUTWmP 2151T4'PA=TMPA*TmPA/TPP 2.152PAcT,K.L)=THf,Tf1PA**.5 P153ITPUI 2154

LAML 2155!V(L-.LE.NATA) Gfl To 2550 2156

TF CTTP.LT.1) ITPxl8 2158LAZI V 2159

255C IFUPr(IK) .LT..OO11.OU.SO(TTP,LA).LT..000 13 RA(I#K#L)uO. P160?tCL .GT.?dqTA, Gn TU 2560 2161.4A(Tp1i.X)2RACTKoL) 2162

?s~c cr~kTINULE 2163IT~p=NvQ3*12+t 2164TFCm.(,E.!TMP) GO TO *580 P165TC P:O (1,K) 2166bOn ' r7O Ls.,PjITA 2167T'41 C(MIp ) pi160TF(T?tP.EnT) GO TO 2570 2169

L~2~.8?AP170

IF (TrP,flT.12) ITP:1 2172tA"(ITP,L.LX) :bCA4 CITP,L.Ly) *1 2173

SIA (ITP.L.LX)m30A (ITP,LKX.1TP*TM4P 2170SOP (TT0.L,LXx):SQJ CZ(17,t V)#7P*P 217XPAR(TTP,L.Lx):xPA8(1TP.L,LX)*TP*TMP 2170I1:( 'A!)CITPL,LvJLE.2) GO TO 257n~ 2179TF,'0:P C.AFiCTpDL .LX) 2100T"P.F:(Or)ACITPL,LX)-SLJ*A(ITP,t ,LX)hsumA(TTP,L,LX)/TEIP)* 2101

1 Cr ITT,,.-lm)IT t ),8*UIF4ITPLLX)/TEM40) 2182JF(TM4P.LF.*. GOf TO 2570 2183rpi ;1 * 214

ThPPAXPA0i~tlL ,Lx)-3M* CTP,L,LX),MUM8(ZTPLeLX)TE4P 2145TF (T',PA .L.

0 .) T ,Pl-TpMPB 218bTm~PA=T A* TP4PA /14P 21476:Af!TP,LLx)=T#41p8&TA41PA,..5 218IF(Ir)CIo) .LT..O'OCI.OD.80C(IVPuL).LT..O0I) RA(ITPLLX)8O. 2189

'T70 CM'TfktlE ?190p~p cnrT 2191plqc C"IvTwuIE 2192POVMC CnkTTNUE 21932051C rF(TAb4AL.LE*f) fqO TO 3100O 2190

Cm # * * * CaNVEQT 3TA14 fCARO l.'yTATEs TO FLUO ' *a. 2195IF C,".'8.LE.I) GU TO 263C 2196

7v~pu~jQS.1* 12197

?FCIOqTAP. 0ITAP) GO TC 2.30 2199NV& C TUTAP) 2200

P62C LATAP2LOTAP*1 2201P63C 4PI'TV(hot0) 2202

WRITE L6,2640) 2203P640 FO-'4AT(3w RFCCQOEO AND gFCOWITITIJTEO FLOW$) 2204

265C Ffrh-Artu P48,1t3i 2206

*17

EUNIOIT.T*I

?P S

S

1Frx GT.NKTX1 *IT~ v6b: 2209

P66C FIQ4AT C/114 S1'A YfAiflImfjA6x*5TOTAt.I 2210600fl 1 211'In ;1760 J11IDIYRA 2212

TTpuo 2213On ?720 Tutle 2214

!4-- + 221!5TF4Pm(MpX)2236

TwfPc3KEW0~i,I() 2217I" (TMP.NE.O.) TEMPE(TYIP.(TrMP.TrP/p,.)/6..1.)"*

3 ". )*Rsiy"P 22115(flP(i,K).NF*C) Go Tr 2b~n 2219IFCFMP.GY.2..AND.SDC!,A) .f?..3I y~w~mZ.,(TEiiP.)*.3/SOCIrX) 2220IF(CuP.LT.-.OlO1.OR.TI'P.GT..0001) "PXp(-2.)1TMP1F (SX"W9Tp) ififD

