Library, H.w. Bid*

SEP 9 1963

^ecknlcuL vtote 92c. isi

COMPUTER PROGRAM FOR IONOSPHERIC

MAPPING BY NUMERICAL METHODS

MARTHA E. HINDS AND WILLIAM B. I0NES

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

Functions and Activities

The functions of the National Bureau of Standards are set forth in the Act of Congress,

March 3, 1901, as amended by Congress in Public Law 619, 1950. These include the development and maintenance of the national standards of measurement and the provision of means

and methods for making measurements consistent with these standards; the determination of

physical constants and properties of materials; the development of methods and instruments

for testing materials, devices, and structures; advisory services to government agencies on

scientific and technical problems; invention and development of devices to serve special needs

of the Government; and the development of standard practices, codes, and specifications. The

work includes basic and applied research, development, engineering, instrumentation, testing,

evaluation, calibration services, and various consultation and information services. Research

projects are also performed for other government agencies when the work relates to and supplements the basic program of the Bureau or when the Bureau's unique competence is required.

The scope of activities is suggested by the listing of divisions and sections on the inside of

the back cover.

Publications

The results of the Bureau's research are published either in the Bureau's own series of

publications or in the journals of professional and scientific societies. The Bureau publishes

three periodicals available from the Government Printing Office: The Journal of Research,

published in four separate sections, presents complete scientific and technical papers; the Technical News Bulletin presents summary and preliminary reports on work in progress; and the

Central Radio Propagation Laboratory Ionospheric Predictions provides data for determining

the best frequencies to use for radio communications throughout the world. There are also

five series of nonperiodical publications: Monographs, Applied Mathematics Series, Handbooks,

Miscellaneous Publications, and Technical Notes.

A complete listing of the Bureau's publications can be found in National Bureau of Standards Circular 460, Publications of the National Bureau of Standards, 1901 to June 1947 ($1.25),

and the Supplement to National Bureau of Standards Circular 460, July 1947 to June 1957

($1.50), and Miscellaneous Publication 240, July 1957 to June 1960 (includes Titles of Papers

Published in Outside Journals 1950 to 1959) ($2.25); available from the Superintendent of

Documents, Government Printing Office, Washington D.C. 20402.
NATIONAL BUREAU OF STANDARDS

technical ^Ttote 1S1

Issued August 20, 1963

COMPUTER PROGRAM FOR IONOSPHERIC

MAPPING BY NUMERICAL METHODS

Martha E. Hinds and William B. Jones NBS Boulder Laboratories

Boulder, Colorado

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U. S. Government Printing Office Washington, D.C. 20402

Price 50£

TABLE OF CONTENTS

1. INTRODUCTION ___

1

2. NUMERICAL MAP EXECUTIVE PROGRAM-. 7

2.1 Introduction 7

2.2 Screen Points _ . °

2.3 Program Description 10

3. DATA READ SUBROUTINE 01 __

2 3

k. FOURIER ANALYSIS SUBROUTINE 02 27

5. GEOGRAPHIC FUNCTIONS SUBROUTINE 0^ - ____ 31

6. SYNTHESIS SUBROUTINES 05-10- 35

6.1 Explanatory Remarks 35

6.2 Program Description (for subroutines 08, 09 and 10) 38

7. RESIDUAL SUBROUTINE 11

^

8. GENERAL DATA FITTING SUBROUTINES 15, 17-20 _ ^5

8.1 Explanatory Remarks ^5

8.2 Program Description ^5

9. INTERCOMPARISON COEFFICIENTS SUBROUTINES l6 AND 21 55

9.1 Summary of Method and Formulas 55

9.2 Program Description 58

ACKNOWLEDGEMENTS _ ^1

10. REFERENCES _ _ 6 3

APPENDIX A 65

APPENDIX B _ _. 75

11

COMPUTER PROGRAM FOR IONOSPHERIC MAPPING

BY NUMERICAL METHODS

Martha E. Hinds and William B. Jones

A solution has recently been given to the problem of

representing the complex variations of ionospheric characteristics on a world-wide scale, including their diurnal

variation, by numerical analysis of ionospheric data as measured at a network of stations [Jones and Gallet, 1962a]

.

The present paper describes the IBM 7090 (FAP) program of

the methods of numerical mapping referred to above.

Included are detailed flow charts of the program logic, and

all necessary information for applying the program. Thus

it fills the gap between the publications giving the

scientific bases for the methods of mapping and the practical

problem of producing ionospheric maps. This program,

applied to ionospheric characteristics foF2 and F2-M3000,

forms the basis for the new series, Central Radio Propaga- tion Laboratory Ionospheric Predictions .

1 . INTRODUCTION

A solution has recently been given to the problem of representing

the complex variations of ionospheric characteristics by numerical

analysis of ionospheric data as measured at a network of stations [Jones

and Gallet, 1962a] . The methods employed consist of well-defined

mathematical operations which are readily adapted to high-speed automatic

2 computing. The principal output of these methods is a set of numerical

coefficients defining a continuous function of latitude, longitude and

time which represents the ionospheric characteristic on a world-wide

scale, including its diurnal variation. The ionospheric representation

thus obtained is called a numerical map.

T'or a brief summary of the problem and its solution the reader can refer to [Jones and Gallet, i960]

.

2The need for world-wide mapping methods based on numerical

analysis and the use of high-speed computers has been felt for many

years [C.C.I.R., 19591-
An integral part of the work in forming and testing the mapping

methods referred to above was the parallel development and application

of computer programs. This work evolved over a period of several years,

beginning with an IBM 65O computer (in SOAP language), then with an IBM

"JOk (in SAP language) for its increased size and speed, and finally with

the IBM 7090 (in FAP language). The present paper describes the 7090

program, referred to here as the Numerical Map Program. The 7090 FAP

listing of the Numerical Map Program is contained in [Hinds and Jones,

1962], which has been revised and condensed to form the present NBS

Technical Note

.

The numerical methods of mapping and computer programs referred to

above, together with extensive applications made with the ionospheric

2 characteristics foF2 and F2-M3000, form the basis for the new series,

Central Radio Propagation Laboratory Ionospheric Predictions , commencing

in January 1963 [Ostrow, 1962; CRPL, 1963] • Among the advantages of

this new series is that it is based on objective methods of mapping

which are repeatable and well-defined in the mathematical sense, so that

anyone starting with the same data will obtain an identical map . Although

most of the mapping methods appear in published papers, there are many

details of the mapping process which can be given only in a description

of the computer program, for example, detailed flow charts of the program

and all necessary information for applying the Numerical Map Program.

Other 7090 computer programs (closely related to the one given

here) have also been developed and extensively used. These include:

(a.) a Numerical Predictions Program for computing predicted numerical

maps of ionospheric characteristics for future months (or days) and

(b) a Contour Map Program for computing world-wide or polar contour

maps in either universal time or local mean time.

2This series replaces the former CRPL Series D, "Basic Radio

Propagation Predictions".
Flow Chart 1

NUMERICAL MAP PROGRAM

SUMMARY FLOW DIAGRAM OF MAIN PROGRAM STEPS

Read: (SR Ol)

Header card

Fixed data

Ionospheric data

(A and B data)

(SR 07) Evaluate

Fourier coefficients

a*(\,e) and bj(\,e)

at screen points

(SR 09)

Compute and print

2k hourly (in LMT)

values of Y{\,d,t)

at screen points

(SR 15, 17-20)

Compute

(SR 16, 21)

Compute and

print h

gk

->

Compute < SR °

2 ^ Fourier coefficients

a- and ~b± corrected to LMT

Evaluate (SR OU)

Geographic functions

at station coordinates

(\± ,9±

) i=l,2,...,N

Read

screen point

coordinates

(to generate

C data)

(SR 15, 17-20)

Compute and print screen analysis results WvVv D

sk

using as cutoff t= SI

Combine screen point

Fourier coefficients with

original Fourier coefficients

Combine geographic

function values with

original function values

(SR 15, 17-20)

Compute and print WvVv D

sk

using as cutoff t=S2

(or a 10/q rejection)

Yes

Read

rkj> tkj

and^(Tk

,Tk

)

Yes

JXL Compute ( SR 1]-) residuals and

their RMS

for A and B data

No

File mark tape

and transfer

to start
Thus the purpose of the present paper is to fill the gap between

the publications which give the scientific basis for the methods of

mapping and the practical problem of producing ionospheric maps. Moreover, it is designed to complement the research papers already available

by an overall treatment of the mapping processes, several of which are discussed here for the first time

.

The backbone of the Numerical Map Program is an "executive program"

(see section 2), which first enters the data using the routine 01 (SR 01)

and then directs the operations until the final output is obtained. The

main steps of the operations themselves are performed by 17 routines at

the command of the executive program (see Flow Chart l) . Each of these

17 routines forms a logical unit, which often is a relatively large

problem in itself (for example, SR 17--the Gram-Schmidt Orthogonalization; see flow chart 8, second sheet) . Even more, several routines are sometimes linked in a quasi -independent loop, with a loop executive

program of their own (for instance, SR 20--Executive General Data Fitting)

.

The 17 main routines are discussed in sections 3 through 9- For the

executive program and each routine, a detailed program writeup is given

to describe the input, output, storage, card formats, program logic, and

other necessary information. Sample printouts of input and output are given in the appendices

.

Input to the Numerical Map Program consists of the 2k hourly meas- urements of an ionospheric characteristic from all available stations

for a given month (or day) together with such basic information as station coordinates and various parameters defining the mathematical functions

to be used (section 2.3a). The principal output of the program is a set

of numerical coefficients D , , defining a function r(X, 0,t), of

latitude, longitude, and local mean hour angle, which represents the ionospheric characteristic, including its diurnal variation, on a world-wide

scale (section 2.3b).

It will be noticed that in the numbering of the subroutines,

numbers 3; 12, 13, and lk are missing. These subroutines are not

included since they are no longer used in the Numerical Map Program.
Although the basic theory for the methods of numerical mapping has

been published [ Jones and Gallet, 1962a] , some essential procedures used

in the Numerical Map Program have not been justified in scientific literature. In particular, the problem of the "stability" of the geographic

representation in areas where no stations are available appears to be

solved by a method of "screen points", which has been extensively applied

and tested. While the method is described in section 2.2, further justification and illustrations will be given in a subsequent paper.

Section 9*1 describes a method for generating a special set of

coefficients, h , for intercomparing numerical maps from month to

S J£ month or from day to day. Explanations of other new procedures and

formulas are included in the text where they occur. It should also be

mentioned that many of the routines in the present program were originally

written for the 70^- and are now retained with only slight modifications

for purposes of economy. This is at no loss of program efficiency and

accounts for certain differences of techniques appearing in the program.

This paper is intended for two types of users: (a) those who wish

to apply the program as it stands, and (b) those who wish to use the

program with modifications. For the former, a reading of only sections

2 and 3 will largely suffice. The remaining sections are included

mainly for the latter. The terminology and notation used conform, whenever possible, with the reference papers [Jones and Gallet, 1962a and

1962b] so that most of the formulas and definitions are not repeated here.

As a result, some knowledge of the above references will be needed for a thorough understanding of the program.

2. NUMERICAL MAP EXECUTIVE PROGRAM

2.1 Introduction

The primary function of the numerical map executive program is to

direct the operation of the various subroutines. Section 2.2 discusses

the concept and application of "screen points". Section 2.3 describes

input, output, intermediate output on magnetic tape, storage requirements, and subroutines used. Section 2.3 also includes: (l) a summary

list of sense switch settings, (2) a storage plan for the Numerical Map

Program, (3) card formats for input and output, and (h) a flow chart

of the numerical map executive program. Sample printouts of input and

output are contained in appendices A and B, respectively. Before proceeding to these sections, however, it is desirable to review briefly

the choice of time and geographic functions [Jones and Gallet, 1962a,

chapter 3l

A number of options are available with regard to input, output, and

types of analyses (section 2.3). The choice of the time and geographic

functions to be used is considered here. A particular set of functions

is specified by the following parameters entered on the header card

(section 2.3a): (l) The total number of harmonics H used in the diurnal analysis. (2) The numbers k~, k, , and k? = K (referred to in

the program by the symbols PP1, PP2, and PP3 = P, respectively) which

determine a particular set of geographic functions (table 1, section 5)

Note that k_ = PP1 must be greater than or equal zero. (3) In the

geographic analyses, the residuals arrive at the noise level at a much

lower degree for the high order harmonics than for the low order ones. Therefore, it is frequently necessary to truncate automatically the

series of geographic functions for all harmonics of order higher than a certain value, e. g., HI. This can be done by entering HI and a special cutoff, k = PH2, for the geographic series on the header card.

(An example of values commonly used are HI = k and PH2 = k.)

(h) Finally, a numerical code FNCD, is used to identify the choice of

time and geographic functions.
2.2 Screen Points

An important modification included in the present program is the

use of "screen points" for stabilizing the geographic representations

in areas where few or no measurements are available. As was- pointed out

in chapter 5 of Jones and Gallet [1962a], the heavy grouping of stations

in some regions, such as Europe, and the absence of stations in other

regions tends to produce a sort of mathematical instability in the

representation function --that is, unrealistic behavior in areas where

no data are available. The best representation that can be expected for

such a region is a smooth continuation of the variations from surrounding

stations. The instability is alleviated by computing smooth continuations at "screen points" chosen inside the gaps. The "screen point

values" for the ionospheric characteristic are obtained from a deliberately oversmoothed geographic representation of all the data. A second

analysis is then made using both the original data and the screen point

values (see flow chart 2).

The oversmoothed representation in the first analysis is effected

by a radical truncation of the orthonormal series of geographic functions

[see section k.2 of Jones and Gallet, 1962a]. By using a rejection

criterion considerably higher than 5 percent, all but the most significant terms are rejected. For example, the value t = k.O or 6.0 (for

the variable in Student's distribution) has been found to give a satisfactory cutoff in the first analysis, whereas t = 2.0 is generally

The set of screen points for the data of a given month is selected,

prior to using the program, in such a way as to fill all large gaps where

no stations are available and where consequently unacceptable instabilities would be produced (section 2.3a, input (^)). In practice, the set

of screen points remains essentially unchanged from one month to the next,

2A slight variation in the method of defining the screen analysis

will be described in a later paper entitled "Representation of diurnal

and geographic variations of ionospheric data by numerical methods,

II. Control of instability." The screen analysis given there is made

by including only the main geographic variation.

8
Flow Chart 2

NUMERICAL MAP EXECUTIVE PROGRAM

/oOSTj—

Set

" overflow-underflow

trapping mode"

Read data from

tape A2 (system input tape)

Compute

geog. functions

(SR 0*0

Compute Fourier

coefficients

(SR 02)

<-

Read data from

tape Al

Read header card A and B data*

(SR 01)

Write Fourier

coefficients and

geog. functions

on binary output

tape Bl

Write station codes X,0,T.C, and ionospheric data on Binary output tape

Bl

Read and check Fourier coeff. and geographic

functions for A and B data

Compute for each

screenpoint

aj,bi-Fourier coeff. Gk

(X, 9) geog. functions

r(x,S,t) --PRINT

Read geographic

coordinates (X,0) of screen points

from input tape

Compute and print ak>Ek> e

k> dk/ek- Compute Dsk using SI as cutoff.

(SR 20)

Compute and print

^^k'^^k/ekCompute Dsk using

S2 or UF2 as cutoff.

Write D . on A3 for printing

(one per card

format)

Write Dsk on B^

for punching

(one per card

format)

Compute local

residuals and

RMS for A and B

data. (SR 11)

Read station

code, X,0,T.C.

from tape Bl

Punch column binary cards

of coeff. Dsk

on tape B^.

Yes

Compute and write

on B2 r-kp ^kj and ^(Tk

,Tk) using 139 covering points.

(SR 17) No

Read r-'kj> ^kj and <J(Tk

,Tk) from B3

©

Write hsk on tape Bk

for punching

~fc No

^

Write

end of file

on A3

Compute h . (SR 21)

Yes Write hsk on tape A3

for printing
used in the second analysis. These values of t are denoted in the

header card "by SI and S2, respectively. When it is not desired to use screen points, it is possible to make only one analysis. This option

is also specified in the header card.

When the number of stations N is so small that the number of

degrees of freedom (DF = (N- k-l), where (k+ l) is the number of

geographic functions) is less than or equal 28, it is assumed that only

one analysis will be made, and the value of t is for a two tail, 10

percent rejection, depending on the number of degrees of freedom (see

section 8. 2d)

.

In addition to screen points described above, it has also been found

helpful, in filling large gaps in the data, to use "predicted data" at

certain stations for which data were not available for the given month

or day being analyzed. Such "predictions" are made from correlations of

measurements with a solar index. For purposes of identification in the

present paper, we shall refer to measurements as A data, to predictions

as B data, and to screen point values as C data.

2.3 Program Description

(a) Input (see sample printout, appendix A)

The following list gives the different types of input, ordered

as they follow the program. Card formats and sample printouts are given for each type of card input

.

(1) Header card (card format l)

.

(2) Fixed data cards (card format 2) --see section 3«

A data cards precede B data cards.

(3) Ionospheric data cards (card format 3) --see section 3«

A data cards precede B data cards.

(h) Optional screen point coordinates on cards if a second

analysis is to be made (card format h) .

10
(5) Optional input (on binary tape 3; channel B) r.., t , and

, kj kj

n/(T , T, ) . In this case these numbers can be computed in the

first analysis and then entered as input in tape 3> channel B

in each subsequent analysis by having sense switch 2 down.

The IBM 1^01 is used to convert the binary program deck and the

input data deck to magnetic tape.

If it is desired to use the Fortran monitor system, sense switch 3

must be up. In this case, tape 1, channel A is the system tape and the

program and data are read from tape 2, channel A (the system input tape).

There are two program options if the Fortran monitor system is not used:

(l) if sense switch 3 is up^the self-loading program must be on tape 1,

channel A and the input data must be on tape 2, channel A; (2) if sense switch 3 is down, the self-loading program followed by the input data

must be on tape 1, channel A.

(b) Output. The following are regular and optional types of output:

(1) Tape 3> channel A, BCD output (see sample printout, appendix B)

First analysis :

cl , E, , e , cL/e, , k = 0, 1, ..., K (for each Fourier

coefficient)

.

Second analysis (optional):

T values at screen points and cL , E , e , cL/e . (The

following are output from analysis 1 when there is no second

analysis.) Coefficients D (if sense switch 1 is down);

residuals and their root mean square; intercomparison

coefficients h , (if sense switch 1 is down), sk v

(2) Tape k, channel B, binary output to be punched into column

binary cards by 1^01 (see card formats 6 and 7) • These cards

contain the coefficients D , and are stored for permanent

records and later use in predictions. First card is binary

identification followed by the coefficients D n . These cards sk

are punched in absolute locations for use in prediction

programs

.

11
(3) Optional binary output of coefficients D is obtained on

SK. tape 2, channel A, when sense switch 3 is down. This output

is generally used for immediate applications such as the com- putation of contour maps. (Note: if sense switch 3 is up,

tape 2, channel A is used for input)

.

(k) Optional BCD tape k, channel B will contain the coefficients

D , and h . when sense switch 1 is up. These coefficients sk sk * are then punched one per card for later use (see card format

5) . Note: if sense switch 1 is down, these coefficients will

be included in output 1 above.

(5) Optional binary output r . , t . , and v(T , T ) will be

i£j kj K K

written on tape 2, channel B if sense switch 2 is up (see

input 5 and also section 9)

(c) Intermediate output

(1) The geographic functions and Fourier coefficients for A and

B data are written on tape 1, channel B if two analyses are

used. This is done so that corresponding screen point

results can be combined for the second analysis.

(2) Geographic latitudes and longitudes, time corrections, and

ionospheric data (A and B data) are written on tape 1,

channel B for subsequent use in the residual subroutine (SR ll)

(3) Tape 2, channel B is used to write the intermediate triangular

matrices an ., b, ., for use in SR 17 and SR l8 (see section 8) kj' kj'

This tape is subsequently rewound and used for output if the

option is chosen to compute the ?,.j t (see output 5) kj Jsj

rather than read them from input.

(d) Storage

At most instances during the operation of the program, the computer

storage capacity of 32,000 + storage locations is used. See

storage plan (h) for matrix limits and locations.

