AD-762 070SYNTHETIC BATHYMETRIC PROFILING SYSTFM

(SYNBAPS)

Roger J. Van Wyckhouse

Naval Oceanographic OfficeWashington, D.C.

May 1973

DiSTRIBUTED BY:

National Technical Information ServiceU. S. DEPARTMENT OF COMMERCE -5285-Port Royal Road, Springfield Va. 22151

TR-233

TECHNICAL REPORT

q SYNTHETIC BATHYMETRIC

PROFILING SYSTEM (SYNBAPS)

ROGER J. VANWYCKHOUSE

MAY 1973

teProdvc1d by

NATIONAL TECHNICALINFORMATION SERVICE

U S Depart'mcn of Co•n rce

5 .,9,dVA 22 5

Approved for public release;

distribution unlimited.

NAVAL OCEANOGRAPHIC OFFICEWASHINGTON, D.C. 20373

ABS TRACT

The Synthetic Bathymetric Profiling System (SYNBAPS)consists of 10 FORTRAN IV computer programs, a random-accessstorage device, and an initial bathymetric data base of over3 million data points. SYNBAPS is designed for rapidgeneration of random omnidirectional bathymetric profilesin digital form along great-circl paths. The initial database will cover most of the Northern Hemisphere and will beextended to other regions as suitable bathymetriL contourcharts become available.

Data derived from the bathymetric contour charts arestructured into a gridded data surface by the application ofa cubic spline algorithm. The gridded data are stored on arandom-access storage device by 5-degree-square areas. Anaccessing program, initiated by a user's request, extracts the5-degree-square b]locks of data for processing. The interpolationof the final profile is accomrp]ished by orienting a cubic splinealgorithm along a great-circle path and interpolating the depthvalues from the 5-degree squares falling on the path. A statusprogram checks the content and condition of the random-accessstorage device.

SYNBAPS will provide bathymetric profiles at about one-fifththe cost and one-hundredth the time of present semiautomatedmethods.

Ocean Science Department"Science and Engineering Center

L4 ilo aapit. SNBP sdsge o ai

UNCLASSIFIED

DOCUMENT CONTROL DATA R & DSoc .-o ( i,°fr• {.m, oto a l , at itl'. taodl I . flair r .ooJ ,oak,,, .Nn."ots n , siý b , 0t c -0 ... e. 1.e, th- b, -1t.. drpo.t, s . - repohrdt

I . toGs" A TIG 'C "1 .- .- O W ) Z&. 14L FOR I S.CUPl IY CLAss1FO , AT•. t

Ocean Science Department UNCLASSIFIEDU.S. Naval Oceanographic Office jZ GouDWashington, D.C. 20373 N/A

3 RiPOR? Tl FL-

Synthetic Bathymetric Profiling System (SYNBAPS)

4 r C111 P - 1 1. V NO t I (Type 0 f repofad 'rt u.' daes

Technical Report

Roger J. Van Wyckhous3

I REPORiT DATE 7s. TOTAL- NO OF PAGrS Th no o•r E"S

t.. CONRI-C O P ANT• % O TOR'S REPORT NUMEROjIS

TR-2 3b. PROJECT NO

C, R T.R REPORT NOIS) (Any other number3 that may be *lsstlnedthis report)

NONEd

I0 0151RiIPUTION SIATCK4ENT

Approved for public release; distribution unlimited.

II 5VPPLCME.TAqV NOTES Itý SPO1NIORONG1 MIL'IIARY1 AC TI VIT

U.S. Naval Oceanographic OfficeIWashington, D.C. and Office of/20373INaval Research, Washington, D.C.

,i , .... cT 20375

"The Synthetic Bathymetric Profiling System (SYNBAPS) consists of 10FORTRAN IV computer programs, a random-access storage device, and aninitial bathymetric data base of over 3 million data points. SYNBAPSis designed for rapid generation of random omnidirectional bathymetricprofiles in digital form along great-circle paths. The initial database will cover most of the Northern Hemisphere and will be extendedto other regions as suitable bathymetric contour charts becomeavailable.