2bq0,2ht0Q 2222

267C 1F(rEmP.GT.T-1P) TEPIN371P 22231;n TO 2490 R224

264C TFCTFPP.LT.TiP) TE"PuTiP0 22252690 T"-PmTfMP*'%D(Te()+AVCIpK) 2226

-10' KIN tlO.*T-P.0a (I K) 2227

2229

IF(FTMP.LE.01 GO TO 2710TF40xn. 2232

10 7?0 L31IT P2233

27flC TFPTm~ntX 2235tF('fMvXI.G?.TEmP) GO TC 2710 2236

,A er * ADJ 2237

?vfn0(a,N).NE.E) GO TC 2710 2238Z"(T)XA0J1 2239

K I SE14P 2402YtC ri2241;?72C ITF'=TTP+10(1) 220a

-v .LE.hATX) Gfl 73 27r6O 22 at

!F('PCHfO.IF..O16n TO 274" 2245

273C F r'v~fAT(214, iPTb) 2247

;!? dC ' .T lKIi TE(6p 75!)8,1A ( I, I I; (I Q IUP I Ip 1)O) 2249

276C C~f"TINUE 22501w(P!0AS.LE.1) rf TO 2765 2250-1

P tr-ffQCOIf.LE,.o) r TO 2l8I0 2?53e 0 * * *RECfl4

0 i1TC ?4F.AN Air 3TANDAFIO DEVIATION 0 ? 254or R770 tal.12 2255

I , xI 0. 2257???C -j~(t,'()3O 2258

."1 2259

~7q~ 7O *0r92lN S 2260, = -- 0 12262

?PPALOGCQel,X).D)Qe1.K))*.4342q45 2261

5fT()UKj2A I,*TEmP*0 2264

P79C r..", r INuE 22147I- "MOO) Tuttle 2268IF-M1AVCZ.X) P269?F-A=SCI.X) ??70Tp*) 2211IP (Tm0.LT*Os) ,"i'OO, 2272Av (?.W)NTfMP/kNTIR 2273

Sn~j,)8TM**.52271T-p=SKEw(If%) 227S

F ~ (,W) O *1276

I~~,(,)LE.90 6 0 TO 2800 2971

CVNI4?tT 6 *left

5 IW ,X,(UANYRS,2T.P3.*AYP0TEMW*TMPA2,OTE4Pi*JI 2?74I r~ygCAVl31.)(py5P.*SO(I.K)-.3) 0279

PaflC c"'JNtIe 2240281C Cnk~TI'NUE 2241

LOTAPSNOTAP 26

IFIRC .0) GO Tn(!I( 2930 . 12),OTNCTE C.0f) ro Tt,),!3I,12 2281

C PQI")T ADUN8STEDT CAEVIENCA TATlN C 22A61~a82C 4pfTE(610 228

flfl TFl62W 217f

C01 PUNCT/3H ADJ CUCTE Y STATINCSTAICSTI 2?31

rn t*60 XUNSTYX,N15TA 232w~rTE (,101) !YAO )(A T,(IX* tulu2) 2303

APIT (6102) ( n~tx),al,2) 237

C84 cO'4PIirE 2296!iTINFLW asC T~~ 2309

289C IF (ICHS*LE.) GO TO 240 2300I HP INriS 1PGEC 3AIT 231DP! ?86 K=?45TlPv3T 2302

I ~ ~9~ ~~1,~~tW~2303~ VA 2314

I (' K) 0 *2306

?Ahr -,nTIP4[E 2320PC co4m.TINCOBIATONFLW 2301

C 2322

267 I("KCS.LE.0) GG TO 2910 2310

j ~TP LE.0 CU T5243 2311

PA90x XxI , ic rmpt2313.(=KlNsTA23314

Ar P0 . K C . 2T'l 313

On -JA 0:0 TT 2335

c o*A aa CO~xml~i'()+(i#ITGEEI)*CSTATXLISTCRA33) I400 a23

C10 CV.IAG CfQPLTIN OFFCI 2320PqrC CM*q5N 23021

Lc .T 2303Cn MAX ANDL MIN PE*SI DF1W 23239ir' ;= 0 O 11 2324

TYPNSU7.,L 2300

P92 I(L.E.V uI,( TO 2q) 23.2~90~ AV tI.L)*RV(KL*TP29

l4V(.L~~AV(,L~12.230

.14. EwiPPXPC5 233

w'nTTE(6.70)!STA(K),!STACL),RAV(KL) P350

C AVE91AGE LOG!; FCR VbF7 ANDO OQY 3FASONS 2AVPXK(X)6AV(11,IitAVC12,K)$AV(,() 2353

AVI'N(K)M&VNXCK) 235!

TMP8AV(12.x)+AV(1,K)+AV(2#N) 2357IF(AVHX(K).GV.TiP)un yu ?960 A3158AVPV(K)flTMP 2359

IMI(XI022360Gnf r0 2970 2361

796c AVYNCK)=IMP 2362Z.N (K)tA. 25313

c IND AVENA(UE STANDOARD DEVIATION 23642y7c snav(x):snci1,x)#s$ic2,x) 2365

Dm 299'j 133DI ?366V'~A(K)U0AV K).SUK)2367~MpZVCT.~K)AV(I1,UA~tK)2368

lrAm()rFTPG O 29P0 P369AvMV~(I()"m 2370tIXI(KINT 2371

2qJC IF1AVmN()AF.TMP)r,0 TO 2990 P372AVMNJ(X) CrMP P373IIS(K 3a 1 2370

;-iQc clK rrNIJF P375Avymx (w ) mAX ( )~ /3* 2376AvMI()vAv'!(K)/.5. 2377ilfV (K) uvAV (K) /ti2 P378