12
(e) Share subroutines used

Punch B, UA-SPHI, and UA-BDCI, along with those share subroutines

incorporated in each of the seventeen subroutines.

(f

)

Remarks

Trapping mode is set for use in controlling underflow. End of file

is written on tape 3> channel A after each set of data.

If consecutive months of data are to he run, push start at the

program halt or return to system.

If at any time during the computation it is desired to see the

off-line BCD output written on the on-line printer, put sense switch 6 down. The printing may again be suppressed by putting

sense switch 6 up.

(g) Sense switch settings for Numerical Map Program

1 up* writes coefficients D , and h . (as above) on tape h, sk sk ' channel B.

down writes coefficients D and h in BCD one per card

format on tape 3> channel A.

2 up computes r, ., t ., and n/(T , T ) and writes output on

kj kj k k

tape 2, channel B. Computed values are used as input to

SR 21.

down assumes tape 3> channel B contains 3 binary records

rkj't

kj'

and ^T

k'

T

k^ ( see inPut ("5)) for input to

SR 21.

3 up reads data (monitor system) from tape 2, channel A. Omits

writing binary record of coefficients D , on tape 2 } Sl£ channel A.

down reads program and data from tape 1, channel A. Writes

binary record of coefficients D on tape 2, channel A.

6 up normal operating procedure.

down BCD records are written on tape and the on-line printer.

13
(h) Storage Plan for Numerical Map Program

Analysis 1. Max(N.+NT3 )=l80 A D

Max H=8 Max P=80

Analysis 2. MAX(N.+ED+lO=220 A d L

Max H=8 Max P=80

Fixed Data 510l(lst Loc)

Station code 5101 ... +N

Geog. long. 528l ... +N

Geog. lat. 5^61 ... +N

Time correction 56^1 ... +N

Ionospheric Data 5821

Hour 5821 ... +N

Hour 1 6001 ... +N

• •

• • Hour 23 9961 ... +N

Maximum elements 50U0 (=28 x 180)

Fourier Coefficients 510l(lst Loc)

a

Q 5101 ... +(N+NC)

b 5101+ (N+NC) ... +(N+NC)

a

i :

• •

• •

DH

: a^ 5101+2H(N+NC) ... +(N+NC)

Maximum elements 37^0 (=17 x 220)

Fourier Coefficients 11

1

a

Q

11!

b (11581-

a

i :

•

• *

a~ (11581+21

Maximum elements 3060 (:

?8l(lst Loc)

?8l ... +N

hN) ... +E

IN) ... +N

=17 x 180)

Geographic Functions

LM=5101+(2H+1)(N+NC)] (1st Loc)

G M ... +(N+NC)

G M+(N+NC) ... +(N+NC)

• • G M+P(N+NC) ... +(N+NC)

Maximum elements 17820(=8l x 220)

Intermediate Storage 27228

Same order as Analysis 1

Geographic Functions

[M=1158l+(2H+l)N] (1st Loc)

G

Q

M ... +N

G

1

(M+N) ... +N

• • • •

• • G

p

(M+PN) ... +N

Maximum elements 1U58O (=8l x 180)

Residual Subroutine (restored

from tape Bl as in Analysis l)

Fixed Data 510l(lst Loc)

Station code 5101 . . . +N

Geog. long. 528l . . . +N

Geog. lat. 5U6l ... +N

Time correction 56^-1 . . . +N

Ionospheric Data 5821

Hour 5821 ... +N

Hour 1 6001 . . . +N

• •

• •

• • Hour 23 9961 ... +1$

Maximum elements 50^0 (=28 x 180)

Program Origin 101

Intermediate Storage 27

P(P+l)/2

Maximum elements 32^-0

Coefficients D

sk, 30*

228(lst Loc)

^68 (1st Loc)

Maximum elements 1377

Ik
Card Format 1

NUMERICAL MAP HEADER CARD

N CO CO 000

* s t

1 1

1

222

333 444

SSS S66

777

888 999

4 S $

00

44

000

IS II II

1 1 1 222 333 444

555

666

777 888 999

15 16 17 9j9 9

00

x si n

1 I

000

12 43 44

1 t 1 222

333 444

555

666

777 888 999

42 43 44

000

16 41 18

1 1 1 222

333

444

555

666

7 77

999

16 41 41

0000

50 SIS? SI 1111 2222

3333

4444

5555

6666

7 777

9999

S0 5I J

00000000

57 58 59 60 61 62 63 $4 11111111

22222222

3 3 3 3 3 3 3 3 44444444

55555555

66666666

77777777

99999999

51 58 S9 60 61 62 63 "

0000

65 66 67 68 1111 2222

3333

4444

5555

6666

7 7 77 8888

9999

3 67 68

0000

70 71 72 1111 2222

3333

4444

5555

6666

77 77 8888

9999

'3 71 7?

00000000

7] 74 75 76 77 78 79 80 11111111

22222222

33333333

4-4444444 55555555

6 6 6 6 6 6 6 6 77777777

99999999

13 V 75 76 17 18 79 80

CARD COLUMN DESCRIPTION REMARKS

2 3 Header card

k-6 N (xxx) Number of stations (A and B data)

8-9 P (xx) P+l = K+l = Number of geographic functions

11 HI (x)

Highest harmonic for which the geographic

analysis is made with P+l functions

13 H (x) Number of harmonics for diurnal analysis

15-17 FNCD (xxx) Function identification code

19-20 PP1 (xx) k^: Highest term for main latitudinal variation

22-23 PP2 (xx)

k. : Highest term for first order

longitudinal variation

25-26 PP3 (xx) k„=K: Highest term for second order

longitudinal variation

28-29 PH2 (xx)

Highest term used in geographic analysis

of harmonics HI < j O.

31-32 SF (± n) Scale factor i

3^-35 SI (xx) 1 Student's t cutoff in first analysis

37-38 S2 (xx) 1 Student's t cutoff in second analysis

ko TA (x) Option of 1 or 2 analyses

k2-kk NA (xxx) Number of stations with A data

Program automatically places a decimal point between the first and second digits.

15
Card Format 1 (Cont.)

NUMERICAL MAP HEADER CARD

See previous page

C C

i i i 4 j ) i itoiiinjHi!i«iiiiis»jina?«»»J'aa»jinn)4]i»j7»»««i««)»4««4)««i»ji»us4sss«5ji«i«ioiiiioH«5«i)a«»ioiinnMB)in)»n«i

1 1) i 1 11 11 I I 11 11 1 II ! 11 II 1 I II I I 11 It 11 I II 11 11 1 1 11 It I 1 1 I II I 11 1 1 II I 1 I 1 I I 1 1

I II I 1 II I I I I 22222222222222222222222222222222222?2?22?22222?22222222222

3333333333333333 3333333 3 333333333 333333 33 333 3 33333333 33 333 4444444444444444444444444444444444444444444444444444444444

555555555555555555555555555555555555555555 555555555 5 55 5555

6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 66 6 6 6 G 6 6 66 6 6 6 6 6 B 6 B 6 6 6 6 6 6 6 6 6 777777777777777777777777 7 77 77 77 7 77 7 7 777 77 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7

222222222222222222222?

3333333333333333333333

4444444444444444444444

555555 555 55 5555 5 555 5 5 5 66666666S6666666666666

7 777777 77777 7777777777

8 8 8 8 8888888888886688888888888888888888886888888888888888888888888888888888888888

99999999999S9S99999999S999 9 99 9999999999999 999 9 99 9 99999 99 9 9 9 9 9 9 999 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9

i i j 4 s t i I i io nil ii i» is « 17 ii is » 2i n n m » » n » » » ]i 3» 33 m is » n » ji 40 « « c 44 45 « « 4« • » si y sj » a * si si a ti o b •• e « n ii b is ii n n i' n » » ii n »

CARD COLUMN DESCRIPTION REMARKS

1+6-48 WC (xxx) Number of screen points

50-53 S (xxx.x) Sunspot number

55-56 MN (xx)

Order of months (or days) for use

in prediction program

65-68 YYMM (xxxx) Year and month

69-72 DDLC (xxxx) Date, layer, and characteristic (see card format

for ionospheric data)

16
Card Format 2

FIXED STATION DATA

L03TC

P O coo

xxx.x DO 000

J 4 5

1 1

1

222

333 444

555

666

777

999

3 4 5

0000

1)11

1 1t 1 2222

3333

4444

5555

6666

7777

9999

iiii

±xxxxx>cx00

000

I) 14 IS

1 1

1

222 333

444 555

666

777

888

999

II » 19

0000

IS 17 It 19 1111 2222

3333

4444

5555

6666

7777

9999

IE IT II

XJKOOC.X

<D,* SH

EH

000

24 29

1 I 1 222 333

444

555

666

777

999

21 24 15

8

00 i xxx

0000

26 27 78 28 Mil

2222

3333

4444

5555

6666

7777

9999

26 27 78 29

J.

000

)2 13 34 35 1111

222 333

4 44 555

666

77 7

999

a v is

- Blank —

0000000000000000000 0000000000000000000000000

36 37 » 19 40 414? 43 4J 45 46 1) 41 49 50 91 92 51 54 55 55 57 58 59 60 SI 67 61 64 85 66 67 S8 69 70 71 73 73 74 15 76 77 78 79 80

1 I I 1 I I 1 1 1 1 1 1 1 1 1 1 I 1 1 I 1 1 1 1 1 1 H 1 II I 1 I 11 1 I 1 I 1 1 1 1 1 222222222222222222222222222222222222222222222

333333333333333333333333333333333333333333333

444444444444444444444444444444444444444444444

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 666666666666666666666 66666666666666666666 6 666

7 77777 777777 77 77777777 7 J 777 7 77 77777 7777 7 77 777 888888888088888888888 888 88 8888 8 8 88888888 8 8888

99999999999999999999999999999999999999999 9999

16 17 31 33 40 41 42 43 44 49 46 47 41 49 SO 91 77 53 54 SS 56 97 59 59 60 61 62 63 «4 '5 St 57 69 69 73 71 77 71 V 75 76 17 18 79 SO

CARD COLUMN DESCRIPTION REMARKS

1 1 Ionospheric data

2 Fixed station data

3-5 STC Station code

6-9 OOO.OSxxx.x<360.0

Geographic longitude (0) in degrees east of

Greenwich.

10-11 OO Constants

12 11 or 12 Punch

Sign of geographic latitude. 11 indicates

southern latitude, 12 indicates northern latitude.

13-15 OO.OSxx.xS90.0 Geographic latitude (\) in degrees

16-19 OOO.OSxxx.x< 36O.O Reference longitude (9p) for time zone See [Jones and Gallet, 1962a, section 3- 1-1 20-21 OO Constants

22 11 or 12 Punch Sign of time correction. 11 indicates negative

correction, 12 indicates positive correction.

23-25 x.xx Time correction (in hours).

T.C. = (e - 6r)/15-

26-29 OOO . OSxxx .x < 36O .

O

Geomagnetic longitude: see Smithsonian Physical

Tahles, Ninth Revised Edition, pp. 493-501.

30-31 OO Constants

32 11 or 12 Punch Sign of geomagnetic latitude. 11 indicates

south, 12 indicates north.

33-35 XX.

X

Geomagnetic latitude: see Smithsonian Physical

Tables, Ninth Revised Edition, pp. 1*93-501.

17
Card Format 3

IONOSPHERIC DATA

IDENTIFICATION

• oj •po

coo 000

] 4 S

1 1

1

222

333

444

555 666

777

999

] 4 S

Date

Y

HOURLY MEASUREMENTS

HR R S

14 I) It II 1111 2222

3333

4444

5555

6666

7777 8886

9999

14 IS 16 IT

HR

oooc

n ?o i in Mil

2222

3333

4444

5555

6666

7777

8888

9999

8 20 21 22

HR

R 3 0000

24 2128 21 1111 2222

3333

4444

5555

6666

7 7 7 7 8888

9999

24 28 21

HR

R 3 0000

29X11 12 1111 2222

3333

4444

5555

6666

7777

9999

29 X )l 12

HRR S 0000

» IS K 31 11M

2222

3333

44 4 4 5555

6666

7 7 7 7 8888

9999

V K 16 31

HR

B 0000

99 40 41 42 1111 2222

3333

44 4 4 5555

6666

7 777 6888

9999

13 40 41 *i

HR

R 3 0000

4S«4T 11 1 1 2222

3333

4 4 4 4 5555

6666

7 7 7 7 8888

9999

44 45 46 41

HRR S 0000

49 10 II 12 1111 2222

3333

4444

5555

6666

77 77 8888

9999

19 50 51 J

HR

0000

11 MIT 1111 2222

3333

4 4 44 5555

6666

7777

9999

14 51 « 11

HR

R 3 0000

59 60 61 62 1111 2222

3333

4 4 4 4 5555

6666

7777

99999

59 60 61 62

HR HR

R S 0000

64 45 66 61

1 1 1 222

333 444

555

666

7 77

9999

u e« «

R 3 0000

an ii n

1 1 1

222

333

444

555

666

77 7

9999

S9 '9 II 27

Blank

0000000

14 15 16 11 1! n K 1111111

2222222

3 3 333 33 4444444

5 5 5 5555 6666666

7 777777

9999999

1' 15 18 11 n 29 M

CARD COLUMN DESCRIPTION REMARKS

1 1 Ionospheric data

2 1 or 2 1 refers to hours from 00:00 to 11:00

2 refers to hours from 12:00 to 23:00

3-5 STC Station code

6-7 YY Year

8-9 MM Month

10-11 DD Date: 01 S DD § 31 indicates day of month

DD = U5 indicates monthly median

12 L

Ionospheric layer: L = 0, F2 -layer j L = 1,

Fl-layer; L = 2, E-layer; L = 3, E s -layer

13 C Ionospheric characteristic: C = 0, foj C = 1,

fxj C = 3, M3000; C = h, h ; C = 5, &

lk-73 Hourly Readings .Twelve readings of five positions each

First four positions --numerical reading (R)

Fifth position—qualifying symbol (s)

18
Card Format k

SCREEN POINT INPUT

sX

100

I I J

1 1

1

222

333 444

sss

666

777

888 999 999

sX

000

1 i 9

1 1

1

222

333

444

S55

666

777

999

i i i

000

1? 1) II 19

1 1

1

sX

222 333 444

5 5 5 666

777 888

999

1} U 19

000

l( I) II 111 222

333 444

555

666

777

888 999

IS 17 II

sX

000

19 2011

1 1 I 222

333

444

555 666

777

888 999

COO

22 23 M

1 1 1 222

333 444

555

666

777

999

27 23 2*

SX

000

29 212)

1 1 1 222

333 444

555 666

7 77 868

999

2S2S2T

000

9 30 31 32 13

1 I 1

sX

000 ana

I 1 I 222 333

444

555 666

777 888

999

21 2S 30 31 32 33

222

333

444 555

666

777

888 999

000

M19D

f 1 I 222 333

444

555 666

7 7 7

999

sX

000 nan

1 I 1 222

333 444

555

666

777

999

00

<o«i

I 1 1 222

333 444

555

666

777

999

M 35 36 3? 31 33 1*3 41 «? 42 44 45 999

sX

000

43 44 45

1 1 I 222 333

444

555 666

77 J

000

45 *7 4S 19 50 51 000

sX

1 1 1 222

333 444 555

666

7 1 1 888 999

« <l tl 19 50 51

1 1 1 222

333 444

555

666

77 7 888

999

000

92 9] 94

1 I I 222

333

444

555

666

777

999

sX

00

95 56 97

1 I 1

222

333 444

555 666

777

888

999

00

99 colli a a

1 1 1

000

SI59SC

1 ' ' 222

333 444

555

666

777

999

51 59 GO

sX

222

333 444

555

666

7 7 7

999

61 62 63

000

E4C9R

1 1 1 222

333

444

555

666

77 7

999 U5»

sX

000

67 an

1 1 1 222

333 444 555

666

777

999

5168 69

000

7172

I 1 1 222

333 444

555 666

7 77

999

'0 71

sX

ooo

73 74 75

1 1 1 222 333 444

555

666

777

999

7' 75

000

77 71

1 1 222

333 444

555

666

777

BBS

999

'6 77 relra so

00

19 60

1 1

22

33

44

55

66

77

68

99

CARD COLUMN DESCRIPTION REMARKS

1, 7, ••-, 73 s Sign of geographic latitude

("blank for plus and — for minus)

2-3, 8-9,

....7U-75 XX Geographic latitude (degrees)

k-6, 10-12,

....76-78

eee Geographic longitude

(degrees east of Greenwich)

19
Card Format "5

COEFFICIENTS D , AND h , DEFINING NUMERICAL

sk sk

MAPS OF IONOSPHERIC CHARACTERISTICS

IDENTIFICATION FUNCTIONS SN Coefficient D , or h ,

CM XXX .X ±x.xxxxxxx E ±yy

000

I 2 ]

1 1

1

222

333 444

55S

666

777 888

999

i ? }

000

I I 10

1 1 1 222

333

444

555 666

777

999

I I 10

00D00

IS II II IS II 11111

22 222 333

444 555

666

777 888

999

IS 16 Hi II li 20 21

CO

2! 23

I 1

22

33

44

55

66

7 7

88

99

22 23 24 25 2S|21t2l 29

000

(4 25 21

1 I 1

222

333 444

555 666

77 7 888 999

000000|0

17

I I

000

43 41 42

1 1

1

222

333 444

555

666

777

0000

M45 4I

I I 1

222 333

444

555 666

7 77

41 42 4]|U4S

1

999

40 41 42 999U4S4S

00000

41 4! SO SI 11111

22222

33333

44444

55555

66666

11111

88888

99999

II 41 49 SO 51

000

S2S1S4

1 1

1

222

333

44 4 555 666

777

999

USJ

00

X y>

1 1

22

3 3

4 4

55

66

77

88

99

000

SI SIM

1 1

1

222

333

44 4

555

666

777

00000000000000000

12 13 64 B 66 61 H « 10 II 12 73 74 75 It 17 71 11111111111111111

2222222

3333333

144444

(55555

6666666

7 777 777

222222222

333333333

444444444

555555555

666666666

777777777

999

SI SI so 999 99999999999999

3 6» 67 61 69 13 71 77 73 V 75 76 17 18

00

is no

1

1

22

3 3

44

5 5

66

7 7

99

79 K For Ds

i£ or hs -^ the number given "by the first eight digits and sign is

multiplied "by 10 raised to the power given "by the last two digits and sign.

CARD COLUMN DESCRIPTION REMARKS

k-5 yy Year

6-7 MM Month

11-12 DD Date: See Ionospheric Data Card Format.

13 L

Ionospheric layer: See Ionospheric Data

Card Format

.

Ik C Ionospheric Characteristic: See Ionospheric

Data Card Format

.

17-19 NNN Number of stations used in the analysis

22-23 P P+l = K+l = Number of geographic functions

27 H Number of harmonics for diurnal analysis

30-31 FNCD Function identification code

3^-35 PP1 kn

= Highest term for main latitudinal variation

38-39 PP2 k. = Highest term for first order

longitudinal variation

^3 T

T = 1 for coefficients Dsk

T = 2 for coefficients h^

1+7-51 XXX.

X

Sunspot number

55-56

60-6l

sskk

Indices for coefficients D sk or hsk

[Jones and Gallet, 1962a, chapter 7]

65-78 ±x. xxxxxxxE ±yy Coefficient D , or h in floating decimal form

SK Sl£

20
Card Format 6

NUMERICAL MAP BINARY IDENTIFICATION

ouo 000

119

1 1

1

222

333

000

1 1

1

222

333

000

'< 13

1 1

1

222

333

000

IE IT II

1 1 1 222

333

000

19 20 21 000

a h

1 1 1 222

333

1 1 1 222

333

000 aan

I 1 I 222

333

000

2129 30 000

31 J2 «

1 1 1 222

333

I I I 222

333

000000000000000000000000000000000000000

»»37M»<0 4l«l3mi<HI»<1»5IP5354iSi6 57M59B)tlPt3H«5B6>6iail)ll7; 1)1111111111111111)11111111111111111111

222222222222222222222222222222222222222

33 33333333333333 33 333 3 3 333 33 33 3 33 333333

00000000

73 7< 75 7f 77 78 79 BO 11111111

2222222?