Data derived from the bathymetric contour charts are structured intoa gridded data surface by the application of a cubic spline algorithm.The gridded data are stored in a random-access storage device by 5-degree-square areas. An accessing program, initiated by a user'srequest, extracts the 5-degree-square blocks of data for processing.The interpolation of the final profile is accomplished by orienting acubic spline algorithm along a great-circle path and interpolatingthe depth values from the 5-degree squares falling on the path. Astatus program checks the content and condition of the random-accessstorage device.

SYNBAPS will provide bathymetric profiles at dbout one-fifth the costand one-hundredth the time of present semiautomated methods.

DD FORm1473 PAGE • UNCLASSIFIEDS/I 0101.807-6801 Secuityv Clas. I si~aon

II

UNCLASSIFIEDSecurity Classification

14 LINK A LINK S LINK C

ROLE WT RlOLE WT ROLE WT

BathymetryBathymetric profilingBathymetric data bankAcoustic propagation modelingNorthern Hemisphere, bathymetryDigital computer softwareGreat circleRandom-access storage device

DD NovR. 14 7 3 UN,,,K) UNCLASSIFIED(PAGE 2) Security Clas~ificatIon

FOREWORD

This report describes a computer system and programs thatwill establish a world-wide bathymetric data bank and ,,-neratecomputer-drawn bathymetric profiles. The research was performedby the Naval Oceanographic Office in support of the Off ie ofNaval Research, Long Range Acoustic Propagation Project, wricbprovided funding. It is part of a major bathymetric char4iro,,project covering the North Atlantic and North Pacific Oceans.Bathymetric data, usually in the form of profiles, are e&s.ntialelements in the development of acoustic propagation models 'ndpredictions, which are required for naval planning, systersdevelopment, and operations. The computerized bathymetricprofiling system and specialized data bank described here willgenerate computer-drawn bathymetric profiles at a small fractionof the time and cost of manually produced profiles. Thisspecialized data bank will be operational when approximately600 5-degree-square areas have been structured on a random-acceE."storage device. Presently, the ccntour data required for thestructuring procedure are being d:gitized under ONR-LRAPPcontract No. N00014-72-C-0466.

P. V. PURKRABEKCaptain, U.S. Navy",n[.mander

U.S. Naval Oceanographic Office

CONTENTSPage

Introduction .................................................... 1Outline of System Operation ..................................... 2Source Material ................................................. 1System Description .............................................. i

A. Structuring Programs ................................... 11B. Accessing Programs ..................................... 23C. Status Program ......................................... 32D. CDC 3800 System Subroutines and Functions ............ 35

Profile Output .................................................. 35Furtir Modifications, Additions, and Other Applications ....... 40Summary and Conclusions ......................................... 41References ................................ i ................... 42Bibliography .................................................... 44Glossary of Selected Terms ...................................... 45List of Acronyms Used in Computer Programs .................... 55Appendix A - Preparation of Charts for Digitization ........... A-IAppendix B - FORTRAN Programs for Structuring SYNBAPS ......... B-1Appendix C - FORTRAN Programs for Accessing SYNBAPS ........... C-1

ILLUSTRATIONS

1. Synthetic Bathymetric Profiling System Diagram ............ 32. SYNBAPS Logical Data Grid ................................... 53. Marsden Square Chart ........................................ 64. Marsden Square Quadrants as MSQLOC Areas .................. 75. Example of MSQLOC Area ...................................... 86. Example of Synthetic Track Orientation .................... 97. SYNBAPS Structuring Programs Flow Diagram ................. 138. Output Deck Structure from SYNTRACK ....................... 149. SYNCHEX Control Card for Track Plotting of MSQLOC