30('c CrnKT!N(IF 2379I-P!TEfb,100) 23P0fl3010 X2101TA 2381

JYPZIX(K)232IT~'!M11(K)P363

3('I ~TF.(,t20IST(K),A(K,&VCK)S0AVK),0CIP),M(ITP) 384C *~ * *AIPitY rJENERALIZED STATISTICS.* Al 0Aa** 23F5

il?C 1F(tfNkLj-.i-)Gfl To 31rjl 238be~ 3041) KCjIWSTA ;S387<Vrwe N 3TA 2348

C rIEfRPE0IATE eCkTH~S 23892390

~ 2392ly"l 3040 TclIi2 2393

C STI~jOAR0 DEVIATION LJNIFCRM, SKEW ZERO 2390ix I * K) O 2395

,f(T,K)ft5AV(K) P39710 1030 L21.'JSTA 2398

C ZE~n CnIREL&TIC% WITH OTSE4 STLTIONS ANO PPECEnIkG MONTH 23q%LY:LNSTA2400~& (~kL)~O.2401

IF(L.rE.X)r,n TO 3030 P402C I!NIFn,1'4 SERIAL CCRREL TITERMEDIATE MCNT143 AND INTER-STA 2403

;A(T#*L) 2!4AV v (eL) 2004;A(TL.K~qA~jjL) 405

3mic CnlTTNLiF 200626(7 ,K,K'i):'qV(K,K) A4407

N A(7, K* K)~ *2408

AndC Ld'NTINUF P409c '4 fA~i AND SERIAL C1,RREL, WE? &NO PRV SEA504S a410

tMPNRAVCK.IX) .15 pa11frP,2T142. *3 241afF (?mpGT..qA;Ympa.98 241JIF (TE"P.LT.O) TEMPxOS 24t4tpaIKX(K) 241!tv(7?P.X)2AV!NX(K)..1 2416

1 3(TTP~k.Kx)%TEHP 2417

IFr(ITP.LT.1) 172212 2419AV TTP.K) 2AVlX (K)..2 2420

2A~l~~x~xwzTEAPaila

EX'47E!' &20

IYP:,4x()..2 2422

UF(TTP.Lr.1)!TP*1YP+12 2423AV (T'rP.K) :AVIIX(K) ..1 2424t.tA (I TP, K kX) --T"P ;0425ITPOIMN (X 24a26AVCT1'P.X)XAV4N() 2427RA(TTPK,KX~mn7P 2428lTP21MN(IV).t 2429

!FCYTP.Lr.1) iTPUIP 2430AV (T4,I()AV-lN(IC) 2431RA CTTP.X.Kk)zTMP 2432ITPUINdN(g)-2 P433IF(TTP.T.IjTIPt*1? 8434Av(T?0.K~AVmAJ(X) ?433

4 (YTP,.Klx)m?tp 2436

C HESJ3S FCR MO'kTIN F(ILLOWING WET 3EA8ON 2437!F(NHivM?.LT.1)Gfl TO 30bfl A438

ITPZIXCK) 439

T~lm0u(&AVMV(K)-..1AYMN(K))/1EKP 2441011 1050 !X2I,NMKMHN P442

T4P=T'i 2443

101C AV (Z,X)=Av(ITP,K) .TEMPTYqP 2446c "r4AS Ffl4 tiOIhTI5 FCLLCwING DvY 6EA30.4 244?

106C IF(N~lNMV.LT.j)Ca T(O 309r, 2448

1TpriNa(K) P449T F0t00NMN X*1 2050TFmP. fAVNm(K) -.1 -AVmN R) )/hEfP 2'451Dn 3070 IX,NNp~X 2452T4PCIV 2433I=PN (Id .rX 2454

1,17C AV (I.X2AV(lTP~,K),TEmP*TMP 245610AC Cr'kTlNUE 2.457

309C IrKPL90 t145819CONSO 2499rf' TO 1730) 2460

l31)C IF(I YrG'.LF.fl.AND).NP CJ.LE.0,AN0.NPA3S.LF,1) GO Tn 15o 24161CP * * * * * FL(Iii GENEqATTOk EGLIATIONS 0 *0**0o 2462

NT '0 P2 N STA 2463,VAR1k,4TA*1 2464nr 3200 Y21PI2 24651P--T.1 2466IF (IP.LT.1) IP2 2467i,, jqqo k1,113TA 2468

c Cf N FA.ATIONS IN CURQEKT PONTY4 ?470

IF IL.GE.P) (r! TO 3120 2471K:(l,NVAQ) a f)'4L(QAIpKL)~ P072000-m .4110 LA=L.,'SA 2473LV'TL-A+IPTA 2474IF (LA.LT.K) R(LoLA) a ltBL(4A(I,L.LA)) 2475000IF CLA.GF.A) -I(LLA) ObLtUFA(!,L,LX)) 241600

311C i*aLA,L):mQ(L#LA) 2477ri Tn 3100 2478

C Cr!P-4ELATInN3 kt7k PPECEDNG 14ONTN 247931PC LvzL*N3.4TA 2440

J(LNVA41) 2 tn"LE(AA(1p,~LV) 211810000rM ItI0 LA=LNSA 24424fL.L4 1 ) u fMLF(QA(IPvI.,LA)) 24A3000

'13C '4(LA.i.)2Q(L#LA) 21084114C COITINUE 248S

C m2222 2486CLL CAOLICl1) 2487

c x2musu:333 2488flo M50 LulpISTA 2489

313C lFTA (l,',L)n4(0) 2490IF(flTp'iC.Lt.t.) GO TO 3570 2491

w$IE C6,3160)1I,K.OYRIC 2492316C Fnqt''' CJ0 INCO~iT3TF'.y crRREL MATRIX FOR ta,13g44 KUlp 249J00