33333333

444

S5S

666

444

555

666

444

555

666

444

555

666

444

555 666

444

555 666

444

555 666

444

555 666

444

555 666

44*44444444444444444444444444444444444

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 666666666666666666666666666666666666666

44444444

55555555

66666666

777 888

9_9_i

777

Hi

777 888 111

777

111

777 888 111

777

999

777 888 Li!777 888 Hi777

888 LI

7 7777 7777777 77777777777777777777777777

888888888888 8 88888888888888888888888888

9999 99999 9 9 99 9 99 9999 9 999 99 9999 999 9 9 99 99

77777777

, 99999999

M»»J1MB««l««4445«««eSSIUUMS^SJSl»BS10t3S««!«S7aii9>9 1177 t] V 75 76 77 7« 79 M

CARD COLUMN DESCRIPTION REMARKS

1 7 and 9 Punch Column binary

2-3 Absolute binary location (100) _

k-6 Check Stun

7-9 YYMM Year, month

10-12 DDLC Date, layer, characteristic

13-15 N Number of stations (A and B data)

16-18 P P+l = K+l = Number of geographic functions

19-21 H Number of harmonics for diurnal analysis

22-24 FNCD Function identification code

25-27 PP1 k • Highest term for main

latitudinal variation

28-30 PP2

k-, : Highest term for first order

longitudinal variation

31-33 PP3 kp = K: Highest term for second order

longitudinal variation

21

3. DATA READ SUBROUTINE 01

The data read subroutine (SR Ol) is employed by the numerical map

executive program for reading and storing the header card, fixed data^

and ionospheric (A and B) data. Although most of the necessary information concerning input is given in section 2, certain additional information is necessary, in particular, the discussion of the scale factor

and the list of stops resulting from improper input (section 3g) • Other

topics include: output, storage, calling sequence, subroutines used,

general remarks, and program logic (flow chart 3).

(a) Input (see sample printout, appendix A)

Input card formats and sample printouts were discussed in section

2. One fixed data card and two ionospheric data cards must he read

for each station (for A and B data) . All fixed data cards precede

the ionospheric data cards, and the latter must be paired by stations

in the same order as the fixed data. In each pair, the type 1 card

(col. 2) must precede the type 2 card (col. 2). Also^the stations

with A data must precede those with B data.

For ionospheric data other than foF2, a special scale factor must

be inserted in the header card. The ionospheric data are assumed

to be given by four digit numbers (XKXX) (see card format 3). If

no scale factor (blank) is punched on the header card, the program

places a decimal point between the second and third digits (XX.XX).

For other characteristics, however, (such as M3000) the position of

the decimal point is specified by the scale factor. A scale factor

of plus (or minus) n (n ^ 0) moves the decimal point n places

to the right (or left) from the position at the right of the fourth

digit. "Minus zero" places the decimal point to the right of the

fourth digit. For example, for M3000 the scale factor is -3 so that each ionospheric reading is taken as X.XXX.

(b) Output includes: station code, geographic longitude (0) and

latitude (X), time correction, and ionospheric data.

23
Flow Chart 3

DATA READ SUBROUTINE 01

/Read one card

>J record from

input tape

(Header card)

Unpack and store N,P,H1,H,FNCD,

PP1,PP2,PP3,PH2,

TA,S1,S2,NA,NC,

S,MN,YYMM,DDLC —

Set

Col. 2 test

location(OlAD)

to zero

Read one card record from

input tape

Unpack and store station code, geog. long., geog. lat., and time correction

Initialize instructions for storing: station code/

longitude, latitude, and time correction (T.C.)

from fixed data card

No

Yes

Set

i 01AD

= 2

Initialize 01BA - ST0(LMEDNS)+N,1

(store ionospheric datum instructions)

Yes

Yes

Modify

01AY-01AY+5 01BA-O1BA+180

Store datum

hy 01BA

Obtain

ionospheric datum for

one hour

No

2k
(c) Storage (see storage plan in section 2)

The input uses maximum, storage of 50^0 locations starting at

(5101) Q

. SR 01 itself takes 157 locations.

(&) Calling sequence

C L A (EXTIN)

S T OLXX

TRA 01ST

( extin ) tra (next)

(next) (continue)

(e) Subroutines used

Modified share subroutine PE-CSMO, which includes: READT, FLOAT,

FIXED, SCALE, and BCDPK.

(f) Remarks

(1) Index registers A, B,and C are used with no provision to

restore them.

(2) In order to read data on tapes other than Al or A2^

a

modification must be made in READT.

(g) Stops

SR 01 stops at 01AC for the following conditions:

(1) An ionospheric datum is zero or blank.

(2) Input cards not in proper order with respect to column 2.

Proper order requires: (i) first card has 3 in column 2,

(ii) the following N cards have in column 2, and (iii) the

following 2N cards have alternately 1 and 2 in column 2.

(3) Column 2 contains a number other than 3> 0, 1> 2.

(k) Identification of ionospheric data cards does not match

identification on header card or ionospheric data cards

(in pairs) are in different order from fixed data cards.

25

k. FOURIER ANALYSIS SUBROUTINE 02

SR 02 is used to compute Fourier coefficients for the diurnal

analysis of the ionospheric data. The coefficients are then corrected

to local mean time [Jones and Gallet, 1962a, section 3«l]« SR 02 is

entered one time for each set of (A and B) ionospheric data (i.e., N

times) . This section gives a general description of the subroutine

including the program logic (flow chart k) .

(a) Input

(1) Hourly values y , y~, . .., y_> of ionospheric data from

one station.

(2) Number H of harmonics.

(3) Time correction T.C. (in hours).

(b) Output

Fourier coefficients an

, a., and b., amplitudes c. and phase

angles i|r. corrected to local mean time (LMT) for j = .1, 2, . .., H

J (see [Jones and Gallet, 1962a], section 3-l). Note: the c. and

J

i]/ . are merely intermediate results and hence are not permanently

J stored.

(c) Storage

There are k (H+ l) storage locations required for output:

A0 to A0 + H, BO to BO + H, CO to CO + H, and PSIO to PSIO + H.

The routine itself (not including subroutines) takes 328 storage

locations.

(d) Calling sequence

C L A (EXTIN)

S T 02XX

(EXTIN) T R A (next)

(next) (continue)

(e) Subroutines used

Share subroutines: UASQRA, NA0331, UA-S+CL, and UA-SPRT

27
Flow Chart 1+

FOURIER ANALYSIS SUBROUTINE 02

(x = zone time hour anglej x. = (l5°i-l80°); i = 0,1,..., 23)

Initialize: Index B = j=0 (float.)

j=0 (fixed ) sin JX~°

° s

' cos JX=1

sin 15j=0

cos 15j=l Compute

15(T.C.)

©

Yes ©^-

Compute and store a

o

=c o= h z yi p =V°

Yes Compute

partial

Yes Yes

12

No

Compute and store a = (l/l2) za

f^ = (1/12) ZP

'3 "3^3

Compute

Part. lat=Zy

± cos jx± Part. £©=2y. sin jx.

No

Compute cos jx. . = cos jx. cos 15j-sin jx. cos 15j and sin jxi+1

sin jxi cos 15j+cos jxt sin 15j

Store

cos jx1+1

-» cos jx

± sin Jxi+1

-* sin Jx

±

Compute and store

P.

* . = arctan —

(see special flow

chart, 2nd sheet)

O^Compute and store ^=<M-15j(T.C)

(phase angle

corrected to LMT)

Compute and store aj-oj cos tj

Ujocj sin tj

(Fourier coeff. corrected to LMT) No

Compute cos 15(j+l) = cos 15 cos 15j-sin 15 sin 15j

sin 15(J+1) = cos 15 sin 15j+sin 15 cos 15j

Store

cos(j+l)x

Q

sin(j+l)x

-cos jx

Q

-«cos jxQ

-sin jx -*sin jx

r

Store

(floating andy

fixed point)

,

Store

cos 15(j+l)-»eos 15 j sin 15(j+l)4sln 15 j

Compute and store

Pj= o

'3 XJ XD

28
Flow Chart h (Cont.)

Special Flow Chart for Computing *. (Second Sheet)

29
(f) Remarks

(1) The AC and MQ overflow indicators should be off at entry to

SR 02.

(2) Index registers A, B^and C are used with no provision to

restore them.

(g) Stops

A halt will occur at 02BM +2 if an attempt is made to take the

square root of a negative number.

30
5. GEOGRAPHIC FUNCTIONS SUBROUTINE Ok

SR Ok is used to evaluate the geographic functions G, (X,0) at

station coordinates and at screen point coordinates (see table l) . These

functional values are subsequently used in the geographic analyses. For

this purpose, SR 0^ is entered one time for each of the N stations and

once for each screen point. SR 0^ is again entered once for each of the

N stations for computing residuals (section 7) • A general description

of the subroutine is given, including the program logic (flow chart 5).

(a) Input

(1) Geographic coordinates (x.,0.) for one station

(X. = latitude, 9. = longitude)

.

(2) Parameters PP1 (^ l), PP2, and PP3 = P defining the choice

of geographic functions G, (X,0). If no longitude terms are

desired, we set PP1 = PP2 = PP3 = P. See table 1 (this

section) and the discussion of the choice of functions in

section 2.1.

(3) Function identification code FNCD (see header card).

(h) If OkST entry is used, N, N-l, ..., 1 must be in index

register A.

(b) Output

Geographic function values G, (X.,0. )> k = 0, 1, ..., K.

J£ 1 X (c) Storage

(1) Entry through OkST causes the G, (X. ,0.) to be stored in

i£ X 1

matrix form involving N(K + l) elements.

(2) Entry through 0UST2 causes the G. (X.,0.) to be stored in

K. 1 X consecutive locations starting at FUNCT. This involves

(K + l) elements.

(3) SR 0l+ (not including subroutines) itself requires 286

storage locations.

31
TAI3LE 1

GEOGRAPHIC FUNCTIONS Gk

(X,0)

3

o

-P -H

•H -P P> 03

cd -H ^

a as

o

•H

13•H>

id •H

-d

•H

ido

PId

H

1

•P•H

13

pi

d

CDX

•Hg

3

P

•H

bO

idO

PI

sd •H

0) nd

Sh O

-P

CO

£n •H

5

Pi P

•HO

PI

id •H

in

cu o

d

ido

o

(U CD

k Gk

(x,e)

1

2

• • • k

o

l

sin X

sin2 X

• # • sin• \X

V1

V2

cos X COS

cos X sir

kQ+ 3

kQ+U

sin X cos X cos

sin X cos X sin

• • •

• • •

• •• ••• •••

*•• ••• •••

sin X cos X cos

sin X cos X sin

V1

k,+2

2 cos X cos 20

2 cos X sin 20

1^+3

2 sin X cos X cos 20

2 sin X cos X sin 20

• • •

• • •

• •• ••• • • •

• •• • • • •••

K-1

K

q2 2 sin X cos X cos 20

q2 2 sin X cos X sin 20

32
Flow Chart 5

GEOGRAPHIC FUNCTIONS SUBROUTINE Ok

= Loc. of Gk

(X

1 ,0± LGK ), i = 1,2, ..., N, k = 0,1, ..., P. FUNCT = Loc. of G.(X,e), k = 0,1, ..., P.

(oIseJ—

Initialize

ohm-* sto(lgk) +n,i

0UBL-* N

Initialize

O^AR- STO FUNCT, 1

0l+BL-> 1

Store Gk*y

O^AR

Store

Gk(in AC) in O^AP © Store

sin X

in O^AI

<r

JL. Compute

sin X, sin

cos X, cos

Modify instructions

_^| in Ol+AR by

+ amount in OkSL

Compute

G, = cos X sin 9

©

Yes

No

Compute

in AC

Gk= G

k-2 -Sin X

Compute

cos X sin 29

Yes

Compute

G. =CO£ in AC

=cos X sin 9

>

uk

Compute

G. sin X

(in AC)

Compute

cos X cos Zi

No

Set

G.k-1

33
(d) Calling sequence

C L A EXTIN

S T ota

T R A OhST (or 0^ST2)

EXTIN T R A (next)

(NEXT) (continue)

(e) Subroutines used

Share subroutines: UA - S + CL and U

(f) Remarks

(1) The AC and MQ overflow indicators should be off at entry to

SR 0^.

(2) Index registers A, B, and C are used with no provision to

restore them.

i
6. SYNTHESIS SUBROUTINES 05-10

6.1 Explanatory Remarks

Six subroutines are described in the present section. These subroutines are used to compute the value of the function r(X,0,t). One

frequently needs to evaluate r(x,0,t), (a) at many locations for a fixed instant of time, or (b) at a fixed location for several different

instants of time. In such cases, considerable savings in computer time can be gained by use of the following subroutines . The techniques

employed are described in detail in section 3*1 of [Jones and Pallet,

1962h]

.

(a) SR 08 should be used when, for successive computations, T is

evaluated for a fixed t and varying \ and 9. The entry for

the first of such computations is 08ST, and for all following

08ST2 until t changes.

(b) SR 09 should be used for fixed \ and 9 and varying t. The

entry for the first of such computations is 09ST and for subsequent

computations 09ST2 (until \ and 6 change)

.

(c) SR 10 should he used for successive computations of V for fixed

T and 9 and for varying X. SR 10 is entered initially at 10ST

and then at 10ST2 until T and 9 are changed.

The following three subroutines are used in connection with the above:

(d) SR 05 computes sin jt and cos jt for j = 1, 2, ..., H, given

t, H, and TRA exit instruction in 05XX.

(e) SR 06 computes D, (t) for k = 0, 1, ..., K, given the matrix of

coefficients D , sin jt and cos jt (j = 1, 2, ..., H),

H, K, and TRA exit instruction in 06XX. For an explanation of

D,(t), see section 3»la of [Jones and Gallet, 1962b].

35
Flow Chart 6

SYNTHESIS SUBROUTINES 05-10

Store

1 for 1st of series

-£

Compute and store

sin t (set sin Jt=sin t) cos t (set cos jt=cos t)

Compute and store sin jt«-sin( j+l)t = sin jt cos t + cos jt sin t cos jt«-cos( j+l)t = cos jt cos t

- sin jt sin t

7K

Add -2 to

Index A

Store

sin jt (STO C0S0T,1 ) cos jt (STO COSOT+1,1)

Compute

P + 1

JL

LDSK = Loc. of D

k

(t) LDM = Loc . of D coefficients

Initialize locations 06AC-6T0 LDSK+P+1,2

06AD^AD LDSK+P+1,2 ^ 06ae-6t0 ldsk+p+1,2

o6af-<cla ldm +p+i,2

OoAI-FMP LDM +2P+2,2

Initialize

06AH -» LDQ

C0SOT+1+2H,!

Compute and add

one term to

Dj

s(t) partial by

06AH, 06AI , 06AD , 06AE

^

Set D (t) partial

by 06AF, 06AC

Compute

2H

J0,k

Yes Modify

06AI by P+l

FUNCT = Loc. of G (\,0), k = 0,1, LALBT = Loc. of a.(\,9) and b.(\,f

,, P.

/ N Compute

Compute and add one term to part. L using 07AE and 07AF

Initialize

->) 07AC -» STO LALBT X 2H+1, 1

Compute

P + l

Initialize

07AE-CLA FUNCT -P+l, 2 07AF-*FMP LDM+P+1,2

Modify

07AF by +(P+l)

36
Flow Chart 6 (Cortt.) (Second Sheet)

Compute r(X,0,t) for fixed t and varying X and

Compute

cos Jt, sin Jt

i = 1, ..., H

using SR 05

Compute Dk

(t) k= 0,1,..-,

P

using SR 06 *->

Evaluate G

k

(X,0)fc=O,l,,

using SR Ok

(0i(ST2)

•,P

Set

E =

Initialize

08AH-»IDQ LDSK+P+1,1

08AI->FMP FUNCT+P+1,1

Compute

Z part, using

08AH

Yes Store

r(x,e,tn) ^/Rxi£\

^Uoxx/

Compute P + 1

Compute r(X,S,t) for fixed X and and varying t

Compute G. (X,0)

k= 0,1, -.., P

using SR OU

(014ST2)

Set Z =

Compute Z part using

09AH and 09AI

Yes

Compute

Sj (x,0)

using SR 07

bj(X,0)

Compute

cos Jt sin jt

J = 1, ..-, ^ using SR 05

Initialize

09AH-€DQ C0S0T+2H+1,1

09AI-*MP IALBT+2H+1,!

Store r(x

o

,0o

,t) = z

Compute

2H+1

Compute r(X,0,t) for fixed T = t-0 and varying X

Compute

*o = 9o

+ T

o

Compute

r(X,0,t

Q

) by SR 08

(08ST) —^uoxx/^

Compute

r(X,0,t

Q

) by SR 08

(08ST2)

37
(f) SR 07 computes a (X,0), a.(X,0) and b.(x,e) (j = 1, 2, . .., H)

,

J J given the matrix of coefficients D , the functional values

Sri Gk

(X,0) (kaO, 1, ..., K) from SR 0^4-, H, K, and TRA exit

instruction in 07XX. For an explanation of a.(x,0) and b.(X,9),

J J see section 3«lc of [Jones and Gallet, 1962b]. (Entrance to SR Ok

is through 0teT2.)

6.2 Program Description (for subroutines 08, 09 and 10)

(a) Input

(1) X = geographic latitude,

(2) = geographic longitude,

(3) t = local mean hour angle, or

T = universal hour angle.

(k) Matrix of coefficients D , s = 0, 1, ..., 2H and

k = 0, 1, . .., K.

(5) PP1, PP2, and PP3 = P.

(6) H = number of harmonics for the diurnal analysis.

(b) Output

The desired functional value, r(X, 0,t) or r(X,0, 0+T) where

t = + T.

(c) Storage

Subroutine 08 and 09 each take 72 storage locations, not including

other subroutines used. SR 10 takes 11 storage locations in

addition to the locations used in SR 08 and other subroutines.

(d) Calling sequence

C L A EXTIN

S T 08XX (or 09XX or 10XX)

TRA 08ST (or 08ST2 or 09ST or 09ST2 or 10ST or 10ST2)

( EXTIN ) TRA (NEXT)

(next) (CONTINUE)

38
(e) Subroutines used

SR 08 uses subroutines 0^, 05 and 06 (see remarks) and hence all

subroutines used "by these. SR 09 uses subroutines Ok, 05, and 07

(see remarks). SR 10 uses SR 08 and all subroutines used by it.

(f) Remarks

The AC and MQ overflow indicators should be off at entry to

subroutines 08, 09, and 10. They, along with their included subroutines,use index registers A, B, and C, making no provision to

restore them.

39

7. RESIDUAL SUBROUTINE 11

SR 11 is used to compute residuals between the original ionospheric

data (A and B) and the values computed from r(X,0,t) and their root

mean square. Examples of such results are given in the sample printout

in appendix B. These results are used to test the "goodness of fit" of

the function r(X,0,t) and to spot undue irregularities in the data.

Separate results are obtained for the A and B data, since the residuals

for the latter are in general systematically higher than for the former.

The program description is followed by a logical diagram (flow chart 7) •

(a) Input

(1) v Matrix of coefficients D 1 , sk'

(2) Ionospheric data (A and B)

,

(3) Station latitudes X. (i = 1, 2, . . ., N),

(k) Station longitudes 9. (i = 1, 2, . .., N),

(5) Time corrections,

(6) Station codes,

(7) N = number of stations (A and B data),

(8) PP1, PP2, and PP3 = P,

(9) H = number of harmonics for diurnal analysis, and

(10) Exit instruction TRA, in 11XX.

(b) Output (see sample printout 2, appendix B)

(1) For each station (A and B data) the 2k hourly residuals

(original ionospheric data minus values computed from

r(x,e,t) /

(2) Root mean square (RMS) of the 2k residuals from each station,

(3) RMS of residuals from A data stations taken together,

(k) RMS of residuals from B data stations taken together, and

(5) RMS of residuals from all stations (A and B data) taken

together.

iH
Flow Chart 7

RESIDUAL SUBROUTINE 11

->

Store

N-NA-«NB -decrement

of 11BU

->

Initialize

11AC CLA LSTCDS+N,1

11AD CLA LSTCDS+N+l80,l

11AE CLA LSTCie+N+360,l

11AF LDQ LSTCDS+N+S^O,!

-> Initialize

iiag-cla LMEDNS+N,!