Area ......................................................... 1610. SYNGRID Control Cards for Gridding Track Data ............. 1811. SYNCON2R Control Card for Contour Plotting ................ 2012. SYNBAPS Accessing Programs Flow Diagram ................... 2413. SYNLAPS1 Profile Request Centrol Card ..................... 2514. Accessing Programs Detail Flow Diagram .................... 2615. Quadrants for Subroutine BmTHY ............................. 2816. Profile Extraction from Gridded Data Base ................. 3017. SYNPLOT Control Ca d........................................ 3118, Difference Between Rhumb Line and Great Circle Path

Vithin a F;Ne-Degree Square ................................ 331.9. SYNSTAT Contv.1. Cards ....................................... 3420. Index of Sam?>.e Profiles .................................... 3621. Profile Passinc Through Two MSQLOC Areas .................. 3722. Cubic Spline v,; Manual Profiles ............................ 3823. Mirror Image Picsf-tes Alone Same Path - Different

Directions .................................................. 39

'1

TABLESPage

..i. Example of "Look-up" Table from SYNTABLE ................ 21li SYNBAPS Word Storage Requirements ........................ 22

APPENDIX A

Preparation of Charts for Digitization .................. A-1

FIGURES - APPENDIX A

A-i. Added Contours Around Seamourts or Seamount Group ....... A-3A-2. Added Contours on Domes or Rises ........................ A-4A-3. Added Contours Around a Spur.............................. A-5A-4. Boundary Conditions for Zero Contour Level .............. A-6

APPENDIX B

FORTRAN Programs for Structuring SYNBAPS ................ B-1

APPENDIX C

FORTRAN Program for Accessing SYNBAPS ................... C-i

vi

INTRODUCTION

The need for a computerized bathymetric data bank andtechniques for rapidly manipulating large quantities of databecame evident as demand upon the Naval Oceanographic Officefor bathymetric profiles increased and became more urgent. itbecame increasingly difficult to satisfy these demands throughmanual compilation of depth soundings, contouring, and profileconstructions. A massive recompilation and reanalysis ofbathymetric data, systematic revision of all bathymetric chartsin the North Atlantic and North Pacific Oceans, includingextension of chart coverage to the equator, was underway. Atthe same time the impracticality of using the existing data bankof bathymetric soundings for machine generation of profilesbecame apparent. The need for a specialized bathymetric databank to support acoustic - oceanographic modeling gave rise todevelopment of a synthetic bathymetric profiling project usingthe new bathymetric contour charts as the data base. The projectdeveloped procedures for digitizing the contour charts, andcomputer programs and subroutines for data storage and retrievaland for profile generation. Mr. Thomas M. Davis, Naval Oceano-graphic Office, provided special assistance in developingprograms SPLINT (SYNGRID), BURNS (SYNCON2R), BATHY (subroutineBATHY) and DAWHAT (SYNCHEX) and contributed to the basic philosophyregarding SYNBAPS. Mr. J.D. Brown, Naval Oceanographic Office,assisted in the software development and digitization of the testdata.

Funds for this project were provided by the Office of NavalResearch through the Long Range Acoustic Propagation Project.

One of the basic inputs to most Navy long-range, acousticpropagation models are bathymetric profiles in digital form. Theseprofiles usually are plotted along a great-circle path (glossary)as a function of range versus depth. Two methods of generatingsuch profiles generally have been employed. In the first, a shipsails a predetermined great-circle path collecting continuousbathymetry using a precision depth recorder (PDR). if the courseis ac-'urately adhered to, the PDR record can ne merged with thenavigational record to obtain the bathymetric profile. If thenavigational record is poor, the track of the ship will have tobe adjust-I and normalized to obtain a satisfactory bathymetricprofile. A profile thus produced is accurate and retains mostof the high frequency information but is costly in ship time,hard to schedule, and usually results in only a single profile.

MOO

A second means of obtaining a bathymetric profile is to plota great-circle path on a bathymetric contour chart, or series ofcharts, and digitize the range and depth at the intersection ofthe path with each bathymetric contour. When a large number of~great-circle profiles, each several thousand miles long, involvingdA nens of bathymetric charts, are constructed, the labor costs areconsiderable. Profiles produced manually from charts tend to beschematic, blocky, and subject to human error. Most importantly,both of these methods are slow and cannot be achieved in real time.