-210 EXIBIT b

t'li4 orR'iSnF603) ?494000ITANSUZ 49

i~TO 1730 2496117C !F(flTQMC.(GE.O.) nC TO 3114,0

.r.JTE (bp70)! .,DTPNC

lIAC '[-CFTC I. Km(I .-O)TIMC)aa.S 2500l19C CnkTTNUE 20

32nCCnNTNUE2502(C a tNTU * * * aE4,0 FLa 250i

IF(NPAS.I.tE.1) GLI TV 3240 ?505321C IF(LSTAT.Eg.NSTAT3 GO Tr 320 2505

(ISTA( ) 2506

LqATtLATAT*1 2507i-,, TMl 3e,10 2508

12?C 250ITATUNSTAT+1 25t0

IqATUN5iTAT P511NI 1230 Kru.N~ITA 251.2

1 !4ET& (1 ,KCL) .La1,PSTA),ALCFT(I'K) .IXl12) 2514

1.3TATONSTAT 251bTF(TiAS5.LT..PA3S) GO Tr 200 2517

324C *1"I 2)518:OAASU1 2519

25202521

!F CNR4fJ.LF.0) t;O TO 3310 P522C~a* * * * P,^nj[.TEfn FLCW 1E'ENCES aaa* aaaaaaa aa 252 3

32tC .A=TYRPJ.TYRA P52 a,IZLYRJ.Tyqh25253

Ir. j , 526TPjMTHPJ-IMNTH.j 2527

IF(ITP.NE.0) GO TO 3260 25281 T p * 122529

3P6 ! (IrP.LT IPCITP1-T 2 2531

7' q 1290 (l'TA 2533!~ 5~ P,'), st To 3280 253a

2536!F iSKFWTT,).FPn..) GL TO 32 qO 2537T I.5~~*j aKFW (IT P, X) a P H V(CK)*I 1 2538

T *~c . 2539r-(FOrFM)r TO 3210 2540

rf-'vf-EMP) 2501'T'" (-TAP) 2542

327( -,; rvf()cb*T Pa*TE'Paa(1*#3.).1)/AKEi(ITPM)*8r(Ew(rTMK).I6. P50i

'11 T 3290 250443?pr P545

jiztvppj.1 2547

C N 2.!)'UE'CE kr.o M4 8 MON.T1 NO,# JX d YEAR HC. 2548311C '130-1 ;)5a9

T) 3330 ssoC ITAv'T 41TP4 lqrP OFVTATION AT ALL STATIONS3 ;.5 51331C 53P0 KcI,K.3 TA P5121321, I"Ev()n. 2b53

C CE-q4ATE 2 YEARS FOR D!SCARDING ?3

JVX* 2 25196333C IF '"ASqLF.j) Gl; TO 3uCC P5

lciIPkS5.GT.I) %7JO 3340 25387'F.' T~ ISTAT 21559.ITAPSO R560(9I APSQ 25131

334C Pr Io IOTAP 25362L. IT'P90 .3563

PF~I(ISTAT)'~qTXX,%5Th, (I3TA*(KI@NSA) 251#4.'src~l~w~l 565

IC04STI.LE.0) GO TO 3380 ?5&6

EVHI4HT 6 82

Ic(!PASS.Lf.t) GO Tfl 3360 26139L G.FAn(onyAp) ryE"P#,CQP',K) p,PoITP) 2570

Lq)TAP8L0TAP.1 25711(tTTFMP.NF.I3TA(K)) GU T17 3350 ps72

33hf :rAD(!8TAT, 0 AC,)SlIKKE(g K,)nI6Lu ?S73l#K'5YA).ALCFT(IK)pXU1,12) 2574

337C Cn TINUE 251113$C "'I 339V KZNTYXN3TA F576

ISTAP81STAP.1 ?I??tFCN.GT.O) )vfJEV(K)xQ9TAP(j9TAP) 2578

3 3;C : r A )C tjT A T) i f, p( A v ( r 4) pSfln K 3XE w CI K)D Q C IK) CE TA I K L I L 1 25791,-j3TA),AjLcFr(T#K)#j:1#!?) ?Sao