Set

h

zt = ° (zone time)

C orapute t=-l80+15T.C. using 11AF

£- Set partial Z loc. R =0

<r- fSet / Index

Store Station code for I.D.,11AC

Xfor I.D. and comput. ,11AD

Qfor I.D. and comput., 11AE

Write out I.D., station

code

X, 0, headings ^

Compute

r(X,0,t) using

SR 09 (09ST)

Print

h, T, R, y

Compute and store for printing

Residuals = R = y-r through 11AG

Restore

Index A

and

Index B

Store r(X,9,t)

for printing

~*~

Compute R

partial 2 Partial Z R'partial Z loc .R

,2

Modify

1LAG by +180 t-t+15

h-h+1

Compute

r(X,0,t) using

SR 09 (093T2)

Yes

Compute

local R

2 =l/2U Zloc.R2

Store R. Compute K_ as floating point number

Print

local,

with I'.I

No

Compute and print

k2
(c) Storage

SR 11 uses 185 storage locations (not including other

subroutines employed)

.

(d) Calling sequence

C L A (EXTIN)

S T 11XX

T R A 11ST

(extin ) t r a (next)

(next) (continue)

(e) Subroutines used

Share subroutine UA-SPRT, SR 09, and all included subroutines.

(f) Remarks

(1) AC and MQ overflow indicators should be off at entry to SR 11,

(2) Index registers A, B, and C are used making no provision to

restore them.

(g) Stops

if an attempt is made to take the square root

(2) 11BQ - k ) °f a neSative number

J+3

8. GENERAL DATA FITTING SUBROUTINES 15, 17-20

8.1 Explanatory Remarks

The general data fitting method described in chapters 2 and 6 of

Jones and Gallet [1962a] is performed in the present program by five

subroutines:

SR 20 Executive general data fitting,

SR 15 Inner products,

SR 17 Gram-Schmidt orthogonalization,

SR 19 Least squares fitting, and

SR 18 Coefficients D , . sk

SR 20 sets up the necessary requirements for input, output, storage,

and number of entries to each of the other subroutines, and restores all

index registers. Input, output, storage and calling sequences for SR 20 are included in section 8.2. The descriptions of the other subroutines

are given in section 8.2e. The program logic for each of the five

subroutines is given in flow chart 8.

8.2 Program Description

(a) Input (to SR 20)

(1) First of N (K+ l) consecutive storage locations used

successively to store the functional values G, (X.,0.),

Ak

(X

i ,0i

), and Bk

(X

i ,9

1

), i = 1, 2, ..., N, and

k = 0, 1, ..., K.

(2) First of N (2H + l) consecutive storage locations used for

the (2H + l) sets of N Fourier (time series) coefficients

for geographic analysis.

(3) First of K(K+ l)/2 consecutive storage locations used

successively to store the triangular matrices of coefficients

*ky V V L

kj (k=1> 2

> •••> K arid

j = 0, 1, ..., k-i).

^5
Flow Chart 8

GENERAL DATA-FITTING SUBROUTINE 15, 17-20

SR 20 Executive General Data-Fitting

Set up calling sequence

for orthogonalization

SR 17- Put address of matrix

to be used in address & decrement 20AB, 20AH.

Set up calling sequence

for original function

SR 18 and MLS SR 19- Put matrix address in address of 20AD, 20AL, and 19CB.

>

Set up storage area for P(P+l)/2

locations

Compute (2H+1). Put in calling sequence

of first entry to to SR 19.

<$- Place SI or S2 in Kl

for N > 28

<£-

_E_

Set up locations

for Fourier coeff

.

input to SR 19

\f

Compute( 2H+1) -( 2H1+1) Put in calling sequence

for second entry

to SR 19.

•£

Put (P+l) into

calling sequence for first entry to

SR 19.

-=»

Put (PH2+1) into

calling sequence for second entry

to SR 19.

Enter SR 19 TSX 19ST, k PZE(P+l),0,(2Hl+l)

(least squares fitting)

£-

J±

Enter SR 17 TSX 17ST, h PZE (A),0,(B) PZE b

kJ (second

orthogonalization)

4-

Enter SR 17 TSX 17ST, k PZE (G),0,(A) PZE ak<j (first

orthogonalization)

Place - TCO

for second entry to SR 19

-5»

Enter SR 19 TSX 19ST, k PZE(PH2+1),0,

' 2H+1 \

-2H1+1/

->

Backspace tape B2 one record

for reading

bkj

-^

Enter SR 18 TSX l8ST. k PZE (bkJ ) ^

(compute a. )

Initialize tape

writing in SR 17 and SR 18

-£

Place

1 - TCO

for first

entry to

SR 19±.

Rewind tape B2 for reading

Rewind tape B2 for reading a, .

Jl

Enter SR 18 TSX 18ST, h PZE (a^j)

(compute D k

SR 15 Inner Products

Set up location

from first term in calling sequence

[A+N] - 15AC

JL

Restore

Index A

<r Yes

->

Set up location

from second term

in calling sequence

[B+N] -» 15AD

Form AC and MQ

sum for greater

precision

£-

Store

zero in

2 sum

cells

Form product of 15AC,1 and 15AD.1

Yes

Form AC and MQ sum

No

Sum =

-> Round to

8 places

he
Flow Chart 8 (Cont.) (Second Sheet) SR 17 Gram-Schmidt Orthogonalization

->

Save

contents

of Index C , (17DF)

-^. Compute

P+1-17BG

Set up locations

of matrices obtained

from the calling

sequence

(A and B)

Set up location for triangular matrix

ak,j or bKi to he computed and written

on binary tape B2

->

Store

AQ

(x

1)-« (x1

) = 1

Compute

(Bk

,Bk

) IPS, 1

->

Modify

1TAK by +1

Store k =

-»1TAK

Yes >

Compute 17AK • N

Modify location

of output matrix

Bk

(x

i

) by N

Compute and store

Increase Index A

^y (-D

Modify triangular

matrix locations

by +17AK

Modify location

of A

Q

(x

i

) by

(k-N)

Initialize location

of output matrix

Bjx.)

k^ x' ^

Add A^(x

±

)

sum cell-*17BD

Compute partial

k-1 I

b

kJ V^

-* sum cell, 17BD

Modify location

of input matrix

(x

±

) by N

Yes

Modify location

of output matrix

Modify output

locat by +Nlocation B, (x.

)

k i

Load

Index A

from

17BF

Write on binary tape B2

one record of

a, . or b, . k,j k,j

S-

^7
Flow Chart 8 (Cont.) SR 19 Least Squares Fitting

(Third Sheet)

No

Store from calling

sequence

F -* 19AC X - 19G-A

Store zero into k

(190P+1)

Put first

location of matrix Bk

(i) -19EA

Yes Store

P+l - 19FP

N( float ing)-*TJ

Initialize

location for Fourier coeffs,

Store 2-19FZ Store 0-19SC 4r

_^k_ Set up location for

b, matrix

k

Set

Index B \ , >

Index A

_ n / 'V _ lOAr1

Set

19AC

Compute

1, (y> V

Compute

\= \ ^w

Compute

Compute

ek=-s/Ek

/[N-(k+l)]

Subtract

** for E,

Place

Ek-1

in AC

Compute NI-Y, for E

i=l Store 1-*19GC

Yes

Compute

Vek

Yes k < 2Yes

Compute degree of freedom N-(k+l), and look up Kl from table of Student's t variable No

Modify location

of matrix

Bk(i) (19EA)

by +N

Put

k+1 - k

(190P+1)

<r

Print cL

k

on output tape A3 ^

Modify

Index B K

- by -1

Place k

(190P+1)-19FZ

Store zero in location of b. + (P+l), 1 ±>

Put

F = P+l for harmonics § j S HI,

= PH2+1 for harmonics HI < j § H . X = 2H1+1 for harmonics § j S HI,

= (2H+1)-(2H1+1) for harmonics HI < j S H..

Modify

location of

b, matrix for k

Modify location

of Fourier

coefficients

)+8
Flow Chart 8 (Cont.) (Fourth Sheet) SR 18 Obtaining Y in terms of £ D. G,

->

Put 2H- 18AG ^

Initialize

locations of

bk+ P

bv + P+l

Initialize location -1- for intermediate

storage of * _ or L , Ok qk

ORC -+ 18CA

ORC+P -» 18CF ORC+P+1 -> 18CD

^

Store

l8CF-» 18CB 0-18AI

£-

Modify

location

for sum check of

next record

<- Read triangular

matrix of b- or a^j from

tape B2

kj £-

Initialize locations

for input matrix bk

. or a^j read from

tape B2

loc hki i (F+l)P

->l8BC,

Store PP- 18AL, 18AC P+l -» 18AD ->

Set

Index

= P+l > [

Store hjj (k = 0,1, ..., P) in ORC + P+1,1

No

Modify

Index A and B by -1

Yes

Compute V °r L

lk

18CB LDQ

18BC FMP 0,1 18CD FAD 0,2 18CA STO 0,1

2

Compute

a. or D

sk

Increase Index C by +1

Modify 18CF by -I8AD

Modify location

of bk

+P

and bk+P+l by P+l

Yes

18AL=

Modify

l&AG by -1

Modify

18AL by -1

±.

Modify

l8AD by

+ I8AL

No JL

Modify 18AC by +18AL

ORC+k = location of i Q k, k = 0,1, ..., P . 0RC-(k+l) = location of & x k

k = 0,1, ..., P-l. q

' ORC - 2 (P+2-£)-(k+l) = location of £ a k, k = 0,1, , P-q, for 2 S q H P. j=2 qj "L Computation starts with £., (or L- 1

) followed by £ , I p__ ... etc.

k9
Note: The matrix £, . is used after second orthogonalization to

transfer Z b B to the form Z a A , see section 6.2 of Jones

and Gallet [1962a]. Then the matrix L is used to transfer

Z a, An to the form ZD . G. (see section 2.2 [Jones and Gallet, k k sk k

v ' 1962a] )

.

(h) Output (for each of the (2H+l) sets of Fourier coefficients

written on tape 3> channel A) (see printout in appendix B)

(1) Orthonormal coefficients cL, k = 0, 1, . .., K.

(2) Sums of squares of residuals E, , k = 0, 1, ..., K.

(3) Root mean squared residual e , k = 0, 1, . .., K.

(k) Ratios \/%> k= 0, 1, ..., K.

(5) Coefficients D , k = 0, 1, ..., K.

SiC (c^ Storage

(1) N (K+ l) locations for input (l) above.

(2) K (K+ l)/2 location for input (3) above.

(3) (2H+1) (K+ l) locations for the coefficients D

( s = 0, 1, . . . , 2H and k = 0, 1, . .

. , K)

.

(d) Calling sequence

T S X 20ST, h

P Z E (G), 0, (ADFC)

(LFC), 0, (Kl)

Note; Kl denotes the value of Student's t variable

used for truncating the orthonormal series Z &, F . All terms are rejected after the last term for which

I cL /e I ^ Kl. The number Kl is either SI or S2

(see header card) for the first or second analysis,

respectively. Kl could also be the value of t for

a two tail, 10 percent rejection depending upon the

number of degrees of freedom

DF = N - (k+l),

50
Table 2

STUDENT'S t VARIABLE FOR

TWO TAIL 10$ REJECTION

1

[Degrees of Freedom (D.F.) = N - (k+l).]

D.F. t

1 6.31U

2 2.920

3 2.353

k 2.132

5 2.015

6 1.9^3

7 1.895

8 1.860

9 1.833

10 1.812

11 1.796

12 1.782

13 1.771

Ik 1.761

15 1.753

16 1.7^6

17 1.7l»0

18 1.73^

19 1.729

20 1.725

21 1.721

22 1.717

23 1.71^

2k 1.711

25 1.708

26 1.706

27 1.703

28 1.701

Reference: [C.R.C., 1957]

51
where N is the number of Fourier coefficients being analyzed

and k+ 1 is the number of functions used at this point in

the analysis (see section 2.1). Table 2 contains the values

of t for a 10 percent cutoff.

A different percent can he used for the rejection criterion by

replacing the values of t in table 2 by a different set, as follows.

The program must be reassembled with the new table of values in locations DF2 to DF2 + 27. The following card format should be used.

Table 3

Card Format for Change in the Rejection Criterion

Card Column 2 8 12 18 ._1

_. 72

DF2 DEC X.XXX,X.XXX, ...,X.XXX, ...

JJiiiU -A. • Xj\J\ , -A. • y\_A_X. , . . • ,.A. . A_X_X. , • • • DEC X. XXX, X. XXX,

•

Note: No columns after 72 can be used. A blank after column

11 causes all remaining information on that card to be

ignored.

(e) Description of subroutines used

(l) SR 15 is used to form inner products of two N dimensional

vectors. Suppose U is a vector whose components are stored

in locations A, A + 1, . .., A+ N - 1 and V is a vector with

corresponding components in B, B+ 1, ..., B+N-l. Then

given N and the locations A+N and B+N, SR 15 computes

the inner product (U, V) and leaves it in the accumulator.

The calling sequence is:

T S X 15ST, k

P Z E (A+N), 0, (N)

P Z E (B + N)

52
(2) SR 17 is used to orthogonalize a set of K+ 1 linearly

independent vectors of dimension N. The method employed is

the Gram-Schmidt orthogonalization and reorthogonalization

process described in sections 2.2 and 6.2 by Jones and Gallet,

[l962aj. SR 17 forms the orthogonal functions B,(X,0) from

the geographic functions G, (X,0) (table l) . Given the

locations for input (l) and input (3)> SR 17 first computes

the values A, (x.,0.) and stores them in place of the

G, (X. , 0.). Following this, it computes the values B (X.,0.)

(from the second orthogonalization process) and stores them

in place of the A, (X.,0.). The intermediate coefficients

an

. and bn

. are also computed, the b, . being stored in

kj kj ' kj

place of the a, • • (Note: in order to conserve storage space

the input and output locations determined by SR 20 are the same as used here) . The triangular matrices of coefficients

a, . and b. . are -written on tape 2, channel B for later use

kj kj 3 in SR 18. The same storage locations are also used by SR 18

for intermediate storage of matrices JL . and L, . . The

kj kj

calling sequence is:

T S X 17ST, k

P Z E (C+W), 0, (C + N)

P Z E (D)

where C is input (l) and D is input (3) above.

(3) SR 19 is used to fit successively, by least squares, the

orthogonal functions generated by SR 17 to each of the 2H+1

sets of N Fourier coefficients (input (2)). Output from

SR 19 includes output (l), (2), (3), and (k) listed above.

The orthonormal coefficients cL are set equal to zero for

all k greater than the last k for which |cl /e | ^ Kl.

When fitting Fourier coefficients for harmonics less than or equal HI, the calling sequence is:

T S X 19ST, h

P Z E (P+ 1), 0, (2H1 + 1).

53
For harmonics j such that HI < j ^ H }

the calling sequence

is:

T S X 19ST, k

P Z E (PH2+ 1), 0, 2(H-H1).

(h) SR 18 is used to compute the coefficients D (output (5)

above) . Input to SR 18 are the orthonorraal coefficients cL from SR 19, and the triangular matrices of coefficients a, . kj

and "tx, . on tape 2, channel B. SR 20 determines the number

kj * ' of entries to SR 18 and the position of tape 2, channel B.

The calling sequence for SR 18 is:

T S X 18ST, k

P Z E (IGK), 0,

Note: location LGK which was used in SR 17 for storage of

the matrices of orthogonal values is now free to be used for

the storage of the triangular matrices b. . and an & & . as

kj kj

they are read from tape 2, channel B.

5^
9- INTERCOMPARISON COEFFICIENTS SUBROUTINES l6 AND 21

9.1 Summary of Method and Formulas

For intercomparing numerical maps of ionospheric characteristics

from month to month, it is desirable to use series of orthonormal functions, since the terms in such series are independent. The orthonormal

functions F, (X,0) used for a given month (or day) depend, for their

construction, on the particular set of stations available [Jones and

Gallet, 1962a, chapter 2] . Therefore, since the set of available stations

changes from day to day and month to month, one cannot use the orthonormal

coefficients cL for intercomparison purposes. For this reason we have

made use of a special set of orthonormal functions IL (X,0), constructed

relative to a fixed set of 139 points which cover the globe approximately

uniformly. The coordinates of these points are given in table h. Thus,

it is possible to represent the function r(X, 0,t) in terms of a fixed

set of orthonormal functions 9.and the resulting& coefficients h , can be

, sk

intercompared from one month (or day) to the next.

The construction of the functions H. (X, 9) is completely analogous

to the construction of the orthonormal functions F (X,0) [Jones and

Gallet, 1962a, chapters 2 and 6] . One begins with the same set of geographic functions G, (X,0), with the station coordinates (X.,0.)

replaced by the set of 139 covering points in table k. The first

orthogonalization provides:

(9.D

k = 1, 2, ..., K

TTote: The index s in h n is used here in the same sense as sk

(56) in [Jones and Gallet, 1962a].

R

o k-1

v—

1

\ I

r

kj

R. + Gk

55
Table h

COORDINATES OF THE 139 COVERING POINTS

X = Latitude 9 = Longitude

± 90 0°

± 80° 25° + 90°i, i = 0,1,2,3

± 70° 10° (i+6i), i = 0,1,2,3,^5

± 10° (l+2k), k = 0,1,2 20° (1+21), i = 0,1,. ..,8

± 20°k, k = 0,1,2,3 1+0° i, i = 0,1, ... ,8

56
where

A second orthogonalization yields:

To R

ok-1

v-1 T

k

—

) K- T - zL kj j + E

k

(\, V

kj ( V V

•

k= 1, 2, ..., K,

k=0

to the form

K^ ! Y

k

= k=0

\ Hk

•

The first step is:

K

r—

i

Y

k

= I

k=0

rk Rk

>

(9.2)

(9.3)

(9.^)

The orthogonal functions T, (X, 0) are then normalized Toy

T

\= , = k=0, 1, ..., K. (9.5)

V(t7^)

Consider now the problem of transforming the expression

K

\= > D

k

Gk

(9.6)

(9.7)

(9.8)

"The inner product notation (G , R.) is used here to denote

a summation Z G, (\,0) R.(l,0) over the set of 139 covering points

(table h-).

57
which from (9«l) and (9.6) provides:

K

rk

= D

k

- ^ rjk

V., k = 0, 1, ..., K-l, and

j=k+l

(9.9) rK

= D

K

'

This gives

K

\ =

2.. \ \ ' (9.10)

k=0

where from (9-3) and (9-8)

K

tk

= rk

" 7, t jk r

j

' k « 0, 1, ... , K-l, and

0=k+l

(9.H)

t

K

_ rK

" D

K '

Finally the desired coefficients in (9-7) are ohtained from

\=\^\T\) f k=0, 1, ..., K. (9.12)

Two subroutines are described in this section. SR 21 is an executive subroutine which employs SR 2.6 to compute the coefficients

r, and t , the numbers *", ., "tv

- and n/(T, , T ) being obtained from

the numerical map executive program (see input 5, section 2.3). The

program description is given in section 9«2.

9.2 Program Description

(a) Input

(l) Triangular matrices r and t , k = 1, 2, ..., K and

j = 0, 1, ..., k-l defining orthogonal functions for the

139 covering points. (Note: these numbers are either com- puted by the numerical map executive program (section 2) or else read in from tape 3> channel B. See input 5 and output

5, section 2.3)

.

58
Flow Chart 9

INTERCOMPARISON COEFFICIENTS SUBROUTINES 16 AND 21

SR 21 Intercomparison Coefficients Executive Subroutine

Compute

(P+l) - 21AJ

(2H+1) - 21AG

~7K

Set Index B |^_ 2H+1

Set up calling

-^| sequence for

SR 16 in 21AC,21AD

Compute -tjj. using SR 16 TSX 16ST, k PZE tjk,0,rk

Compute

h , = t. s/(T. ,T. ) sk k

v k' k'

^ Modify

21AE and 21AF by P+l

<-

->

Compute location IBM+P+1 for

output (rk

or tk) from SR 16

JL

Compute rk

using SR 16 TSX 16ST, k PZE t.. ,0,D . jk' ' sk

SR 16 (Computes r, or t. )

-^

No

Save

Index C (16BA) 16AH

->

Compute

location of ^sk or ns+P *

i6al,i6as,i6at

-9>

Compute

location of

rk or tk

-> 16AI, 16AJ ^

Compute

2H+1

-•decrement 16AD

Store zero - 2 cell

(16AW)

Store P -» 16AC P-l - 16AE <-*

Store P- 16AY <r

Change location

of rkj or tkJ by

P(

g+1^ ->1oAG,16AE ^

Set

. -s Index B

-, i6ac

Compute partial

S r^ Dj or Lt rj by

16AS LDQ 0,1

16AE FMP 0,2

Increase

Index A by +1

Modify

16AC by +16AH

16AY=0N

Modify

16AE by +1

16AY by -1

Compute

P

rk

= Dk

" Z r

lk D1 or " p k k jak+i jk j

Jik Modify

16AH by -1

Yes

Store

*p-*P

Restore

Index C (16AD)

Modify ^ location D

sk or rk

by P+l

Place location

of r .. or t .. Jk jk in AC

Restore

Index C (16BA)

Compute rQ

first, starting with the term r D .