Although various phases of both methods have been automated,within the Navy and elsewhere, no totally satisfactory solutionhas been achieved to the present time. The system prcposed inthis report is one approach to solving the above problems.

The Synthetic Bathymetric Profiling System (SYNBAPS) is acombination of digital computer software (programs) and a random-access storage file (presently a CDC 813 permanent disk) of griddedbathymetric data, employed to generate random, great-circle,bathymetric profiles suitable for acoustic propagation modeling.SYNBAPS is completely automatic, requiring only the input, via acontrol card, of the latitude and longitude of the beginning andend points to extract the desired profile. The profile also canbe generated given the latitude and longitude of the beginningpoint, the bearing, and the maximum range. The generated profileis available in two forms. The first is a computer-drawn profilewhere range in whole nautical miles is plotted against depth, ineither meters or fathoms; the sccond is a ounched card deck ofthe same data. The profile outputs in card image are available onmagnetic tape where large quantities of data are involved.

A bathymetric profile along a great-circle path of about8,000 nm can be generated in approximately 3 minutes of computertime on a second generation computer and can be plotted in about3 minutes on an incremental plotter. A cost comparison shows that,by present semiautomatic methods, a set of 19 short profilestotaling 9,000 nm required 144 man-hours at a cost of $900. Thesame profiles could be produced by SYNBAPS in 1.4 man-hours at acost of $50, for a savings of 18:1 in dollars and 100:1 in time.

OUTLINE OF SYSTEM OPERATION

The SYNBAPS software can be broken down into chree distinctprogram functions associated with structuring, accessing, andstatus (fig. 1).

The structuring programs create a gridded bathymetric database and structure it on a random-access device in a preciseform. The smallest cell of the data base is a 5-minute-squaregrid where the north-south side is in meridional minutes or parts

2

USERREQUEST

i

ACCESSINGPROGRAMS

-STRUCTURIN•G STATU

RANDOM ACCESS STORAGEDEVICE

OF GRIDDED BATHYMETRICDATA

FIGURE 1. SYNTHETIC BATHYMETRIC PROFILING SYSTEM DIAGRAM

p,3

and the east-west side is in longitudinal minutes. On aMercator projection contour chart this is a 5-minute rectangulargrid. The bathymutric data are logically formatted to placedepth values at the intersection of each 5-minute grid crossingas shown in figure 2.

The next level of structuring is to index the 5-minute cellsinto 5-degree squares called Marsden Square Locator numbers (MSQLOC)using the Marsden square system which divides the earth surfaceinto 5-degree squares (fig. 3). Further subdivision of theMarsden square by quadrants is shown in figure 4. The MSQLOC isthe quadrant number followed by the Marsden square number asfollows:

Marsden square number+quadrant = MSQLOC

Example: 036+2 = 0362

The MSQLOC is a unique worldwide reference to each 5-degree squareof gridded bathymetric data. The MSQLOC area includes a 5-minuteoverlap of all sides as shown in figure 5 for MSQLOC 0362.

The gridded bathymetric data base is created following theprocedure used by Davis and Kontis (1970). However, accuratesynthetic data derived from large and medium-scale bathnmyetriccharts are used instead of original survey data. The synthetictrack data are derived from charts by superimposing parallel tracklines, 5 minutes apart, over the MSQLOC area. Extraction of thedata usually starts from the lower left corner. The orientationof the track lines can be any direction from west-east (900 bearing)to nearly south-north (10 bearing), but not true north, whichnecessitates changing several statements in the gridding program.The only other restriction is that the first track be a west-easttrack across the MSQLOC area. The remaining tracks may be of anyorientation and in any order.