C* * * * * rE'NFfOTE. CORAFLAME 3TANDARI) OEUIATE '* . a *2541

:jr1isCHM C" (pASSj.Ej. ) NMZX2

-T n~cfluTND 'i( IP AS5)134i20 KutI'.ITA 2583

:1r) '4410 121.12 2S64&~G 1.1(30.254S

ilitcC n.TT1NI 2540

j F ti. j_ , 0) rn TO 3440 2589.Q[TE(b,10) 2590,I)!TE (6,31130 N 2591

3uJ3C rriAT (21H ';FPERATED FLCwS FOR PFIIOD,13) 2592000IF ('NPA~q.GT.1 ) wR!TEC6,26560) IPA3S 2593

344" 1: 510 JZJANj 2594!=I?*f-tl~l2595

'r '0012,i2 2596.3597

IF(NSTY.LE.0) Gil To 3460 P5981(; 34501 K-0j,'ST.% 2599

TV (H.LPF.Ph) rc To' 3500 6

1490 KZIf'T'AA,v9T4 2602

c 1WAN~fle COMPON~hT 2603Y ~F' :0 * 2604

11 1-70 L3 s 2605T P=F F P. '4PN tF%(.C XX) 26C6

3i ?C TVP=T(>0-i )iAN~(,X) 2607

?.-f:TFmp.*%LCFTCZ,'K) p26 18

Jm' f4AO Lc1,'STA Pb0934 7 ; :T E w0 T AC I , K pL)*Q1E V (L) 2610

',vf; IX) Avr( ,K)+ EMP 611

* rO-,KI:TEMP 2613

w;' F ( K ) = TEM 2614. I, I'. hiNJE 2615

3~' ' TINLJE 2b6

tF~053L.)Go TO 330f 2618St(L0lT A 0. ,).'O9T 4P) GO0 T C 3530 2619

* F n (T(nTAP) 2620I.'!TAF'UL0TAVP* 2621;n Ff 3520 2622

353C TTP=Nlts.!1l 2b?3

IqT 2(x~qTI'..'RTA*NSTX 2624

JI UI( V 7APII I( T A(K, C QCP , K).M22.1P) 2b26Y APPJ()T AP+ 1 2629

iI fhPajsTAV+1 2620:F (15TAP.IrT.1(STAP) 0)0 71! 160 2630

3IIf'.ITAP(I8T*Ph:!((IyP,K) 2430355C I"r MN J J A #1 3

WO i.'o M-..TXNSTA 2634W(NJ*JVT47rT0) WQZTE(6,266O) CpOMP)151012) 2633 a

4'ir n e)zAvr;,(j,U() ANLCQ 63

5nvr!.X1(3,,V(x,a.AVuZI,K)..l.AL6)/PLCGa)tto 2b6

.p3-?

j v2Jy T4'2ill) 1660 jajA.NJ 2641

JN*J+% ph26'

IF (JX.LE.0) GO TO 3660 2&44

on 3690 Talolp

IF (MjEF.MAl SC Ta 3640 2b6

c rU*ANiSvFOM TO LCG PFA4S3tw TYPE LII VAPIA7E (FLOO) ?b09

f jt,,)V (2CV',K) -AVG( CToK) ) IND V(1#9) 2651

IF (TPE(. GOC TO) 36rC IaTD~ 652a

I~ K~vgt,1Y) 3,380,.3902655

t51 F (TMP.GT.T!)Y?4PzEPP 265b

5n1 TO 3810 265?

15q(' tF(1I4P.1.T.TE"P) TMPUEMP 2650

qn To 3610 ?659

3~C TU!M,~O2681

?I~FT~i*~0 I~h)4AYCT K)?b62

ZF(TTMI'.Lf.0) Gn TO 363C

TFV'0S0 * 266b

LvZrST(KsLolT4 33j3?C rFv~mE1P+(4(.X1 bb9

3AO ~(( VO110. QWt~CTK)~ Q(MtK) 0. 2071

!6QC Cr"NTINIIF P614

c NITHOREV 2615

I(t 31atTP 261b

- ITF (6, 100) 1314 X)*Jyo(117(l)plt# 3,1 2617

I~fti'CW.L.C')G TI) 36 20111

v'iTff,c??f0) LaTA(K), jx*gf(0C1),Tl1i2) 2079

3b"C CONTINIUC WbO

37C C 0 . T INJEF 26A

1Ff ,raj.LE..1) r 0 TO 3720 2b8

5 710) JUJA,*4j ?6A3

c Cfl~4PwTF Cr4TJN'ATlfN FLaO.3 2881

,=x+S TA 26L*9

1TP=NTI%7h(KA, JP&33)(!4,)CO.2691

-i !SAO SLZ,TT' ?b9?

I h 1). C; I TK I.L N (A ?S

37nc C-i'kul 269b

j71r Crmr.VtIUF 2b51

37?C f;,:<.LT.N' 1jn1 c.0 in lzia ?b,48

IFi4MxGtr.))GO TOJ Van sb0

C 1. 44X A~Sn mjN GkKERATfO FLnw$ 0B00*0 2700

1r(JK:L./IG- TO 1970 2701

C 3919PAXMIN IF NE"ANIN0 VEA43 INUFFICtEftT 210a

IFVYXE.V?.O.A. .NjoL.k~.Yo XG)CO TO 136l 2103

171c T1U4,I0 ~2105On 3800 K3J0TwxolYP arGb

r.Pi I4 ALV.OAi PC lot?, NAV MO l3s 6-140 14, 14-MO 15 210?

n3,00 t27i 01

3740 i'41)(1.K)ENT 2709C M4IN 0ALENDAp4 lit P..27, 11IN mOj 20g.m 1g 9, 54vmu 30 2710

[in~ 3750 1218.30 Rill13750 31"OCTvK).T 2712C TMP R A.14OP ?CO.P 2 434.Mq VOLUME, 7MPP a I-MO) 2713

TFI'Dafl* 2719TMiPEO, 2715AVG0(Kx)Uoo 2718

Ntlan2717

IF (JTRNS.OT.0) mm(N.1) *1EXNC312*1 2719,rl 37q0 JU1IJ 2720~fln 170 1.1.12 2721N~2I11 272H VIA + 272314 PA: 0CM, K) 2724yGl(lk)XAVG0CPO*TM'h 2725