59
(2) Square roots of inner products n/(t , T ), k = 0, 1, . . . , K.

(Note: these numbers are also either computed by the numerical

map executive program (section 2) or else read in from tape 3>

channel B.

(3) Matrix of coefficients D , , k = 0, 1, . . . , K,

s = 0, 1, ..., 2H.

(b) Output

Matrix of intercomparison coefficients h , , s = 0, 1, ..., 2H

and k = 0, 1, . .

.

, K.

(c) Calling sequence

T S X 21ST, h

(d) Subroutines used

SR l6 computes the coefficients r and t . The r are computed

when entering SR l6 by

T S X 16ST, k

(LTl), 0,

The t are computed when entering SR l6 by

T S X 16ST, k

(LT2), 0,

(e) Remarks

(1) The index registers are restored after they are used.

(2) Underflow is checked internally in the code.

60
ACMOWLEBGEMEIWS

The authors gratefully acknowledge the assistance they

received from a number of persons. A significant contribution

to the work described here was given by Mrs. G. Anne Hessing

who was responsible for the program development using the IBM

65O computer and for the initial programming on the IBM 70^

Valuable assistance in correcting the flow charts and the program description was rendered by Mr. Ronald P. Graham. Computer

services were obtained from the operators in the Computer

Laboratories of the National Bureau of Standards (in Washington,

D. C, and in Boulder, Colorado). Able assistance in typing

the manuscript and assembling the material for this paper was given by Mrs. Anna von Kreisler.

61

10. REFERENCES

C.C.I.R. (1959), Report No. l62 and Study Programme Wo. 1*4-9, Documents

of the Plenary Assembly, Los Angeles (Published by the International

Telecommunication Union, Geneva)

.

C.R.C. Standard Mathematical Tables (1957), 12th Ed., p. 2kk (Chemical

Rubber Publish. Co., Cleveland, Ohio).

Central Radio Propagation Laboratory Ionospheric Predictions (Jan. 1963),

No. 1 (U. S. Dept. of Commerce, National Bureau of Standards).

Hinds, M., and W. B. Jones (Dec. 1962), Computer program for ionospheric

mapping by numerical methods, Unpublished Report (National Bureau

of Standards, Boulder, Colorado)

.

Jones, W. B., and R. M. Gallet (Dec. i960) , Ionospheric mapping by

numerical methods, J. of the International Telecommunication Union,

No. 12, 260-26)+.

Jones, W. B., and R. M. Gallet (May 1962a), The representation of diurnal

and geographic variations of ionospheric data by numerical methods,

Telecommunication J. 29, No. 5, 129-1^9; and (July-Aug. 1962a)

J. Res. NBS 66D (Radio Prop.), No. k, U19-U38.

Jones, W. B., and R. M. Gallet (Nov. -Dec. 1962b), Methods for applying

numerical maps of ionospheric characteristics, J. Res. NBS 66D

(Radio Prop.), No. 6, 6>+9-662.

Ostrow, S. M-. (Dec. 21, 1962), Handbook for the Central Radio Propagation

Laboratory ionospheric predictions based on numerical methods of

mapping, National Bureau of Standards Handbook 90*

63

APPENDIX A

SAMPLE PRINTOUT OF INPUT TO NUMERICAL MAP PROGRAM

3 154 52 4 8 100 12 36 52 4 -2 60

10687219900+868 210000+066201000+790

10483141700+823045000+645191000+700

10982243900+799285000-2742 39000+810

10J8229 7400 +82628 5 000+0831 70000+850

102800 58000+806045 000+087

10980274100+80028 5 000-0732 35000+860

10178015700+782015000+005012900+744

10J7629 1300+766285000+042 3 5 5000+8 70

10 97426 5100+747270000-03 3289400+8 30

10373080400+735105 000-164162000+640

1077120 3200+713210000-045241200+68 5 10J7029 1400+70 528 5000+043000700+8 19

10169019000+697015000+02 7116200+669

10J69306500+69331 5000-05 70 32700+798

10168033000+69003000 0+02 012600 0+6 30

10167020300+678015000+035115700+652

10166026600+67403 000 0-023120000+640

10266066700+66506000 0+045148 000+570

10165022100+656015 000+047114700+6 29

10164018800+646015000+025111000+6 30

10664186600+644180000+0442 37000+680

10764212200+649210000+0152 56600+646

10964264000+643270000-040315500+737

10 A6433 8200 +64 1345 000-045 7 11 00+701

10 J6329 1400+638285000+043360000+750

10462129600+620135000-036194000+510

10 761210100+612210000+0012 58200+609

10J613 14600+61 231 5000-003036^00+ 71

2

10160030700+600030000+005

10059011100+600015000-026100000+59 5 10159024600+60503000 0-036113000+560

10158017600+598015000+017106000+585

1095826 5800+5882 70000-0283 22800+687

100563558 00+57436000 0-028 083400+607

101560443 00+561045000-005126000+502

10256061100+56706 000 0+007140800+484

103 56084900+565090000-034159700+459

10055013400+546015000-011099000+5 50

1015503 7300+5550 3 000 0+049120600+5 08

10855246700+5462 5 5 00 0-05 5 301000+620

100 5300 5200+521000000+035089500+537

100 52014600+500000000+097097500+500

10352104000+525105 000-007174000+410

10 452 11 3500 +520 12 0000-043 182 100+4 5 10051359400+51536000 0-0040 6 3 300+543