The data are extracted from the chart by digitizing theintersections of the synthetic track with the contours sequentiallyalong the track. Interpolated points must be extracted for thebeginning and end of each full track. These tracks must extend5 minutes beyond the MSQLOC area on all sides as shown in figure 6.Short tracks may be added to emphasize certain topographiccharacteristics such as spot elevations. These can be extractedat any orientation except true north-south as shown in figure 6B.

Each digitized track is assigned a sequence number, but thephysical order of the tracks in the card deck is arbitrary afterthe first track. These digitized tracks are inputs to the griddingprogram. The output from that program isapunched deck of griddedLathymetric data with the point or origin in the lower left corner.

4

IIII I-234 245 301 323 361-

-329 453 580 467 673-

DEPTH__ __ fVALUE

1- 427 469 501 568 690-

5' CELLz

"W-5 5 -612 656 694 7r,5--

- 653 702-----733 -766 876-

-760- 795 842 973 1072-

I LONGITUDINAL MINUTES i

FIGURE 2. SYNBAPS LOGICAL DATA GRID

5

2-

2.2j 2

t uj

S -I .

I-

-~ ~ ~ t -

4 ~ ~ ~ , Z 'q-~-

e It to$1 ... ..

3.:~~~eP .-. fa 2 - ' l

bi

WEST LONGITUDE EAST LONGITUDE0oo o. 100

100 10,o

0014 0013 0363 0364I--0

0012 0011 0361 0362

0 m m00

3002 3001 3351 3352

. I.-n-z

3004 3003 3353 3354

0

too 10.

"100 00 5O4

FIGURE 4. MARSDEN SQUARE QUADRANTS AS MSQLOC AREAS

7 3

K 310 LONGITUDINAL MINUTES*05* 05'N

F - - 05*N-

IIr

I 0362

- -* --

--4--SYNTHETIC TRACKS-. SPACED 5'

4---- .4

0--i - -

4- - 4FIVE-DEGREE SQUARE

_____________ -4- FIRST TRACK(A) ______________ MSQLOC AREA

SYNTHETIC TRACKSSPACED 5'

SHORT TRACK

FIVE-DEGREE SQUARE

-4--FIRST TRACKMSQLOC AREA

FiGRE 6. EXAMPLE OF SYNTHETIC TRACK ORIENTATION

9

These data are physically unformatted. A number of errorchecks are made before and after the gridded bathymetric dataare created. The gridded data then are placed on a random-accessstorage device using a predetermined "look-up" table (list ofacronyms). At this point the data are ready to be accessed.

At present, a bathymetric profile can be generated up to8,000 nm long and crossing 30 MSQLOC areas. This limitation canbe incsreased if necessary. The accessing is initiated bysupplying the latitude and longitude of a beginning and endpoint or the lat4.kude and longitude of a beginning point with thebearing and maxivrn~m range. Combinations of these accessing schern~escan also be used.

The first step in retrieving a profile from the data bankis to generate its great-circle path. At the same time eachMSQLOC area that the path crosses is identified and a searchtable of M4SQLOC areas is created. For each MSQLOC area thesearch table contains the latitude and longitude of the first andlast point in that MSQLOC area, the forward-looking bearing atboth points, the accumulated ranC e from zero for both points,and the MSQLOC area number. In turn, each MSQLOC area is calledfrom the random-access storage device via the "look-up" tableand the profile for that block of data is generated. This partialprofile is then placed on a temporary magnetic tape. The nextMSQLOC area is called from the random-access storage device andthe cycle is repeated. At the end of profile generation thetemporary magnetic tape is rewound. The plotting program isthen called and the partial profiles are linked, punched on cards,and plotted and/or written on magnetic tape.

The accessing program is structured so that long profilesgenerally are processed faster than numerous short profiles thattotal the same mileage. The great-circle path generati.on requiresabout 10 seconds for an 8,000-nm profile plus about 5 secondsfor each full MSQLOC area crossed for the interpolation.