N'12 N a#1. 2726I V (TA4 PA. G T . SH ~I (J. w ) 1 3m 01 9 ) m TM pa 27271 F (MP A LT .V9IJ(X CK) ).S MOC!)X) TMP A 2728

FCT14A.GT.3ltfl13,K))St 0C(13.K) TpA 2729IFCTPA.L.I~if)(S~i))3t0(2#K~nMPA2730

T14P2TNP#YMPA 2731T F, "P2 E MP+THP~'A 2732IP~e9.LT.8,GO TO 3760 2733TriP2ywr'.e)(HM6,) P734

2735

IFU%.LT.56)r0 TO 3710 2737TF'PTE~p (*v5'J.K)?739

*.n~ TO) 37A0 27410 Jl-AC 1t'C4 K) XTMP P7 42

7177' ri -il I . K) 13TE,iP e74337AC Cr''NYIIUE .37440379C!r fi. T INuj P745

c AVEQAGE MONT4LY FLOW 2746TV!'PZN0 P747'4rV(KEAVGqCK) /TFIiP 27?48

3# Oj I-IPNTIN.JE 27494QfTF (4,10) 2750

IF(IR?4.Gf.))AITE~o3PO)PINi 7513II r's1f4AT (1271H *AXImJ4 VULUPFS FORl pE'4IO,1303H OFpta. 27500

I 4-1H YEARS f]F 9CONOEO Ahnf PECflNSjTUTkC FLOWS) 2753fl00IF(?TN3.LE.li4QTE(6,3PiOC)N.Nj P754' 14AT (12114 44YIMUM VOLL14ES FCR PEPICJO,13,3M OF,14, el'55006

12%k YFARI OF 5Y~ITHFTIC FLrtS) 275800.UITF~~plol 757

)n 144 X3NSTXX#ZYP P759iT ,,J3tAVrfO(K)+,5 2760lo 31'3o 121,I'5 2761

364C C-f INUE 2760k f ha fl0) ;!7865

'541.0 KNTV'\,LTP 2767

38AC C!N I I NLIE 2771c TRApSFFR L&Cx TO RECOWITYTUTED FLOW$ ?772

IF(TTQNS.GT.Ol,3 TO 292(t 27733070 . a NyMXG 2774

rTO 3 190 P7753880 aj uiYR 2776loan jF(,lP&SS.LE.j) GO TO 3900 2777

277860 TO 3310 2779

1V(TPAss.LE.NIA.%s) GO TC 3J40 21 80

-25. Evs-IdYT 6

1l'A33I 2781c Go to ,4k~ oa203911 ' IV(NYRG.LI.') G13 TO 150 V7A3

rfNj .GT.W1:?c)NJ=NykG ;P784,YPAUNY146-s:j a761nmr Tn 33no 2746END 2781S319B00UTTP. CPPLUT(9!() 1001

nnLhIALF PJFCI31ICN R,13,RX 1003Crw'4r]h 0TRTiC,CNINDP.B 1004..vAPvNXNnP*1 1005gm a ul 1N1INOP 1006

,'r) to K=1.NVAq 1008

if ri.K)m~y(j~v) 10092c crmkTZNIjF 1010

Tv(qINflP.rnV.1)SO Tfl 30 101l

O~m~(1)aiC1)1013

~ :~ o XO~JVAN1016C 1 FI4IJ MATRIXK/~( *1 1015

If1 40 K-u2, JV A4 1018

AO )(2KNTO 1019

On 60 JzW.*,T'jDP 1020,,, rso I~1.Ir 1021

I 022

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r. ("T 'vrywgjf 1026'' 70 :1TTP 1027

7 r wN F A i LV-R R( 1029~'fclzn8Af ;4 (ix K)) 1030IrrcC'P.rt"..)(00) rGc an 10312T L!CU1 1 t03-3

', TUr tot033PC, r; &VAR )f,? (W.VAic) /P ( ~K) 1030( ~ * a P ACK SOLUTION.aaaAaaaaaaa 1035

(N~h)1y=12"T11P,4AR)1036'n 100 Ix2,;4P'DP 1031j.5%VAq~- I 1038

t: I * 11039

'40 2,019 1041

'n)+L1042

1 11f IO% I P.U 006

tTTD 0cr; a Nf) 1005C 10) NJjI I: i145ir F II AR!V 'AH 1002

Ct r'7F~g '4 t Ct AS 0 -C+ICjI*4X(.NI 104

' j 1)~ J YK 1009-,-rTr(IN Q'. N(TTA) ( E~OT R~N toot

c ~ 'v N 1Ef. cflP Q? lA RFAqYIG AIN 1002C ,aOAF a-I-~ a&~rP aIRF INf 1r(2aaC(PRtYj?)a3 a3a a a 00

c * a a aFc'*i:./2aai)aa 1011C , lw"EQE OnyfF~ TkP BL1tr TC. 7twE INEE !H. OION~ 1012

c 1013~hFP NYLFE C' Nhrqtoc ANTANIA r,11V121/ v- r M 0LClrjE)AT.N 101a

I :!U 1013

e!,4livf 6 *ab"

Trr.~m 1 S71Pj~lot?i~ TYy&~c~Njlots

11 N-,~F Pis IV 1021

FCou3.3S5271lb1 8E-t4 1022

R NG Pt NZ$N Sf. *l'FC~C NJ 10171

END 1021t026

ESdT6

MXUBIT 7

INPUT DATA 723-X-L2340

CARD VARIABLE CO0MMMS

A Three title cards, first must have A in column 1.

B First specification card.

1. IYRA - Earliest year of record at any station.2. INMMH - Calendar month number of first month of water year.3. IANAL - Indicator, positive value calls for statistical

analysis routines.4. IRS - Number of years in each period of recorded and re-

constituted flows for which maximum and minimum valuesare to be obtained, dimensioned for 100.