1065118 3400+51918 0000+023240100+472

10050010100+516015000-033093900+521

10049004600+501000000+031088000+520

10149039700+472045000-035120000+420

10949262600+49927 0000-049 3 22900+58 8 10048007600+481000000+051090000+494

10848236600+48424000 0-023294 300+533

10147019200+474000000+128101000+470

10 547143000+47015000 0-04 7 2 08 500+3 70

2 142 59 1868 58064500

5 8 06

5806

5806

5806

5806

5 8 06

5806

5806

5806

5806

5806

5 8 06

5 8 06

5806

5 8 06

5806

5 8 06

5 8 06

5806

5806

5806

5806

5806

5806

5806

5806

5806

5806

5806

5806

5806

5806

5806

5 8 06

5806

5806

5 8 06

5806

5 8 06

5806

5806

5806

5 8 06

5806

5806

5806

5806

5806

5806

5806

5806

5806

5806

5806

65
10J4730 7300 +476 30000 0+04902 140 0+ 58

4

5 8 06

10046000 300+466000000+002079500+499 5 8 06

10045007300+468015 000-051088700+48 5 8 06

1014 5020500+448015000+037100000+44 5 8 06

10545141700+454135000+045206100+352 5 806

10 945284100+45428 5000-0063 51500+569 5 8 06

10044009000+446015000-040 5806

10144034100+448030000+027113000+390 5 8 06

10 343076900+43207 500 0+013150500+33 7 5 8 06

10041012500+418015000-017092100+42 5 5 806

10040000300+408000000+002 5806

10 J402 8 5900+404285000+0063 54000+5 10 5 806

10 5 39140100+39713 5000+03420 5500+2 94 5 8 06

109 38282900+38 728 5000-0143 50300+5 00 5 806

1023705 8300+379060000-011133000+300 58 06

10837237800+374240000-015298600+4 36 5 8 06

10535139500+357135000+030205500+254 5806

1C03435 3200+309360000-045070000+ 38 5 8 06

10 8 3225 3500+323255000-010317000+4 12 5 8 06

10431130600+312135000-029197900+203 5 8 06

10929279400+28428 5000-0373 47000+39 5 8 06

1032807 7200+286075000+015149000+188 5 8 06

10426127800+263135000-048195700+152 5 8 06

10° 162 8 1800+266285000-02 13 50000+3 8 5 8 06

10* 74121500+2501 2 0000+0 10 189000+ 140 5 8 06

1C 13072600+230075000-016144000+140 5806

1CJ2200 5500+228000000+03708 0000+ 26 5 8 06

10422113600+22212 0000-0432 78000+110 5 8 06

10720203500+208210000-043268200+2 08 5 8 06

10219072800+190075000-015143900+098 5 806

10 J 18292800 + 185300000-04800 2 100 + 2 99 5 806

10416120600+164120000+004189300+050 5 8 06

10A14342600+148360000-1160 54700+215 5 8 06

10313080300+131075000+0351 50 100+03 5 8 06

10311078700+108075000+02 5148500+010 5 806

10310077500+102075000+017014800+006 5 8 06

10909280100+094285000-033348600+206 5806

10308077000+085075000+013146000-014 5 806

10007003900+07400000 0+0260748 00+106 5 806

10J06304800+058360000-3680 15000+ 170 5 8 06

10J0 528 58 00+0452 8 5 000+00534 5000+ 160 5 8 06

10104018600+046015000+024089000+0 50 5 806

10102030200+015000000+201991800-019 5 8 06

10301103800+013105000-008172800-101 5 806

10 10K028800-02 3030000-008097300-0 38 5 8 06

1050K140800-025000000+9392 11000-120 5 806

10 10M0 15200-044000000+ 101 083600-029 5 8 06

1090M2 78700 -0462 8 5000-042 3 50000+066 5 8 06

10A0N324900-05333 0000-0340 34000+040 5 806

1090P2802 00-068285 000-03 2 349000+040 5 806

1090R28 1400-091285000-024350000+02 5 8 06

101 1J027500-1 16000000+183094100+ 12

7

5 8 06

109 1K284700-12 028 5 000-00 2 3 54000-00 5 5 806

10 J 10292000-165300000-053000900-0 50 5806

1071P210700-177210000+005283000-150 5 806

66
1021Q047500

1011R017700

1051R146700

1072J200200

10J2L313500

10120028100

10J20294600

1052P152900

10430115900

1013M018300

10J3M301500

1053N149000

10J3O287000

1054K.147200

1064L172800

10J4L294700

1024R070300

10J5J302200

1065K169200

1055M159000

10J6L299300

10J6M296500

10360093000

10460110500

10560140000

10170023300

1067K170300

10A7O333400

10A7P318900

1C67Q166800

1077Q197800

10880240000

10090000000

10471128900

10919260500

10513144900

10111043200

10411125000

10705197900

10701202700

1050R147100

1061Q178200

1062R182100

Iono_ 1016R039600

spheric 1047P106900

Data _ 11687580645

12687580645

11483580645

12483580645

11982580645

12982580645

11J82580645

12J82580645

11280580645

12280580645

-18804500

-19201500

19315000

-21219500

-23531500

-26203000

-26930000

-27515000

-30312000

-34103000

-34530000

-35315000

-36628500

-42915000

-43618000

-43230000

-49407500

-51730000

-52516500

-54515000

-63031500

-64830000

-66509000

-66210500

-66713500

-70403000

-72316500

-75533000

-77731500

-7781650C

-78219500

-80024000

-9000000C

+71612890

+19326050

+13614490

+11604320

+11012500

+05919790

+01920270

-09414710

-18017820

-29218210

-69003960

-78410690

000590 06

000540 05

000520 05

000560 05

000570 05

000560 05

000530 05

000600 05

000560 05

000580 05

0+017112500-2

0+018083000-1

0-022219000-2

0+035273800-2

0-010022500-1

0-013091400-2

0-036004000-1

0+019227100-3

0-027185800-4

0-078079700-3

0+010009500-2

0-007224400-4

0+013356000-2

0-019224500-5

0-048252800-4

0-035003000-3

0-031

0+015009300-4

0+028253300-5

0+060243300-6

0-105006100-5

0-023004000-5

0+020146000-7

0+037179000-7

0+033

0-045063000-0

0+035277000-7

0+023017500-6

0+026147000-6

0+012295000-7

0+019312000-7

0+000336000-7

0+000000000-7

0+000

0+000000000+0

0+000213000+0

0+000114000+0

0+000193800-0

0+000265900+0

0+000271400+0

0+000

0+000251200-2

0+000257800-3

0+000780000-7

0+000129000-8

00 0600 0590

30 0500 0500

20 0510 0520

80 0580 0600

60 0580 0585

50 0570 0555

60 0580 0520

90 0600 0600

60 0550 0530

70 0600 0600

37 5806

80 5 8 06

84 5806

09 5806

28 5806

69 5 8 06

60 5806

57 5806

17 5806

27 5806

31 5806

39 5806

50 5806

16 5806

80 5806

20 5806

5806

03 5806

72 5806

10 5806

15 5806

33 5806

80 5806

80 5806

5 8 06

68 5806

50 5806

75 5806

70 5806

90 5806

40 5806

10 5806

80 5806

5 8 06

00 5806

40 5806

69 5806

01 5806

51 5 8 06

22 5806

20 5806

22 5806

00

80

0590 0550 0570 0560 0550 0550 0560 0550

0550U0500 0510 0500 0530 0560 0560 0590

0550 0560 0600 0580 0600 0530 0500 0550

0590 0570 0580 0580 0570 0570 0580 0580

0585 0560 0550 0550 0560 0540 0550 0550

0555 0540 0570 0565 0540 0570 0560 0550

0540 0510 0520 0570 0580 0560 0600 0590

0570 0580 0560 0550 0560 0540 0540 0540

0540 0520 0550 0550 0590 0620 0650 0600

0600 0600 0600 0600 0600 0600 0600 0600

67
11980580645000550 0570 0530 0550 0550 0540 0530

12980580645000580 0560 0570 0580 0580 0580 0580

11178580645000510 0550 0580 0560 0570 0560 0520

12178580645000620 0620 0620 0630 0630 0620 0640

11J76580645000560 0575 0530 0520 0510 0530 0470

12J76580645000530 0560 0575 0580 0570 0580 0595

11974580645000560 0540 0560 0520 0520 0540 0540

12974580645000560 0580 0540 0560 0590 0600 0600

11373580645000600 0600 0570 0540 0570 0530 0560

12373580645000640 0660 0660 0640 0640 0620 0620

11771580645000540 0550 0520 0520 0540 0540 0550

12771580645000520E0570 0600 0580 0600 0600 0590

11J70580645000550 0520 0490 0520 0500 0510 0520

12J70580645000570 0580 0600 0590 0570 0580 0600

11169580645000560 0570 0580 0580 0640 0630 0620

12169580645000640 0640 0630 0620 0630 0630 0630

11J69580645000525 05 20U0520U0500 05OnU0485 0475

12J69580645000610U0600 0590U0560U0580 0575U0580

11168580645000620 0620 0630 0620 0620 0640 0630

12168580645000660 0660 0650 0630 0630 0640 0640

11167580645000560 0600 0590 0610 0610 0600 0600

121675806450006"- 0630 0630 0620 0630 0640 0630

11166580645000640 0620U0630U0600U0660 0640 0630

12166580645000660 0650 0650 0650 0650 0650 0650

11266580645000600 0600 0620 0640 0640 0660 0670

12266580645000700 0710 0700 0680 0660 0670 0670

11165580645000620 0620 0610 0640 0650 0630 0640

12165580645000670 0660 0660 0650 0650 0660 0660

11164580645000630 0630 0630 0630 0640 0640 0640

12164580645000670 0660 0670 0650 0670 0660 0670

11664580645000650U0630U0620 0640 066" 0660 0640

12664580645000600 0600 0620 0620 0630 0630 0640

11764580645000530U0550U0540 0590 0560U0600U0580

12764580645000610 0600 0610 0605 0600 0605 0600

11964580645000560 0540 0530 0540 0510 0530 0530

12964580645000630 0680 0680 0660 066C 0640 0650

11A64580645000500D0540U0520U0530U0530 0560 0560

12A64580645000640 0650 0670 0650 0640 0630 0630

11J63580645000530 0500 0520 0520 0480 0460 0500

12J63580645000660 0640 0640 0650 0640 0620 0630

11462580645000820 0780 0700 0720 07]0 0720 0700

12 462 58 0645 000730R0 7 30R0 740R0 7401^7 6000740 0740

11761580645000530 0520 0540 0550 058^ 0610 0640

12761580645000600 0620 0620 0610 0600 0600 0620

UJ61580645000480U0500U0470U0465U0490 0470 0520

12J61580645000655 0680 0670 0650 0640 0630 0630

11160580645000700 0700 0700 0710 0760 0760 0730

12160580645000720 0700 0760 0700 0750 0760 0710

11059580645000700 0690 0660 0660 0670 0660 0660

12059580645000690 0690 0690 0680 0690 0720 0700

11159580645000700 0690 0690 0700 0680 0710 0680

12159580645000710 0700 0690 0690 0680 0680 0700

11158580645000680 0640 0650 0660 0670 0670 0680

12158580645000700 0700 0680 0690 0700 0700 0700

11958580645000560 0520 0500 0500 0500 0490 0500

0550 0550 0530 0560 0580

0580 0550 0540 0560 0560

0590 0620 0610 0650 0620

0640 0630 0580 0580 0550

E0495 0540 0520 0560 0550

0570 0590 0570 0550 0560

0520 0540 0550 0580 0540

0580 0600 0600 0600 0580

0590 0590 0610 0620 0630

0620 0630 0630 0620 0620

0540 0470E0510 0590 0580

0600 0600 0560 0560 0550

0530 0570 0580 0580 0600

0590 0580 0580 0570 0550

0640 0640 0650 0660 0650

0620 0590 0600 0590 0580

U0480 0530U0560 0555U0620U

0610U0590U0590 0555 0520

O650 0640 0660 0680 0680

0640 0620 0620 0640 0600

0610 0630 0640 0650 0630

0620 0610 0600 0600 0600

0650 0650 0690 0680 0660

0660 0660 0650 0600 0620

0640 0670 0690 0680 0700

0680 0660 0650 0660 0620

0670 0680 0690 0670 0670

0650 0660 0640 0620 0630

064-0 0680 0670 0680 0670

0650 0670 065C 0620 0630

0680 0610 0620 0610 0600

0630 0640 0640 0620 0650

0580 0600 0620 0595 0595

0570 0580 0615 0550 0530U

0550 0570 0580 0600 0600

0620 0600 0610 0620 0610

0560 0580 0600 0620 0630

0590 05 80D058 0U0 550U0 530U

0450 0480 0500 0500 0620

0600 0560 0600 0560 0540

0720 0720 0720R0720R0720R

0760 07f>0 0780 0800 0800

0630 0640 0620 0600 0600

0600 0610 0600 0590 0540

0570 0585 0620 0630 0640

0610 0590 O560U0550U0520

0760 0760 0790 0780 0780

0700 0710 0700 0730 0710

0680 0670 0680 0690 0700

0700 0690 0680 0650 0640

0670 0710 0710 0720 0730

0700 0700 0700 0700 0700

0690 0690 0710 0720 0700

0700 0700 0700 0700 0700

0530 0570 0600 0620 0630

68
12958580645000650 0690 0720 0700 0690 0670 0640 0610 0600 0580 0570 0560

11056580645000700 0680 0680 0680 0700 0670 0710 0680 0690 0690 0700 0730

12056580645000720 0700 0700 0730 0740 0760 0760 0730 0730 0710 0720 0720

11156580645000700 0690 0680 0680 0690 0690 0740 0760 0740 0750 0790 0790

12156580645000790 0760 0740 0730 0700 0700 0700 0700 0690 0700 0700 0710

11256580645000720 0680 0660 0640 0670 0700 0730 0730 0730 0750 0780 0800

12256580645000800 0800 0780 0750 0740 0730 0720 0710 0700 0720 0730 0730

11356580645000740 0710 0690 0670 0680 0700 0720 0720 0730 0750 0770 0760

12356580645000790 0810 0800 0780 0760 0740 0740 0750 0720 0740 0770 0770

11055580645000770 0700 0690 0680 0700 0720 0710 0730 0740 0730 0730 0770

12055580645000760 0740 0750 0730 0740 0750 0780 0780 0780 0770 0770 0780

11155580645000710 0680 0650 0660 0690 0740 0750 0740 0750 0770 0780 0780

12155580645000770 0760 0740 0720 0710 0720 0740 0720 0730 0740 0740 0740

11855580645000520 0500 0500 0490 0500 0530 0580 0610 0610 0610 0630 0630

12355580645000640 0650 0670 0640 0650 0650 0670 0680 0680 0630 0560 0570

11053580645000700 0690 0650 0640 0690 0700 0720 0780 0790 0760 0770 0730

12053580645000760 0760 0740 0730 0730 0760 0750 0780 0770 0760 0760 0740

11052580645000690 0650 0660 0650 0700 0760 0780 0850 0830 0800 0830 0800

12052580645000810 0800 0800 0780 0800 0780 0800 0790 0780 0750 0720 0700

11352580645000780 0740 0720 0690 0680 0720 0750 0800 0770 0740 0780 0800

12352580645000790 0790 0810 0790 0780 0770 0750 0780 0790 0820 0820 0810

11452580645000820 0780 0730 0690 0700 0760 0760 0770 0780 0760 0740 0750

12452580645000760 0770 0770 0780 0780 0780 0780 0770 0790 0820 0820 0820

11051580645000740 0720 0690 0660 0680 0710 0740 0780 0740 0780 0760 0780

12051580645000800 0780 0770 0780 0780 0810 0800 0820 0800 0800 0830 0820

11651580645000660 0620 0600 0590 0590 0660 0710 0740 0710 0680 0690 0690

12651580645000680 0660 0650 0650 0630 0650 0670 0680 0690 0680 0700 0680

11050580645000765 0706 0690 0660 0655 0707 0730 0756 0786 0785 0758 0775

12050580645000778 0768 0769 0764 0760 0768 0779 0824 0796 0798 0793 0792

11049580645000700 0680 0660 0630 0650 0690 0720 0750 0750 0760 0770 0770

12049580645000770 0760 0750 0760 0750 0760 0800 0790U0790 0770 0770 0750

11149580645000740 0740 0720 0660 0660 0710 0750 0760 0790 0820 0900 0910

12149580645000920 0900 0860 0830 0810 0800 0790 0820 0800 0800 0770 0770

11949580645000570 0510 0500 0480 0460 0500 0540 0560 0600 0600 0620 0630

12949580645000650 0660 0650 0680 0680 0680 0700 0700 0700 0700 0690 0600

11048580645000700 0690 0660 0640 0680 0750 0790 0810 0810 0800 0810 0880

12048580645000810 0830 0800 0800 0780 0800 0840 0810 0830 0820 0820 0770

11848580645000520 0480 0450 0420 0430 0510 0570 0590 0620 0610 0630 0650

12848580645000660 0660 0670 0650 0650 0640 065'0 0650 0650 0630 0600 0540

11147580645000720 0690 0670 0680 0740 0790 0770 0860 0900 0900 0870 0870

12147580645000850 0840 0850 0840 0850 0820 0830 0850 0750 0690 0750 0750

11547580645000880 0880 0840 0800 0780 0820 0880 0900 0900 0870 0820 0820

12547580645000840 0840 0820 0820 0820 0820 0820 0820 0860 0860 0880 0910

11J47580645000690 0620 0590 0520 0520 0560 0600 0650 0680 0690 0700 0720

12J47580645000700 0720 0740 0760 0760 0760 0800 0800 0800 0820 0780 0710

11046580645000800U0780U0720U0680U0680 0740 0800U0800 0800 0830 0870 0870

12046580645000880 0870 0860 0860 0860 0850 0860U0870U0880 0850D0 860U0860

11045580645000790 0720 0700 0670 0650 0670 0740 0790 0810 0850 0820 0850

12045580645000830 0850 0820 0840 0800 0790 0790 0820 0800 0790 0790 0780

11145580645000770 0760 0745 0713 0720 0803 0875 0868 0885 0922 0932 0946

12145580645000900 0930 0912 0874 0876 0878 0873 0871 0834 0823 0802 0792

11545580645000840 0820 0780 0750 0760 0840 0880 0880 0850 0810 0760 0800

12545580645000800 0760 0780 0800 0780 0800 0780 0810 0830 0830 0840 0850

11945580645000540 0560 0500 0490 0460 0510 0550 0570 0600 0620 0660 0680

12945580645000680 0690 0700 0710 0720 0720 0750 0800 0800 0800 0730 0660

69
11044580645000720 0720 0710 0700 0670 0680 0750 0800 0880 0850 09?0 0930

12044580645000940 0910 0900 0870 0870 0860 0850 0840U0730 0690 0720 0730

11144580645000800U0760U0720U0700U0700U0780 0860 0900 0880 0900 0920 0950

12144580645000950 0910 0880 0880 0840 0830 0860 0840 0840U0830U0820 0820U

11343580645000790 0770 0740 0700 0690 0780 0880 0920 0970 1020 1020 1030

12343580645001040 1010 1000 0960 0910 0870 0860 0850 0840 0830 0830 0820

11041580645000850 0800 0810 0770 0700 0740 0860 0860 0900 0860 0940 0980

12041580645001000 0950 0970 0930 0890 0880 0880 0900 0870 0870 0860 0880

11040580645000830 0820 0780 0760 0740 0790 0830 0860 0910 0920 0930 0940

12040580645000940 0930 0940 0930 0900 0880 0880 0880 0850 0840 0850 0840

11J40580645000680 0640 0620 0580 0540 0560 0605 0620 0640 0640 0670 0660

12J40580645000680 0700 0710 0710 0740 0760 0780 0800 0820 0810 0785 0750

11539580645000920 0910 0850 0800 0800 0890 0950 0980 0940 0930 0910 0930

12539580645000930 0930 0930 0920 0900 0880 0870 0860 0860 0870 0900 0910

11938580645000700 0650 0620 0560 0530 0550 0600 0620 0670 0690 0690 0690

12938580645000710 0710 0720 0720 0730 0740 0760 0760 0800 0800 0770 0740

11237580645000820R0810R0780 0740 0700 0750 0860 0940 0970R 1000R 1040 1070R

12237580645001080 1080R1080 1040R0990R0940R0910R0870R0860 0840R0840R0830

11837580645000630 0600 0590 0570 0550 0550 0640 0680 0710 0700 0705 0750

12837580645000780 0780 0790 0770 0750 0750 0720 0700 0680 0670 0650 0620

11535580645000940 0920 0860 0830 0800 0860 0940 0970 0960 0960 0970 1010

12535580645001020 1030 1020 1000 0970 0940 0920 0890 0840 0880 0920 0940

110345806450009-jOU0950 0910U0900 0830 0770 0800 0900 0900 0900 0920 1000

12034580645001030 1040 1030 1020 1020 0960 1000 0980 0900 0900U0920U0950U

11832580645000670 0660 0660 0610 0600 0575 0650 0710 0770 0800 0850 0880

12832580645000850 0885D0880D0865 0800 0795 0780 0770 0770 0730 0700 0670

11431580645000980 0980 0900 0860 0830 0830 0900 0930 0920 0930 0960 1040

12431580645001060 1100 1100 1130 1120 1120 1060 1000 0940 0900 0940 0970

11929580645000820 0800 0740 0700 0690 0660 0680 0770 0780 0870 0850 0860

12929580645000900 0920 0900 0890 0880 0860 0860 0850 0850 0820 0800 0800

11328580645000940R0920R0880R0840R0800R0820R0900 0950 0990R1020 1080 1160

1 2328580645 00 1240R1 3 OOR 1320 1 320R1 310R1270R1 190R1 110R1030R0980R0960R0950R

11426580645001075 1045 0950 0895 0840 0785 0830 0865 0870 0910 0970 1040

12426580645001110 1150 1210 1260 1275 1265 1210 1150 1080 1000D1020 1080

11926580645000860 0830 0780 0760 0725 0685 0735 0800 0840 0875 0925 0950

12926580645000950 0960 0950 0930 0935 0900 0915 0890 0880 0860 0840 0830

11424580645001240 1120 0970 0910 0820 0820 0880 0900 0940 1000 1120 1210

12424580645001250 1310 1380 1410 1400 1400 1360 1280 1250 1240 1160 1160

11223580645000900R0840 0760R0710R0700 0710 0780 0930 0950 1000 1080 1220

12223580645001300R1400R1480R1530R1500R1440R1380R1290R1160 1100 0960 0920

11022580645001200D1090R0950 0820D0750 0820 0900 0930 0950 1060 1150 1240

12022580645001350 1400 1440 1470R1490 1470R 1420D 1 360R 1 300D1 3 10D1 280R 1240D

11422580645001300 1280 1120 0990 0810 0730 0800 0880 0920 1000 1080 1200

12422580645001270 1400 1400 1450 1450 1400 1400 1350 1240 1150 1150 1220

11720580645000880 0850 0785 0745 0715 0680 0680 0770 0850 0930 0990 1070

12720580645001125 1155 1170 1225 1260 1210 1145 1100 1065 1020 0930 0910

1 12 19580645 000970R0940R0890R08 30R0770R0690R0760R0970R 1010 I 1040 1120 1210

12219580645001250 1290 1340 1 360R1360R1350R1330R1290R 1240R1 180R1 1 10R1050R

11J18580645001040 0990 0930 0900 0860 0800 0780 0870 0920 1000 1060 1120

12J18580645001180 1190 1180 1140 1120 1080 1060 1060 1040 1060 1060 1060

11416580645001110 1050 0960 0905 0800 0685 0810 0900 0990 1060 1150 1200

12416580645001250 1300 1320 1305 1295 1250 1235 1195 1100 1100 1100 1125U

11A14580645000740R0720R0680R0630R0590R0570R0550R0700 0860 0950 1050 1140

12 A 14580645 001 220 1290R13 50R1 380R1 390R1370R1330R1240U1 110U0980R0 870R0790R

11313580645000900U0850U0830U0750U0700R0730R0910U1090R1150 1220 1150 1150

70
12313580645001140 1160 1170 1 180U1 180U1 1 70U1 100U1 050U0950U0900U0970U0900U

11311580645000990R0940R0860R0770R0680R0660 0930 1120 1170 1200 1160 1120

12311580645001110 1110 1160 1160 1180 1 180R1 160R 1 100R1020R 1050R 1050R 1 030R

11310580645000920R0900R0870R0830R0720 0600 0880 1100 1150 1190 1200 1100

12310580645001080 1090 1110 1120 1140 1160 1160 1060 0940 0910R0940R0960R

11909580645000960 0900 0880 0810 0755 0690 0670 0765 0870 0970 1020 1130

12909580645001180 1200 1230 1220 1180 1140 1100 1030 0970 1000 0990 0990

11308 580645 001 010R09 80R0940R0 890R08 1 0R0660R087 0R 11 30 1230 1270R 1 2 2 OR 1 130

12308580645 001 11 OR 11 40 1150 1 130R 1 150R 1 160R 1 1 5 OR 1 100R0980R0980D1000D1020D

11007580645000520J0520J0560J0570J0500U0400 0840 1130 1290 1360 1330 1230

12007580645001160 1120 1120 1110 1120 1110 1070U0910U0740U0680J0650J0560J

11J06580645001160 1200 1200 1190 1020 0980 0960 0880 0820 0720 0800 0900

12J06580645001000 1090 1190 1200 1260 1270 1260 1200 1170 1130 1100 1060

11J05580645000890 0850 0800 0790 0700 0590 0630 0795 0895 0990 1080 1165

12J05580645001210 1270 1320 1345 1295 1260 1215 1150 1100 1130 1135 1000

11104580645001170R1080R0930R0770R0640R0540 0860 1250 1380 1440 1420 1400

12104580645001400 1310 1250 1280 1240 1250 1200 1 150R 1 1 10R1 120R 1 140R 1 160R

11 102580645 001 120R09 50R0 840R0710R0 860R 1260R 141 OR 1 420 R1420R 1420 1400 1360

12102580645001340R1320 1340 1340 1 340R 1 320R1320R 1 240R1 180R1 1 50R1 120R 1090R

11301580645001230R1100R0950R0810R0690 0560 0700 1140 1360 1500 1510 1480

12301580645001400R1360R1310 1280 1280 1290 1310R1320 1 350R1360R 1 350R 1310R

1110K580645 001560R1400R1180R10 30R0 8 60R07 30R078 1220R 1420R1 390R1370 1410