The only maintenance to be performed to the system is theeventual updating of the gridded bathymetric data based on therandom-access storage device. This is easily accomplished byrecycling through the structuring phase of the system any MSQLOCarea that requires updating and then replacing that bock on therandom-access storage device.

A status report can be generated to check any or all. MSQLOCareas. This report includes the random-access device's compaltibledata block size, the actual column and row sizes, the date thedata block was added to the random-access device, the MSQLOCarea number, the relative address, and the actual data, if reauired.

10

SOURCE MATERIAL

Bathymetric contour charts instead of recorded water depths,are the source for the SYNB&PS data base. No computer algorithm(glossary) that can successfully handle all qualities of bathy-metric-track-line data, resolve all navigational errors, and canapply a contouring philosophy to such data has been developed.These functions require the subjective judgement, based onknowledge of geologic processes, of the bathymetrist whose finalproduct is the bathymetric contour chart. The bathymetrist'svery subjectivity creates the data continuity which is a requisiteelement of SYNBAPS. A long profile requires on omnidirectional,continuous data base, something that is seldom achieved witheither survey or random shi~p track line data alone. Using areashaving high quality anA dense data coverage as a framework, thebathymetrist extends, interpolates, and extrapolates regionaltrends into areas of lesser data to build a continuous pictureof the submarine topography.

Although SYNBAPS is designed for worldwide application,initially a data base will be created only for the NorthernHemisphere, and possibly the Indian Ocean. Other regions willbe added to the data base whei, sufficient continuous data becomeavailable. The charts used for the North Pacific Ocean will belarge to medium scale (1:1,000,000 or larger) versions of theU.S. Naval Oceanographic Office H.O. Pubs. 1301, 1302, and 1303(U.S. Naval Oceanographic Office 1969, 1971A and B). Recentunpublished large-to-medium scale charts compiled by the U.S.Naval Oceanographic Office will be utilized for the North Atlanticand Mediterranean Sea. Where applicable, classified data can beincorporated in the data base without compromising security. Thegridded data point from a classified chart, which was contouredfrom classified data or from amixture of classified and unclassi-fied data, will be indistinguishable from a data point from anunclassitfed chart. Only the originator will know which depthvalues were created from classified data and that they may bemore accurate than other points. The originator will keep aseparate noncomputerized file, indexed by MSQLOC areas, showingthe source of the contours, their evaluation, classification,arid other pertinent information. There will be no reference tooriginal track spacing, area limits, navigation, sounding device,or platform within the data base. Preparation of the charts fordigitization is discussed in more detail in appendix A.

SYSTEM DESCRIPTION

A. Structuring Programs

11

The relationship between structuring programs is given ina flow diagram in figure 7. The main processing programs areSYNTRACK, SYNCARD, SYNCHEX, SYNGRID, SYNCON2R, and SYNBLOCK (listof acronyms). One additional program that is unique to thispa-ticular system is the digitizer scaling program (CALMA 485)which scales on a Mercator chart the latitude, longitude, anddepth for each contour intersection along the track. The outputfrom this proyram is a binary magnetic tape of scaled values.Any digitizer and/or digitizer processor program can be used aslong as it generates the same program elements regardless ofoutput mode.

The MSQLOC area to be digitized is mounted and leveled onthe digitizer table (fig. 7). Starting in the lower left cornereach track is scanned for data points from l.eft to right andfrom bottom to top. The tracks are scanned an additional 5minutes on each end to permit interpolation rather than extra-polation on end points in the gridding program. The MSQLOCidentification and operator name are entered as a header informa-

tion group before the Oeta scanning is begun. The binary codeddecimal (BCD) magnetio ape generated by the digitizer isprocessed by the CALPLA 4&5 processor program to produce a binarymagnetic tape of scaled latitude, longitude, and depth data. Thebinary tape is processed by SYNTRACK which:

* breaks up the data string into tracks,

e checks for missing data points,

e checks for operator errors,

* reformats the data to card image, and

* punches out a header card, track card, data cards(one point per card), and a blank card.