5. NYRG - Total number of years of hypothetical flows to begenerated.

6. NYMXG - Number of years in each period of generated flowswhich maximum and minimum values are to be obtained,dimensinned for 100.

7. NPASS - Number of consecutive passes, each pass consisting ofa new group of stations which can be correlated withspecified stations in previous passes, dimensionedfor 5.

8. IPCIQ - Indicator, positive value calls for writing recordedand reconstituted flows and generated flows on Tape 7.

9. IPCHS - Indicator, positive value calls for writing stat-istics on Tape 7.

10. NSTA - Number of stations at which flows are to be generated,not required if flow data are supplied. NSTA + NCOHB(C-i) dimensioned for 10.

C Second specification card.

1. NCOMB - Number of combinations of stations, the totals ofwhich are used to obtain maximum and minimum flows,dimensioned for 2. If positive, provide D and R cards.

2. NTNDM - Number of tandem situations, compares sum of monthlyvalues of upstream stations with downstream stationand adjusts if value Is less than sum and that station'svalue has been estimated or generated, dimension for 10.If positive, provide F card.

3. NCSTY Number of consistency tests. Adjusts standard deviationof a dependent station in tandem with an independentstation to prevent frequency curves from crossing,dimensioned for 10. If positive, provide C card.

EXMBIT 7

CAo VAMANZ 0aer's

C (Cont'd)

4. IGM - Indicator, + 1 calls for reading generalized stat-istics and using for generation, + 2 calls for cow-Vitin generalized statistics from flov data and usingfor eneration.

S. NPW)J - Number of projections of future flows from presentconditions, usually 0.

6. IYRPJ - Year of start of each projection.7. M)HPJ - Calendar month of start of each projection.8. L RPJ - Lst yea of each jrojection, number of recorded and

reconstituted years plus number of projected yearsdimensioned for 100.

D Identification of combination, NCOB (C-i) sets of Dand N cards.

1. INSAC - Number of stations in this combination, dimensionedfor 10.

2. ISTAC - Station number (!SrAC values).

E Combining coefficients, MCOB (C-i) sets of D and9 cards.

1. NSTAC - Sme as D-1.2. CSTAC - Coefficient of flow used for adding, corresponds to

respective items in D-2.

F Identification of tandem situation, NDM (C-2) cards.

1. I&M - Station number of downstrea station.2. NMX - Number of upstream stations, dimensioned for 10.3. IS"T - Station number of upstream station (NSMX values).

G Identification of consistency test, NCSTY (C-3) cards.

1. ISTX - Independent station number.2. I lY - Dependent station number.

H Flow data, cards in any order, omit if LANAI (B-3) isnot positive follow all flow data cards by 1 blankcard (I card).

1. Cole 2-4, Station number2. Cols 5-8, Year number.

2EnHBIT 7

CARD VARIABLE COMMENTS

H (Cont'd)

3. Cols 9-14, 15-20, etc., Flow in desired units. Units should beselected so generated flows will not exceed 999,999. Use -1 formissing record. If record for entire year is missing, omit cardfor that year.

Card blank after Col 1 to indicate end of flow data,omit if IANAL (B-3) is not positive.

J Identification of stations in previous passes to beused in current pass, supply only if NPASS (B-7) isgreater than 1. The variables NCOMB, NTNDM, andNCSTY apply to the current pass only.

1. NCOMB - Number of combinations of stations, the totals ofwhich are used to obtain maximum and minimum flows,dimensioned for 2. If positive, provide D and E cards.

2. NTNDM - Number of tandem situations, compares sum of monthlyvalues of upstream stations with downstream stationand adjusts if value is less than sum and that station'svalue has been estimated or generated, dimension for 10.If positive, provide F card.

3. NCSTY . Number of consistency tests. Adjusts standard deviationof a dependent station in tandem with an independentstation to prevent frequency curves from crossing,dimensioned for 10. If positive, provide G card.

4. NSrX - Number of stations from previous passes which are tobe used with the additional data in current pass as ameans of maintaining consistent flows between groups ofstations, number of stations from previous passesplus number of new stations dimensioned for 10.

5. rSTA - Station number of station in a previous pass which isto be used in current pass (NSTX values). Must bein same order as stations first appear.

Note: Flow data for current pass supplied As described for H card andfollow data with a blank card (I card), supply NPASS-l setsof J, H, and I cards (also D,E,F, and G, if necessary) whenNPASS greater than 1.

K Preceding-month correlation coefficients for firststation, omit if IANAL (B-3) is positive (NSTA cards).

1. ISTA(K) - Cols 2-4, Number of first station.2. ISTA(L) - Cols 5-8, Number of station from 1 to NSTA (B-1O) on

successive cards. If IGNRL (C-h) = 1, only firstcard is used.

3. RA(I,K,LX) - Cols 9-14, 15-20, etc., Correlation coefficients forsuccessive months between flows at first station andpreceding-month flows at stations from 1 to NSTA (B-10)on separate cards. If IGNRL (C-4) = 1, only general-ized coefficient (in cols 9-14) is given.

3 EXHIBIT 7


L* Current-month correlation coefficients, omit if IANAL(B-3) is positive, (NSTA-1) pairs of L and M cards.