1210K580645001460 1430 1390 1410 1430 1450R 1490R 1540R 1 590R1630R 1640R 1620R

1150K580645001320 1330 1360U1340 1350U1320 1340 1320 1370 1300 1360 1320

1250K580645001350 1350 1260 1160 0900 0840 0800 0730 0650 0980 1300 1350

1110M580645001270R1040R0900R0720R0490R0670R1110R1280 1300 1340 1330 1360

1210M580645001400 1410 1460 1440 1450 1510 1 58 0R1620R1640R 1630R1 590R 1520

1190M580645000940 0960 0960 0895 0740 0615 0520 0750 0875 0965 1010 1040

1290M580645001060 1080 1090 1070 1070 1060 1040 1005 0990 1000 1015 0995

11AON580645 000 510R0500R0490R0480R047GR0460R0450R0 840U1120U1260R1320U1310U

12AON580645 001300U12 50U1200U1210R1210R12 00R1100R0910R0 780R0630R0 560R0 520R

1190P580645000860 0880 0885 0820 0700 0595 0560 0760 0890 0980 1030 1020

1290P580645001030 1050 1035 1010 1000 1010 0955 0900D0860 0895D0895D0860D

1190R580645000820 0840 0820 0725" 0630 0590 0550 0780 0925 1050 1050 1040

1290R580645001020 1025 1030 1000 0990 0985 0920 0865. 0850 0850 0840 0820

1111J580645000560 0400 0350 0310 0410 0900 1190 1250 1220 1250 1200 1180

1211J580645001180 1170 1160 1170 1220 1180 1130 1040 1060 0900 0860 0650

1191K580645000770 0780 0710 0650 0570 0530 0550 0835 1045 1100 1100 1070

1291K580645001050 1035 1000 0970 0960 0950 0900 0840 0825 0810 0800 0770

11J10580645000800 0790 0765 0690 0570 0515 0465 0660 1000 1195 1260 1210D

12J10580645001200U1160U1140 1080 1030 1040 0960 0900 0890 0875 0860 0800

1171P580645001100 0960 0800 0680 0520 0500 0610 1030 1390 1400 1380 1400

1271P580645001330 1360 1360 1350 1420 1500 1590 1 700D1700D1700D1430 1140

1121Q580645000340 0310 0290 0270 0240 0260 0420U0900 1150 1230 1200 1200

1221Q580645001160 1120 1110 1100 1060 1070 0940 0780 0600 0560 0510U0420

1111R580645000360 0324 0302 0276 0250 0247 0426 0850 1130 1208 1220 1210

1211R530645001178 1177 1161 1166 1159 1165 1065 0854 0707 0616 0489 0430

1151R580645000610R0 5 80R0530R0470R0420R0400R0420 840R 1 190R 1 360R1 320U 1 260R

1251R580645 001250R12 30R1220R1200 1 160R1060R096 0R0 850R0 780R0760R0 720R0 670R

1172J580645000700 0620R0550R0480R0420R0440 0650 1090U1350 1440 1330 1290

1272J580645001260 1270 1300 1300 1280U1320U1340R1290R 1 180R1050R0920R0800R

11J2L580645000930 0880 0830 0660 0550 0470 0420 0720 1020 1220 1340 1300

12J2L580645001310 1340 1340 1380 1400 1420U1340U1 130 1140 112C 1110 0980

11120580645000320 0320 0310 0300 0300 0280 0300 0660 0990 1180 1250 1200

12120580645001200 1180 1180 1140 1160 1100 1010 0780 0620 0500 0380 0330

71
11J20580645 001050R09 50R0920 74 0R0600R04 5 0R042 0580R 1 080U1 2 70R 1 4 10R 1 390R

12J20580645 001390R1420R14 30R1450R1460R1440R1350R1290R1260R12 70R12 70R1170R

U52P580645000530 0480 0480 0490 0460 0420 0440 0820 1060 1170 1200 1180

1252P580645001180 1160 1120 1120 1070 1050 0890 0760 0660 0630 0560 0500

11430580645000430 0420 0420 0420U0420 0400 0400R0500R0850D1070R 1 190R 1 2 10R

12430580645001220R12 20R1210R1210R1190R1130R1000R0820R0700R0580R0510R0450R

1113M580645000280 0270 0270 0280 0290 0260 0260 0270 0680 0930 1050 1140

1213M580645001240 1220 1220 1180 1210 1180 1030 0810 0570 0360 0310 0260

11J3M580645000770R0740R0680R0610R0540 0440R0370R0680R 1 000 1120 1200 1200R

12J3M580645 001180R1180R1230R1220R1260 1 1 30R 10 50R 1 070R 1 040R0960R0900R0 840R

1153N580645000500U0490U0480 0490 0480 0430 0420 0580U0940U1 100 1180 1230U

1253N580645001200 1200 1200 1180 1150 1100 0900D0780D0720U0590U0520U0500U

11J3O5806450OO600 0560 0540 0500 0470 0410 0440 0710 1080 1180 1190 1160

12J3O580645001160 1220 1290 1230 1160 1120 0960 0930 0840 0780 0690 0640

1154K580645000420U0420 0400R0410 0390 0370R0360R0370R07O0D0950R 1 1 OOR 1 170R

12 54K580645 001200R12 00D1200D1180R1120R10 30R0900D0760D0620R0520U0460U0440R

1164L580645000530 0490 0470 0460 0470 0470 0430 0400 0640 0930R 1 080R 1 180R

1264L580645001220R1220R1190R1160R1140 1060 0890R0790 0700 0590 0560 0530

11J4L580645 000 580D05 70D0550R0530R0510 0490R0460R04 70 0800R 1 OOODl 1 OOD 1 1 OOD

12J4L580645 001100D1100D1100D1090D1060D1000D089OR0 790RC700R0660R0 620R0 590

1124R580645000270R0270R0260R0250R0240 0230 0260 0300 0500U0780 0900 1050

1224R580645001210 1300 1400 1300 1 1 90U1 030R0850R0640R0480R0350 0290R0270R

HJ5J58064500033o 0330 0320 0320 0330 0320 0280 0380 0680 0910 1010 1080

12J5J580645001070 1000 0950 0920 0740 0580 0470 0380 0320 0300 0310 0330

1165K580645000460 0460 0460 0440 0440 0410 0360 0400 0650 0900 1050 1150

1265K580645001220 1160 1210 1120R1000 0820R0690R0600 0570 0550 0490 0470

1155M580645 000410R0410R0420R0420R0410R0420R0390R0450R0660R0840R1000R1120R

1255M580645 001180R1190R1150R1030R08 30R0650R0560R0500R0460R0440R0430R0420R

11J6L580645000340 0330 0330 0340 0340 0360 0330 0340 0330 0440 0700 0890

12J6L580645000990 1010 1020 0930 0820 0710 0560 0400 0340 O330UO 330U0 350

11J6M580645000230 0230 0230 0230 0220 0220 0220 0230 0310 055OU0750 0880

12J6M580645000960 0980 0840 0740 0660 0520 0340 0240 0210 0230 0220 0230

11360580645000410 0340 0350 0340 0360 0390 0380 0380 0420 0520R0630R0710

12360580645000760R0780R0750 0700R065ORQ6 1 0600 0570R0520R0470 0410 0390

1146O580645 000400RO3 90R03 8 0R0 37ORO36OR0 3 70R038 0R0410R04 70R0600R0750R0 810R

12460580645 0008 30R08 20R0 79 0R0720R069OR0 7n0R0670R0640R0 590R0 5 30R0 470R0420R

11 560580645 000450U0410U0410U0360U0360U0360U034 0U0340R0440RO 580 66 0U0 680U

12 560580645 000710U07 30R0750R0750R0740R0730U0670R0600R05 30R0490R0470R0460R

11 170580645 000200U02 60U0260U0270U0300 03 00UC32 0U034 042 0U0420U0 45 0U0 590

12170580645000710 0760 0870 0820 0800 0710 0500 0340 0240 0210 0210 0200

1167K580645000440 0440 0420 0390 0370 0380U0420 0420 0490 0480U05 1 0U0680

1267K580645000720 0600 0660 0740 070O 0760 0840 0720 0700 0640 0530 0600

11A7O5806450O0200 0240R0270 0320R037n 0400 0400 0420 0370 0370U0400 0480

12A7O58O645000580U0580 0530U0440 0380 0300 0220 0190 0170 0190 0200 0200

11A7P580645 000370R0410R0440R0460R0 470R04 70R044 0U0410R0 370U0 350U0 38 0U0400U

12A7P580645000460 0480' 045OU0375UO340U0260UO2 30 0230R0230R0250R0280R0 320R

11670580645000500 0460 0440 0470 0430U0450 0410 0440 0440 0480 0560 0550

1267Q560645000520 0630 0680 0710 0810 0800 0760 0760 0640 0600 0540 0540

11 770580645 000 520U05 00U0490U0430U0430U043 0U0400UO 38 5U0 3 80U0 335U0 39 0U04 00U

1277Q580645 000410U04 70U045 0U0500U0 5 50U06 00U0640U0650U058 0U0500U0 55 0U0500U

1 1 880580645 00062 0U06 30R06 10R0600R0 580RO 5 10R0440R0 3 50 03 2ORO3O0UO32OR0 340R

12880580645000370R03 60R03 70R0 380R0420R0430R0430R0500R0 580U0620R062 0U0620R

11090580645 000480U05 20U0510U052 0U0600U0540U0510U0 52 0U0 5 30U0530U0 520U0 520U

12090580645 000 500U04 90U0520U0490U0500U05 50U047 0U0440U04 5 0U0470I0480U05 00U

11471580645 000640P0640P0640P06 3 0P0610P05 90P058 0P0 58 0P0 5 80P0 580P0 590P0 6 00P

72
12471 580645 000600P0610P0620P0640PO 6 50P0660P0670P06 70P0660P0650PO 6 50P0 640P

119 1958 0645 000960P09 10P0850P08 10P0760P07 00P0760P0860P0940P 1020P1080P 1 140P

129 19580645 001 190P1 2 30P1240P1220P1 190P 1 160P1 130P 1090P1040P1000P0 980PO 960P

1151 3580645 0009 70P0 9 30P08 90P0 8 30P0760P07 00P08 3 0P0940P0990P10 30P1090P 1 15QP

125 13580645 001 190P1 2 30P1260P1290P1 3 10P1330P1300P1230P1150P1080P1040P1010P

11111580645000800P0760P0720P0680P0630P0570P0790P0980P1090P1130P1150P1140P

121 11580645 001 150P1170P1200P1220P1240P1240P 121 OP 1150P1050P0960P0 890P0 850P

114 11 580645 000990P09 50P0890P0800P0700P 06 10P0840P 1030P 1 120P1 160P1 160P1 160P

124 11 580645 00 1 180P 1 190P 1 190P1 190P1 190P1 190P 1 180P 1 120P 1030P0990P0990P1 OOOP

11 705580645 00 1 160P 1 1 10P1040P0950PO 81 0P0630P071 OP0890P0990P1060P1100P1 130P

12705580645 00 1 150P1170P1200P1 21 OP 1200P1 180P11 50P1080P1050P1080P1 130P1 160P

11701580645 001090P10 50P0990P09 00P0780P0 590P0700P08 70P0990P1050P1090P1120P

1270 1 580645*00 1 130P 1 1 50P1 160P1 180P 1 170P1 140P1090P1050P 1020P 1030P10 70P 11 OOP

1150R580645 000850P0 7 50P0600P0460P0 370P0320P0 5 3 0P0960P1190P1270P1230P1190P

1250R580645 001160P1160P1130P1080P1060P1040P1040P1050P1010P0920P0880P0860P

1161Q580645 000770P06 90P0580P0 510P0440P0400P0530P1040P1280P1360P1370P1360P

1261Q580645 001340P1310P1290P1270P1280P1260P1190P1080P0960P0900P0 870P0 8 30P

1162R580645 000520P05 20P0 5 2 0P0 520P0 510P0480P0450P07 30P1000P1140P1210P1180P

1262R580645 001150P1130P1110P1090P1060P0990P08 5 0P0 730P0640P0580P0 540P0 5 30P

1116R580645 000400P04 00P0 390P0 380P0 380P0400P0430P0450P0460P0470P0 560P0710P

1216R580645 000810P08 80P0 8 90P0 8 20P07 30P0610P04 70P0 360P0 340P0360P0 38 0P0 390P

1147P580645 000340P03 30P0310P0 310P0 320P0350P038 0P0420P0460P0 510P0 560P0620P bcreen

Point 1247P58 0645 000660P06 70P066 0P0 6 30P0 580P0 5 50P0510P0490P04 50P0420P0 380P0 360P

Coordi- 90000 80337 65157 40210 40330 35030 35105 35185 35310 30165 25050 25325 20030

nates 20232 15175 10240 05160 05345 00060 00180 00225 00255-05080-05125-05200-10165

""1 -10350-1510 5-15240-2 0075-20265-2 5 34 5-30095-30 2 2 5-35050-35075-35200-35 265-40 345

-45095-4512 0-45240-4 5325-50015-50045-50200-50270-55105-60000-60 330-6 5 210-65240

» -65265-7506 7-75277-8 003 7-8 300-8 5140-8 52 25

73

APPENDIX B

SAMPLE PRINTOUT OF OUTPUT FROM NUMERICAL MAP PROGRAM

0ATE*5806 DATA=4500 N-154 P = 52 H=8 FN=lOO

PPl* 12 PP2 = 36 PP3 = 52 PH2 = 4 Hl=4 TA=2

NA=142 NC= 59 S=186.8 MN=4

First Analysis

dk

Ek

SUMS IK 6.6465771E 02

6.6402180E 02

1.2655933L 02

1.2603531E 02

1.2397369E 02

1.2232981E 02

1.2231752b 02

1.210e658E 02

1.2C81920E 02

1.2C/3178E 02

1.2Ch9330t 02

1.1986271E 02

1.1862565L C2

1. 1862463b 02

1.0C63424F 02

9.7347503b 01

7.6919057b 01

7.5C26000E 01

7.5005152b 01

7.4823126b 01

7.0705182E 01

6.9967782b 01 6.6440004E 01

O.6430339E 01

6.1691756E 01

6.1317295E 01 5.9401072b CI 5.8966928b 01 4.8610796E 01

4.8438091E n l 4. 7938016b Gl

4.7897401b 01 3.8246920b 01

3.7459693E 01 3.703C0O0E 01

3.4144057c CI 3.03H6747E CI 3.03H3936E CI 3.C363252E 01

2.H311980E 01 2.6797791E 01

2.6425C48E 01 2.6073701b 01 2.3993510b 01

2.5300067E 01

2.5240567b 01

2.512354GE CI 2.3736649b CI 2.3249571b CI 2.3C14013E 01 2.2979292b 01

2.2395848E CI 2.C355163E 01

1.2457914E 02

s k CRTHO COEFF.

9.7796171b 01

1 -7.9743505E--01

2 -2.3183237E 01

3 -7.2388791b--01 4 1.4356329b 00

5 1.28214C2E 00

6 -1.1086683b--01

7 -1.1094761E 00

8 5.1706630E--01

9 -2.9567594E--01

c 10 1.9614815E--01 11 9.003^002E-<01 12 1.1211874E 00

13 -3.1900162E--02 14 4.2415G78E no

15 1.8129360E 00

16 4.519783RE 00

17 -1.3758836E 00

c 18 -1.4433721F-01

c 19 4.2664412E--01 20 -2.0292717E 00

21 -8. 5872000b--01 22 1.8782378b 00

23 9.83U927E--02 24 -2. 176o287E 00

25 -6.1193166b--01 26 -1.384/_770F 00

27 6.538V627E--01 28 3.218C943E 00

29 4.1557774E--01 20 7.0715965b--01 31 2.0153300E--01 32 -3. 1065224E 00

33 -8.8725764E--01 34 -6.5550982E--01 35 1.6988062E oc

36 1.9383783E oc

27 5.3007979b--02 38 K4382064F-•01 29 1.4322262c oc

40 -1.2305239E 00

41 -6.1052668E-'01 42 -5.«274504E--01 43 ?.<<318019E--01 44 6.3273214E-'01 45 2.'»392665E--01 46 3.4209192E-01

47 -1.1776633E 00

48 -6.9790944E--01 49 4.85344CCE--01 50 1.8633364E-'01 51 -2.8886722E--01 52 1.5939509E 00

1 1.1545718E 01

Sl= 6.0 S2=

KMS (EK)

2.0842668E 00

2.090U11E 00

9.1550053E-01

9.1664355E-01

9„1216128E-01

9.0914947E-01

9.1219074E-01

9.1069211E-01

9.1281754E-01

9.1565011E-01

9.1869968E-01

9.1882774E-01

9.1723313E-01

9.2049913E-01

8.5087444E-01

8.3989086E-01

7.4930165E-01

7.4273936E-01

7.4538158E-01

7.4724931E-01

7.2912132E-01

7.2805147E-01

7.1216262F-01

7.1484445E-01

6.9154223E-01

6.9212813E-01

6.8390421E-01

6.8409902E-01

6.2360753E-01

6.2500380E-01

6.2429157E-01

6.2657931E-01

5.6221903E-CI

5.5871648E-01

5.5783193E-01

5.3791859E-01

5.C962317E-01

5.1179144E-01

5. 1383681E-01

4.9834797E-01

4.8697904E-01

4.8573442E-01

4.8466299b-01

4.8611175E-01

t.8l77869E-01

4.8343453E-01

4.8456107E-01

4.7321311E-01

4.7055763E-01

4.7041320E-01

4.7233454E-01

4.7378169E-01

4.4892796E-01

9.0235400E-01

2.0

ak/ek

ORTHO COEFF/RMS

4.6921139E 01

-3.8152758E-01

-2.5323018E 01

-7.8971581E-01

1.5740999E 00

1.4102634E 00

-1.2153909E-01

-1.2182779E 00

5.6647279E-01

-3.2291367E-01

2.1350628E-01

9.7986813E-01

1.2223582E 00

-3.4655285E-02

4.9848809E 00

2.1585376E 00

6.0319949E 00

-1.8524449E 00

-1.9370911E-01

5.7095284E-01

-2.7831743E 00

-1.1794771E 00

2.6373720E 00

1.3752912E-01

-3.1477884E 00

-8.8413059E-01

-2.0240802E 00

9.6315920E-01

5.1604480E 00

6.6492034E-01

1.1327394E 00

3.2164004E-01

-5.5254663E 00

-1.5880284E 00

-1.1751027E 00

3.15811C3E 00

3.8035522E 00

1.0357340E-01

2.7989555E-01

2.8739480E 00

-2.5268517E 00

-1.2569146E 00

-1.2230045E 00

5.8254132E-01

1.7284537E 00

5.0457017E-01

7.0598308E-01

-2.4886532E 00

-1.4831540E 00

1.0317398E 00

3.9449505E-01

-6.0970533E-01

3.5505716E 00

1.2795110E 01

75
Hourly Values of Ionospheric Characteristics at Screen Points

LAK8DA= 90.0 THf-TA- (Geographic Coordinates of Screen Point)

(.13 6.08 6.08 6.33 6.36 6.1 3 6.00 6.00 5.87 5.77 5.77 5.76

5.68 5.55 5.53 5.72 5.98 6.23 6.3*. 6.23 6.16 6.25 6.22 6.12

LAHBDA= 80.0 THETA= 337.0

5.71 5.63 5.6? 5.79 5.81 5.58 5.44 5.43 5.38 5.35 5.39 5.42

5.42 5.40 S.Afl 5.7C 5.93 6.10 6.15 6.03 5.95 5.99 5.90 5.75

LAM8DA= 65.0 THLTA= 157.0

t.03 5.87 5.76 5.72 5.80 5.96 6.04 6.08 6.21 6.35 6.42 6.49

6.51 6.49 6.53 6.57 6.57 6.62 6.68 6.64 6.59 6.53 6.39 6.21

LAMEDA= 40.0 THETA- 210.0

6.97 6.72 6.48 6. IK 6.07 6.44 7.07 7.55 7.79 8.01 8.24 8.36

£.35 8.27 8.07 7.75 7.43 7.3'j 7.36 7.47 7.45 7.37 7.32 7.21

AMBDA^ ttO.O THCTA= 330.0

;.5l 7.05 6.51 6.13 5.95 6.33 7.04 7.64 8.01 8.31 8.60 8.76

^.SO 8.79 8.71 8.51 8.31 8.26 8.38 8.51 8.48 8.35 8.21 7.94

1MBDA= 35.0 THFTA = JO.C

9.62 9.23 3.66 8.03 7.62 7.78 b.49 9.08 9.25 9.43 9.84 10.27 1C.64 10.97 11.12 11.09 10.96 10.80 10.61 10.32 9.92 9. 68 9.72 9.77

LAM8DA= 35.0 THtTA= 105.0 9.88 9.64 9.16 8.57 8.16 8.2 9 8.91 9.38 9.41 9.49 9.89 10.38

1C.84 11.24 11.43 11.39 11.23 10.97 10.64 10.18 9.66 9.41 9.57 9.82

l_AMUDA= 35.0 THETA= 185.0 8.34 8.23 7.99 7.64 7.37 7.52 8. 12 8.60 8.68 8.78 9.12 9.43

S.64 9.76 9. 68 9.41 9.10 8.85 8.70 8.53 8.27 8.13 8.22 8.34

LAM8DA= 35.0 THlTA= 310.0

7.96 7.62 7.26 6.86 6.58 6.78 7.50 8.17 8.45 8.70 9.05 9.27 9.35 9.37 9.24 8.97 8. 72 8.59 8.66 8.73 8.65 8.52 8.44 8.26

LAMiiDA= 30.0 THETA= 165.0 S.53 9.34 8.92 8.40 7.8b 7.73 8.31 8.88 0.89 9.00 9.57 10.20 C.75 11.19 11.33 11.25 11.07 1C.H2 10.53 10.09 9.54 9.26 9.33 9.49

76
Second Analysis

\

s k ORTHO COEFF.

1.1586693E 02

1 2.7317G04E 00

2 -2i7691270E 01

3 -U0710T68E 00

4 1.812C750E 00

5 1.3887605E 00

c 6 2wl874G04E-02

7 -9.0152808E--01

8 4.1653732E--01

9 -1.6968181E-01

10 -2.5998666E--01 11 1.2061695E 00

12 1.7125742E 00

13 -4.7527b78E--01 14 3.4918428E 00

15 2.8463537E oc

16 5.8259027E 00

c 17 -1.0570359E oc

18 5.7026108E--02 19 2.1162752E--01 20 -1.7289138E 00

21 -9»5828191E--01 22 1.2780304E 00

23 2.9435686E--01 24 -1.4432438E 00

25 -7.1608432E--01 26 -1.4521510E 00

27 2.4560481E--01 28 2.0283353E 00

29 8.5172019E--01 30 1.1125955E 00

31 2.0158679E--01 32 -2.1212865E 00

33 -9.7172962E--01 34 -9.4321649E--01 35 1.3584320E 00

36 1.4552336E 00

37 7.0770034E-01

38 2.7800587E--01 39 9.6084980E--01 40 -9.1351G80E--01 41 -3.0404171E--01 42 -8.6670141E--01 43 1-9961724E--01 44 U2900269E--01 45 6.7134I66E-01

46 1.2942037E 00

47 -1.3200679E 00

48 -1.0531998E 00

49 -8.3752718E--01 50 -1.6098626E--01 51 1.0323948E 00

52 1.5491854E 00

1.5186295E 01

1 -5.2349702E 00

2 -8.2212824E 00

3 2.302'6811E 00

4 -3.110S774E-•01

5 1.9968812E 00

Ek

SUMS EK 9.1748523E 02

9.1002303E 02

1.4321663E 02

1.4206942E 02

1.3878580E 02

1.3685715E 02

1.3685667E 02

1.3604391E 02

1.3587041E 02

1.3584162E 02

1.3577402E 02

1.3431920E 02

1.3138629E 02

1.3U6040E 02

1.1896743E 02

1.1086570E 02

7.6923630E 01 7.5806304E 01

7.5803052E 01

7.5758265E Gl

7.2769122E CI 7.1850817E 01

7.0217456E 01

7.0130810E CI 6.8047842E CI 6.7535064E 01

6.5426322E 01

6.5366000E CI 6il251855E 01 6.C526428E 01

5.9288559E 01 5.9247922E 01

5.4748065E 01

5.3803806E 01

5.2914149E 01

5.1068811E 01

4.8951106E 01

4.8450266E 01 4.e372979E 01

4.7449746E 01

4.6615244E 01

4.6522802E 01

4.5771630E 01

4.5731783E 01

4.5715141E 01 4.5264441E 01

4.3589478E 01

4.1846898E 01

4.0737668E 01

3.9949963E 01

3.<9924047E 01

3.8858207E 01

3.6458232E 01

1.6917869E 02

1.4177378E 02

7.4184297E 01

6.8881957E 01

6.8785193E 01

6.4797658E 01

k

RMS (EK)

2.0803270E 00

2.0767536E 00

8.2582319E-01

8.2447437E-01

8.1684725E-01

8.1310862E-01

8.1507837E-01

8.1463417E-01

8.1610746E-01

8.1802843E-01

8.1984670E-01

8.1746848E-01

8.1051307E-01

8.1184818E-01

7.7514232E-01

7.5018002E-01

6.2647226E-01

6.2349841E-01

6.2508989E-01

6.2652204E-01

6.1563450E-01

6.1333700E-01

6.0791903E-01

6.0914898E-01

6.0162829E-01

6.009576-3E-01

5.9308887E-01

5.9441544E-01

5.7696665E-01

5.7510477E-01

5.7075503E-01

5.7213335E-01

5.5150332E-01

5.4a25169E-01

5.4522518E-01

5.3714463E-01

5.2738153E-01

5.2617360E-01

5.2726238E-01

5.2371365E-01

5.2059472E-01

5.2159674E-01

5.1888812E-01

5.2019445E-01

5.2164540E-01

5.2061940E-01

5.1243264E-01

5.0360457E-01

4.9839785E-01

4.9506747E-01

4.9643200E-01

4.9127927E-01

4.7735097E-01

8.9331555E-01

8.1970338E-01

5.9435557E-01

5.7408948E-01

5.7506351E-01

5.5949277E-01

Vek

ORTHO COEFF/RMS

5.5696498E 01

1.3153705E 00

-3.3531717E 01

-1.2991025E 00

2.2183768E 00

1.7079643E 00

2.6836688E-02

-1.1066662E 00

5.1039518E-01

-2.0742777E-01

-3.1711619E-01

1.4754813E 00

2.1129507E 00

-5.8542568E-01

4.5047764E 00

3.7942275E 00

9.2996657E 00

-1.6953306E 00

9.1228651E-02

3.3778145E-01

-2.8083445E 00

-1.5624068E 00

2. 1023037E 00

4.8322638E-01

-2.3989044E 00

-1.1915721E 00

-2.4484543E 00

4.1318712E-01

3.5155157E 00

1.4809826E 00

1.9493397E 00

3.5234231E-01

-3.8463712E 00

-1.7724152E 00

-1.7299577E 00

2.5289873E 00

2.7593565E 00

1.3449940E 00

5.2726285E-01

1.8346854E 00

-1.7547447E 00

-5.8290569E-01

-1.6703050E 00

3.8373581E-01

2.4729959E-01

1.2895056E 00

2.5256074E 00

-2.6212389E 00

-2.1131709E 00

-1.7927399E 00

-3.2428662E-01

2.1014417E 00

3.2453802E 00

1.6999922E 01

-6.3864201E 00

-1.3832262E 01

4.0110143E 00

-5.4092762E-01

3.5690922E 00

77
Residuals and their RMS

Station Code

00687 A DATA

LAMfiDA= 86.8 THfcTA= 219.9 (Geographic coordin

H 111 GAMMA RtSlDUAL Y 6.13 -0.23 5.90

1 6.06 -0.C6 6.00

2 6.13 -0.13 6.00

2 6.22 -0.32 5.90

4 5.96 -0.06 5.90

5 5.64 -0.14 5.50

6 5.63 0.07 5.70

1 5.63 -0.03 5.60

8 5.51 -0.01 5.50

9 5.56 -0.06 5.50

1C 5.68 -0.C8 5.60

11 5.70 -0.20 5.50

12 5.67 -0.27 5.40

13 5.58 -0.28 5.30

14 5.51 -0.51 5.0C

15 5.61 -0.61 5.00

it 5.77 -0.27 5.50

17 5.86 -0.86 5.00

18 5.85 -0.75 5. IC

19 5.81 -O.bl 5.00

20 5.92 -0.62 5.30

21 6.10 -0.50 5.60

22 6.14 -0.54 5.60

23 6.14 -0.24 5.90

LZT = Zone time

Y = Observed value

Gamma = Computed value

Residual = Y - Gamma

LOCAL R*S RESIDUAL

4.105988E-01

00483 A DATA

LAMBDA* 82.3 THETA= 141.7

H LZT GAMMA RESIDUAL Y 5.37 -C.17 5.20

1 5.39 -0.19 5.20

2 5.27 -0.17 5.10

3 5.29 -0.09 5.20

4 5.49 0.01 5.50

5.63 -0.03 5.60

6 5.67 0.33 6.00

7 5.57 0.23 5.80

8 5.37 0.63 6.00

9 5.30 0.00 5.30

IC 5.39 -0.39 5.00

11 5.54 -0.04 5.50

12 5.62 -0.02 5.60

13 5.63 0.17 5.80

14 5.68 0.12 5.60

15 5.79 0.21 6.00

16 5.8! 0.09 5.90

17 5.80 -0.10 5.70

18 5.81 -0.C1 5. HO

19 5.75 0.05 5.80

2C 5.75 -0.05 5.70

21 5.85 -0.15 5.70

22 5.71 0.09 5.80

23 5.41 0.39 5.80

LOCAL RfS RESIDUAL

2.144553E-01

78
00982 A DATA

LAMBDA= 79.9 THLTA= 24 3.9

H LZT GAMMA RESIDUAL Y 5.61 0.09 5.70

1 5.66 -0.06 5.60

I 5.65 0.15 5.80

2 5.6/ 0.18 5.85

4 5.6^ 0.22 5.85

c 5.61 -0.01 5.60

6 5.71 -0.21 5.50

7 5.67 -0.17 5.50

8 5.45 0.15 5.60

s 5. A3 -0.03 5.40

10 5.56 -0.06 5.50

11 5.53 -0.03 5.50

12 5.47 0.13 5.60

13 5.50 -COO 5.50

14 5.49 0.21 5.70

15 5.45 0.10 5.55

16 5.41 0.14 5.55

17 5.36 0.04 5.40

16 5.40 0.30 5.70

19 5.54 0.11 5.65

2C 5.64 -0.24 5.40

21 5.64 0.06 5.70

22 5.55 0.05 5.60

23 5.52 -0.02 5.50

LOCAL RMS RESIDUAL

1.416085E-01

0009- A DATA

LAMB0A=-90.O THETA= 0.