An illustration of this deck structure is given in figure 8. Aftererrors have been corrected, the card deck generated by SYNTRACK isrun through the SYNCARD program. This program checks to insurethat the longitudes of contour intersections are not repeated, buteither increase or decrease depending upon quadrant. In addition,this program tests the depth value to determine if it is withinabout plus or minus two times the contour interval. In regionsof rapid depth change contours may be skipped if they are evenlyspaced. All errors are flagged for correction.

After all corrections have been made, the card deck is runthrough the track plotting program (SYNCHEX). This program plotsthe tracks as they were digitized and annotates each contourintersection on the synthetic track line with cross ticKs. This plot

12

0z

40

u

Nfu

ETC.

T IC

MSQLOC

FIGURE 8. OUTPUT DECK STRUCTURE FROM SYNTRACK

14

insures that the proper and sufficient number of points havebeen extracted from the MSQLOC area. Additional tracks of datacan be created at this time, if required by the complexity ofthe submarine topography. SYNCHEX requires a control card thatis in reality the first data card. The format for this card isgiven in figure 9. If no further corrections or additions areto be made to the data deck, the MSQLOC area is ready forconversion to gridded bathymetry.

The SYNGRID program is fundamental to the structuring phaseof SYNBAPS. SYNGRID transforms the synthetic track line datainto gridded bathymetric data, The mathematical foundation andphilosophy behind the one-dimensional cubic spline used tostructure the gridded data is fully explained by*Davis and Kontis(1970). SYNGRID is a modification by Davis of his originalprogram (SPLINT) to handle bathymetric data instead of gravitydata. SYNGRID is very flexible as it grids track-line-pointdata on either a Mercator projection or a Cartesian coordinatesystem and can compute mean data for varioos size cells on eitherqystem. Summarizing Davis and Kontis (1970), the value of thismethod lies not only in its ability to fit the observed datavalues but to retain the continuity of the first and secondderivatives. This method might be considered the mathematicalanalog of the draftsman's plastic spline.

Because the cubic spline is a function of only one independentvariable, the data obtained along a synthetic track line must beadjusted to lie on a straight line. Under most conditions thiscreates no problem as the data are digitized along straight lines.The interpolation formula used by Davis fits each data exactly,has continuous first and second derivations, and is a simple cubicpolynomiz.l in x within the interval between each pair of datapoints. The distance along the track line then may be interpretedas the independent variable. Therefore, taking the data from onetrack at a time, the position of the data points are convertedinto x, y coordinates and a least squares straight line is fittedto these locations. Because no statistical significance isattached to this operation, either x or y may be considered theindependent variable. The computer program listed in appendix Bconsiders x the equivalent longitude as the independent variable.If the survey tracks happen to run exactly north-south, theprogram should be modified to consider y as the independentvariable.

The perpendicular distance be ,een the least squares straightline and each data point is determined and used to project thepoints orthogonally onto the line with an adjusted data value(based on an estimate of the local gradient) assumed to be afunction of distance only. If the perpendicular distance betweenthis point and the least squares line is less than predetermi.ned

15

NLINE XMIN XMAX YMIN YMAX XIN YIN

A* R1 11I 21 31 41 51 61 71

I FORMAT (1 10, 6 F 10.0)

R = RIGHT JUSTIFIED F =FLOATING POINT REQUIRED

NLINE = TOTAL NUMBER OF TRACKSXMIN minimum number of minutes from prime meridian - east or westXMAX = maximum number of minutes from prime meridian - east or westYMIN = minimum number of meridional parts from equator - north or southYMAX maximum number of meridional parts from equator - north or southXIN = east-west dimension of plot in inchesYIN = north-south dimension of plot in inches

NOTE: 1. North and east ore positive, so.sth and west are negative.2. MSQLOC areas require 50 minutes of overlap on all sides.3. Meridional parts are found in reference:

Naval Oceanographic Office, 1962H.O. Pub. 9-Table 5

FIGURE 9. SYNCHEX CONTROL CARD FOR TRACK PLOTTING OF MSQLOCAREA

16

pivot distance (usually set at 0.2 of a meridional part), thevalue associated with the data point is unchanged. If thisdistance is greater than the pivot distance, then the adjustedvalue associated with the mapped coordinates is computed.