1. ISTA(K) - Cols 2-4, Number of station, progressing from K = 2through NSTA (B-l0) stations on different sets of Land M cards.

2. ISTA(L) - Cols 5-8, Number of station, progressing on different

cards through all stations from L = 1 to K-1.3. RA(I,K,L) - Cols 9-14, 15-20, etc., Correlation coefficient for

each successive calendar month between flows at stationK and concurrent flows at station L (12 items). IfIGNRL (C-4) = 1, only generalized coefficient in cols9-14 is given.

M* Preceding-month correlation coefficients for remainingstations, omit if IANAL (B-3) is positive. Paired withL card.

1. ISTA(K) - Cols 2-4, Same station number as on corresponding L

card (L-1).2. ISTA(L) - Cols 5-8, Number of station, progressing in same order

on different cards through all stations from L = 1 toNSTA (B-lO). If IGNRL (C-4) = 1, only card with L = Kis used.

3. RA(I,K,LX)- Cols 9-14, 15-20, etc., Correlation coefficient for eachsuccessive calendar month between flows at station Kand flows in preceding month at station L (12 items).If IGNRL (C-4) = 1, only generalized coefficient inCols 9-14 is given.

N Generalized frequency statistics, omit if IANAL (B-3) is

positive or IGNRL (C-4) does not equal 1.

1. TSTA(K) - Cols 2-8, Station number for NSTA (B-l) stations onsuccessive cards in same order as supplied by L cards(L-l).

2. AVMX(K) - Cols 9-14, Average mean logarithm for wet season (3months).

3. AVMN(K) - Cols 15-20, Average mean logarithm for dry season (3months ).

4. SDAV(K) - Cols 21-26, Average standard deviation for the 12 months.

* Sets of L and M cards are required for each station from K - 2 to NSTA.

4

EXHIBIT 7


N (Cont'd)

5. MOMX(K) - Calendar number of last month of wet season.6. MOMN(K) - Calendar number of last month of dry season.

0 Mean logarithms, omit if IANAL (B-3) is positive or IGNRL(C-4) equals 1.

1. ISrA(K) - Same as (M-1).2. AV(I,K) - Cols 9-14, 15-20, etc., Mean logarithms for successive

calendar months.

P Standard deviations, omit If IANAL (B-3) is positive orIGNRL (C-4) equals 1.

1. ISTA(K) - Seine as (M-1).2. SD(I,K) - Cols 9-14, 15-20, etc., Standard deviations for suc-

cessive calendar months.

Skew coefficients, omit if IANAL (B-3) is positive orIGNRL (C-4) equals 1.

1. ISTA(K) - Same as (M-l).2. SKEW(I,K) - Cols 9-14, 15-20, etc., Skew coefficients for suc-

cessive calendar months.

R Flow increments, omit if IANAL (B-3) is positive orIGNRL (C-4) equals 1.

1. TSrA(K) - Same as (M-l).2. DQ(I,K) - Cols 9-14, 15-20, etc., Flow increments for successive

calendar months.

Five blank cards with A in Col 1 of first should follow last Job.

Note: Cards K through R are not required if cards H and I are supplied. CardsK through R are as punched by computer when IPCHS is positive.

5

EXHIIBI r 7

EIBIT 8

SUIUARY OF REQUIRED CAMDS723-x6-L23.O

I See Icard)

NPASS-1 iiZ (Ie H I I)I-sets (1)(e Rcad

J COMB NTN4DM NCSTY NSTX I STA fSTA T.. NS X Val a

Mi I lakcard, after all ta,

(1) H UT Q Q Q Q Q (12 Values) format 214, 12F6.0

NCMT cards G 1ST! I

IVUM cards F ISSNSMK 1ST? MM?...18 au

NCO (PTA CSTAC ICSTAC I ..... I WAC aluer

st[D" ( ST"Rn I MAC IISTAC1 .. 0.. 1NSTAC I Valm?

C NCOMB NMD NCff! IaNRL NpROJ rm]RJ KWJ LYRPJ

B DWH rAKAL mKRw8 NYR I11 " IAS IB ' IP I STA:

A WT ITLE1 CARD

A TTLE CARD

Notes:

(1) SupplY Only if ZANAL 0B3) Is Positive. Papeat U card tar eachstation-year of data before supplying I card.

EXHIBIT 8

SUbMY OF REQUIRED CARDSContinued

7'23-X6-L231eO

R IST DI NI le

Q IT SKE SKW...(2Vle)oiti IGIL(4

NSTA sets (4)

(4) N A AVMX AVMN SDAV MOMvc M.gIM

L TA K) IST-A L CRA 1,K,L) HA(2,K,L) ..... RA(12,K,L)

(2)(4) K TA 1 ISTA(L) HA 1,K,LX) RA(2,K,LX) .... (12,KLX)

(2) L designates correlation with current month and LX with preceding month. IfIGNRL.(C4) =1, only one (generalized) coefficient is given following stationnumbers on each card and only 1 K and M card is used for each K station, withL = K. Use sam format as H card.

(3) Repeat set of L and M cards for each K station except first.(4) Omit if IANaI (B3) is positive.

2MIB~hr 8

hec-4 monthly streamfiow simulation · aed-a235 877 us army corps of engineers hydrologic...

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