H LZT GAMMA RESIDUAL Y 4.68 0.12 4.80

1 4.80 0.40 5.20

2 5.08 0.02 5.10

3 5.32 -0.12 5.20

4 5.23 0.77 6.00

5 5.03 0.37 5.40

6 4.96 0.14 5.10

7 4.70 0.50 5.20

8 4.45 0.85 5.30

9 4.77 0.53 5.30

10 5.23 -0.03 5.20

11 5.23 -0.03 5.20

12 5. 08 -0.08 5.00

13 5.03 -0.13 4.90

14 4.95 C.25 5.20

15 4.88 0.02 4.90

16 4.61 0.39 5.00

17 3.94 1.56 5.50

18 3.35 1.35 4.70

19 3.29 l.il 4.40

2C 3.56 0.92 4.50

21 4.00 0.70 4.70

22 4*39 0.41 4. HO

?3 *.6C 0.40 5.00

LOCAL RMS RESIDUAL

6.320838E-01

RMS RESIDUAL

6.318335E-01

A DATA 79
00471 8 DATA

LAMeDA* 71 .6 THE1A= 128.9

H LZT GAMMA RESIDUAL Y

C 5.77 0.63 6.40

1 5.73 0.67 6.40

2 5.66 0.74 6.40

3 5.66 0.64 6.30

4 5.72 0.38 6. 10

5 5.68 0.22 5.90

6 5.64 0.16 5.80

7 5.68 0.12 5.80

8 5.T2 0.C8 5.80

9 5.76 0.04 5.80

10 5.90 0.00 5.90

11 6.03 -0.08 6.00

12 6.21 -0.21 6.00

13 6.26 -0.16 6. 10

14 6.20 0.00 6.20

15 6.06 0.34 6.40

16 5.96 0.54 6.50

17 5.93 0.67 6.60

16 5.90 0.80 6. 70

19 5.84 0.86 6.70

20 5.80 0.80 6.60

21 5.82 0.68 6.50

22 5.33 0.b7 6.50

23 5.80 0.60 6.40

LOCAL RMS RESIDUAL

5.112251E -01 ^

0047P 8 DATA

LAM&DA=-78 .4 THETA= 106.9

H LZT GAMMA RESIDUAL Y

C 4.2^ -0.65 3.40

1 3.90 -0.60 3.30

2 3.59 -0.49 3. 10

3 3.40 -0.30 3. 10

4 3.33 -0.13 3.20

5 3.48 0.02 3.50

6 3.7b 0.04 3. HO

7 3.94 0.26 4.20

8 4.19 0.41 4.60

9 4.88 0.22 5.10

10 5.73 -0.13 5.60

11 6.25 -0.05 6.20

12 6.49 0.11 6.60

13 6.55 0.15 6.70

14 6.43 0.17 6.60

15 6.37 -0.07 6.30

16 6.33 -0.53 5.80

17 6.06 -0.56 5.50

18 5.65 -0.55 5. 10

19 5.34 -0.44 4.90

20 5.05 -0.55 4.50

21 4.77 -0.57 4.20

22 4.62 -0.82 3.80

23 4.5C -0.90 3.60

LOCAL RMS RESIDUAL

4.569347E -01

RMS RESIDUAL

6.237257E-01

RMS RESIDUAL OF

6.312054E-01

8 DATA

A AND 6 DATA

80
One Per Card Coefficients D

gk (See Card Format 5)

Y M DLC N P H FNCT> PP1 PP2 1 SN 3 k

5806 4 500 213 52 8 100 12 36 ] 186.8

5806 4500 213 52 8 100 12 36 ] 186.8 1 5806 4500 213 52 8 100 12 36 ] 186.8 2 5806 4500 213 52 8 100 12 36 ] 186.8 3 5806 4500 213 52 8 100 12 36 ] 186.8 4 5806 4500 213 52 8 100 12 36 ] 186.8 5 5806 4500 213 52 8 100 12 36 ] 186.8 6 5806 4500 213 52 8 100 12 36 ] 186.8 7 5806 4500 213 52 8 100 12 36 ] 186.8 8 5806 4500 213 52 8 100 12 36 ] 186.8 9 5806 4500 213 52 8 100 12 36 ] 186.8 10

5806 4500 213 52 8 100 12 36 ] 186.8 11 5806 4500 213 52 8 100 12 36 3 186.8 12

5806 4500 213 52 8 100 12 36 ]I 186.8 13

5806 4500 213 52 8 100 12 36 ]L 186.8 14

5806 4500 213 52 8 100 12 36 ]L 186.8 15

5806 4500 213 52 8 100 12 36 3I 186.8 16

5806 4500 213 52 8 100 12 36 :I 186.8 17

5806 4500 213 52 8 100 12 36 I 186.8 18

5806 4500 213 52 8 100 12 36 L 186.8 19

5806 4500 213 52 8 100 12 36 L 186.8 20

5806 4500 213 52 8 100 12 36 L 186.8 21

5806 4500 213 52 8 100 12 36 L 186.8 22

5806 4500 213 52 8 100 12 36 L 186.8 23

5806 4500 213 52 8 100 12 36 L 186.8 24

5806 4500 213 52 8 100 12 36 L 186.8 25

5806 4500 213 52 8 100 12 36 L 186.8 26

5806 4500 213 52 8 100 12 36 L 186.8 27

5806 4500 213 52 8 100 12 36 L 186.8 28

5806 4500 213 52 8 100 1? 36 :L 186.8 29

5806 4500 213 52 8 100 1? 36 I 186.8 30

5806 4500 213 52 8 100 12 36 L 186.8 31

5806 4500 213 52 8 100 12 36 L 186.8 32

5806 4500 213 52 8 100 12 36 L 186.8 33

5806 4500 213 52 8 100 12 36 L 186.8 34

5806 4500 213 52 8 100 12 36 :L 186.8 35

5806 4500 213 52 8 100 12 36 I 186.8 36

5806 4500 213 52 8 100 12 36 186.8 37

5806 4500 213 52 8 100 12 36 L 186.8 38

5806 4500 213 52 8 100 12 36 L 186.8 39

5806 450C 213 52 8 100 12 36 L 186.8 40

5806 4500 213 52 8 100 12 36 L 186.8 41

5806 4500 213 52 8 100 12 36 L 186.8 42

5806 4500 213 52 8 100 12 36 L 186.8 43

5806 4500 213 52 8 100 12 36 L 186.8 44

5806 4500 213 52 8 100 12 36 L 186.8 45

5806 4500 213 52 8 100 12 36 I 186.8 46

5806 4500 213 52 8 100 12 36 L 186.8 47

5806 4500 213. 52 8 100 12 36 L 186.8 48

5806 4500 213 52 8 100 12 36 L 186.8 49

5806 4500 213 52 8 100 12 36 L 186.8 50

5806 4500 213 52 8 100 12 36 L 186.8 51

5806 4500 213 52 8 100 12 36 L 186.8 52

5806 4500 213 52 8 100 12 36 L 186.8 1 5806 4500 213 52 8 100 12 36 L 186.8 1 1

u

sk

1.0847341E 01

6.0068659E-01

-2.4230472E 01

1.7365042E 01

1.8869887E 02

-1.1593593E 02

-7.6300942E 02

2.6676274E 02

1.4264726E 03

-2.5996887E 02

-1.2412525E 03

9.1843662E 01

4.0777261E 02

1.4352705E-01

9.6570256E-01

-8.4557281E-01

-4.7783220E 00

-1.3976016E 01

-2.3884222E 01

4.4348199E 01

1.1777619E 02

1.1766320E 02

1.5439476E 02

-2.9505143E 02

-5.8452889E 02

-3.3965383E 02

-3.8447369E 02

7.7576793E 02

1.2218275E 03

3.9903615E 02

4.1502135E 02

-8.8033071E 02

-1.1519065E 03

-1.6575612E 02

-1.6211853E 02

3.6065598E 02

4.0243153E 02

2.8422108E-01

3.9405910E-01

-1.9527271E 00

-3.6131784E 00

-5.2786767E 00

-4.8036404E 00

2.1448102E 01

3.3071747E 01

1.8113526E 01

9.1406965E 00

-4.7457672E 01

-8.1269085E 01

-1.5238267E 01

-3.3477439E 00

2.9248889E 01

5.5277724E 01

1.5654446E 00

-1.7650886E 00

81
One Per Card Coefficients h . (See Card Format 5)

Y M DLC H FNCD PP1 PP2 SN

5806 4500 213 52 8 100 12 36 2 186.8

5806 4500 213 52 8 100 12 36 2 186.8 1 5806 4500 213 52 8 100 12 36 2 186.8 2 5806 4500 213 52 8 100 12 36 2 186.8 3 5806 4500 213 52 6 100 12 36 2 186.8 4 5806 4500 213 52 8 100 12 36 2 186.8 5 5806 4500 213 52 8 100 12 36 2 186.8 6

5806 4500 213 52 8 100 12 36 2 186.8 7 5806 4500 213 52 8 100 12 36 2 186.8 8 5806 4500 213 52 8 100 12 36 2 186.8 9 5806 4500 213 52 8 100 12 36 2 186.8 10

5806 4500 213 52 8 100 12 36 2 186.8 11

5806 4500 213 52 8 100 12 36 2 186.8 12

5806 4500 213 52 8 100 12 36 2 186.8 13

5806 4500 213 52 8 100 12 36 2 186.8 14

5806 4500 213 52 8 100 12 36 2 186.6 15

5806 4500 213 52 8 100 12 36 2 186.8 16

5806 4500 213 52 8 100 12 36 2 186.8 17

5806 4500 213 52 8 100 12 36 2 186.8 18

5806 4500 213 52 8 100 12 36 2 186.8 19

5806 4500 213 52 8 100 12 36 2 186.8 20

5806 4500 213 52 8 100 12 36 2 186.8 21

5806 4500 213 52 8 100 12 36 2 186.8 22

5806 4500 213 52 8 100 12 36 2 186.8 23

5806 4500 213 52 8 100 12 36 2 186.8 24

5806 4500 213 52 8 100 12 36 2 186.8 25

5806 4500 213 52 8 100 12 36 2 186.8 26

5806 4500 213 52 8 100 12 36 2 186.8 27

5806 4500 213 52 8 100 12 36 2 186.6 28

5806 4500 213 52 8 100 12 36 2 186.8 29

5806 4 500 213 52 8 100 12 36 2 186.8 30

5806 4500 213 52 8 100 12 36 2 186.8 31

5806 4500 213 52 8 100 12 36 2 186.8 32

5806 4500 213 52 8 100 12 36 2 186.6 33

5806 4500 213 52 8 100 12 36 2 186.8 34

5806 4500 213 52 8 100 12 36 2 186.8 35

5806 4500 213 52 8 100 12 36 2 186,8 36

5806 4500 213 52 8 100 12 36 2 186.8 37

5806 4500 213 52 8 100 12 36 2 186.8 38

5806 4500 213 52 8 100 12 36 2 186.8 39

5806 4500 213 52 8 100 12 36 2 186.8 40

5806 4500 213 52 8 100 12 36 2 186.8 41

5806 4500 213 52 8 100 12 36 2 186.8 42

5806 4500 213 52 8 100 12 36 2 186.8 43

5806 4500 213 52 8 100 12 36 2 186.8 44

5806 4500 213 52 8 100 12 36 2 186.8 45

5806 4500 213 52 8 100 12 36 2 186.8 46

5806 4500 213 52 8 100 12 36 2 186.8 47

5806 4500 213 52 8 100 12 36 2 186.8 48

5806 4500 213 52 8 100 12 36 2 186.8 49

5806 4500 213 52 8 100 12 36 2 186.8 50

5806 4500 213 52 8 100 12 36 2 186.8 51

5806 4500 213 52 8 100 12 36 2 186.8 52

5806 4500 213 52 8 100 12 36 2 186.8 1 5806 4500 213 52 8 100 12 36 2 186.8 1 1

sk

9.4565125E 01

4.0170246E 00

-2.1605705E 01

-7.8164387E-01

1.4642438E 00

1.3993547E 00

-3.2498074E-02

-3.7577779E-01

1.3522217E-01

-3.9923328E-01

-6.4115469E-01

7.1357547E-01

1.5940220E 00

-9.0769068E-01

1.8921489E 00

2.6680483E 00

5.1834916E 00

-6.0173756E-01

2.8737972E-01

7.5293761E-02

-1.5618081E 00

-8.1786337E-01

1.0628657E 00

3.9685505E-01

-7.7826549E-01

-3.5562921E-01

-1.2530024E 00

1.6143535E-01

1.2648626E 00

7.4794657E-01

1.2934358E 00

6.1983575E-02

-1.8562712E 00

-9.3592011E-01

-9.1538558E-01

1.0113917E 00

1.1285386E 00

3.4079790E-01

3.2231821E-01

8.8341281E-01

-9.1879728E-01

-9.5740420E-02

-6.3193738E-01

1.1002588E-01

-9.0577019E-02

5.0261891E-01

1.2591517E 00

-1.0611030E 00

-1.1026031E 00

-8.0437840E-01

-1.7631563E-01

8.2920978E-01

1.4233196E 00

1.4133058E 01

-3.7146698E 00

-82- GPO 835-527


V. S. DEPARTMENT OF COMMERCE

Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS

A. V. Astin, Director THE NATIONAL BUREAU OF STANDARDS

The scope of activities of the National Bureau of Standards at its major laboratories in Washington, D.C., and

Boulder, Colorado, is suggested in the 'following listing of the divisions and sections engaged in technical work.

In general, each section carries cut specialized research, development, and engineering in the field indicated by

its title. A brief description of the activities, and of the resultant publications, appears on the inside ofthe

front cover. WASHINGTON, D. C.

Electricity. Resistance and Reactance. Electrochemistry. Electrical Instruments. Magnetic Measurements.

Dielectrics. High Voltage.

Metrology. Photometry and Colorimetry. Refractometry. Photographic Research. Length. Engineering Metrology.

Mass and Scale. Volumetry and Densimetry.

Heat. Temperature Physics. Heat Measurements. Cryogenic Physics. Equation of State. Statistical Physics.

Radiation Physics. X-ray. Radioactivity. Radiation Theory. High Energy Radiation. Radiological Equipment.

Nucleonic Instrumentation. Neutron Physics.

Analytical and Inorganic Chemistry. Pure Substances. Spectrochemistry. Solution Chemistry. Standard Refer- ence Materials. Applied Analytical Research. Crystal Chemistry.

Mechanics. Sound. Pressure and Vacuum. Fluid Mechanics. Engineering Mechanics. Rheology. Combustion

Controls. Polymers. Macromolecules: Synthesis and Structure. Polymer Chemistry. Polymer Physics. Polymer Characterization. Polymer Evaluation and Testing. Applied Polymer Standards and Research. Dental Research.

Metallurgy. Engineering Metallurgy. Microscopy and Diffraction. Metal Reactions. Metal Physics. Electrolysis and Metal Deposition.

Inorganic Solids. Engineering Ceramics. Glass. Solid State Chemistry. Crystal Growth. Physical Properties.

Crystallography.

Building Research. Structural Engineering. Fire Research. Mechanical Systems. Organic Building Materials. Codes and Safety Standards. Heat Transfer. Inorganic Building Materials. Metallic Building Materials. Applied Mathematics. Numerical Analysis. Computation. Statistical Engineering. Mathematical Physics. Operations Research. Data Processing Systems. Components and Techniques. Computer Technology. Measurements Automation.

Engineering Applications. Systems Analysis.

Atomic Physics. Spectroscopy. Infrared Spectroscopy. Far Ultraviolet Physics. Solid State Physics. Electron Physics. Atomic Physics. Plasma Spectroscopy.

Instrumentation. Engineering Electronics. Electron Devices. Electronic Instrumentation. Mechanical Instru- ments. Basic Instrumentation. Physical Chemistry. Thermochemistry. Surface Chemistry. Organic Chemistry. Molecular Spectroscopy. VAt mentary Processes. Mass Spectrometry. Photochemistry and Radiation Chemistry.

Office of Weights and Measures. BOULDER, COLO.

Cryogenic Engineering Laboratory. Cryogenic Equipment. Cryogenic Processes. Properties of Materials. Cryogenic Technical Services. CENTRAL RADIO PROPAGATION LABORATORY

Ionosphere Research and Propagation. Low Frequency and Very Low Frequency Research. Ionosphere Research. Prediction Services. Sun-Earth Relationships. Field Engineering. Radio Warning Services. Vertical Soundings Research.

Radio Propagation Engineering. Data Reduction Instrumentation. Radio Noise. Tropospheric Measurements.

Tropospheric Analysis. Propagation-Terrain Effects. Radio-Meteorology. Lower Atmosphere Physics.

Radio Systems. Applied Electromagnetic Theory. High Frequency and Very High Frequency Research. Fre- quency Utilization. Modulation Research. Antenna Research. Radiodetermination.

tipper Atmosphere and Space Physics. Upper Atmosphere and Plasma Physics. High Latitude Ionosphere

Physics. Ionosphere and F.xosphere Scatter. Airglow and Aurora. Ionospheric Hadio Astronomy.

RADIO STANDARDS LABORATORY

Radio Physics. Radio Broadcast Service. Radio and Microwave Materials. Atomic Frequency and Time-Interval

Standards. Radio Plasma. Millimeter-Wave Research.

Circuit Standards. High Frequency Electrical Standards. High F'requency Calibration Services. High Frequency

Impedance Standards. Microwave Calibration Services. Microwave Circuit Standards. Low Frequency Calibration

Services.
NBS