In the computer program for the cubic spline algorithm(SPLINE) contained in appendix B, the pivot distance is selectablevia a control card. This pivot distance is usually equal tothe maximum distance which one could move a data point withoutsignificantly changing its value. In order to minimize the errorassociated with the assumption that the gradient correction isindependent of direction, continuous synthetic survey trackswhich deviate appreciably from a stright line should be brokenup into smaller segments with each segment treated as a separatetrack. The mapped coordinates and adjusted data values maybe considered as irregularly spaced digital samples from afunction whose independent variable is distance along the trackfrom some arbitrary starting point, and whose dependent variableis the adjusted data values.

Utilizing the mapped data, the cubic spline is determinedfor each track. The cubic spline may then be used to interpolatedata values at the intersections of the straight least squaretrack lines and a set of parallel lines whose spacing is equalto the desired final grid spacing (5 minutes). If the directionof the survey tracks is predominantely east-west then the directionof the set of parallel lines is north-south. Similarly, fornorth-south tracks, the lines are run east-west.

The computer program (app. B), is designed to operate ontracks in any direction, except exactly north-south. Thedirection of the Cet of parallel grid lines is controlled bythe direction of track line number one. Since the track numberdesignation is arbitzary, this feature allows the user todetermine the desired orientation (N-S or E-W) of the parallelgrid lines in order to obtain as many intersections as possible.

The interpolated data values generated as outlined in thepreceding paragraph may be regarded as unequally spaced digitalsamples from a function whose independent variable is distancealong each of the parallel lines. Application of the splineprocedure in this cross track direction produces the finalinterpolated values at the desired grid points. If mean anomaliesare desired, grid points are generated at one-half the finalgrid spacing and the resulting nine points are averaged toproduce the mean value for each grid cell.

The control card formats for SYNGRID are given in figure 10.The output from SYNGRID is a new punched card deck of griddedbathymetry with seven points per card. The printout from SYNGRID

17

ISET

1 6

201 FORMAT (I 5)

--*R =RIGHT JUSTIFIED

ISETS number of MSOLOC areas to be processed during a computer run

MEAN

I.! I ,TOT

IJIITYPEALAT ALONG PLAT PLONG GRID I f PIVOT MSQLOC

1 I 21 31 41 51 5456 61 6552

01 FORMAT(5 F 10.0,1 1,1 2,1 2, F 5.0, A 4)

"-4- =LEFT JUSTIFIED -*R RIGHT JUSTIFIED *=FLOATING POINT REQUIRED

ALAT latitude of MSQLOC for lower lefthand corner in degreesALONG longitude of MSQLOC for lower lefthand corner in degreesPLAT = latitude of MSQLOC for upper righthand corner in degreesPý.ONG longitude of MSQLOC fo. upper rigý'.hand corner in degreesGRID = grid spacing for output data in minutesMEAN = blank, no mean computed; =1, mean computedITOT = total number of tracks of input dataITYPE 1, grid is in Mercator projection; -1, grid is in X and Y unitsPIVOT maximum distance from track for pivot testMSQLOC Marsden Square Locator area number

FIGURE 10. SYNGRID CONTROL CARDS FOR GRIDDING TRACK DATA

18

w'lII indicate if the MSQLOC area has been structured correctly.

An even more efficienc method of chejking is t' pass the griddedbathymetric data through the SYNCON2R program.

The SYNCON2R program (fig. 7) plots contours of the griddeddata on a Mercator projection at the same scale as the sourcemanuscript. The source manuscript can be overlain by thegridded-data contour plot, for a comparison of content andform. This plotting check requires a 29-inch drum plotter orequivalent, while the SYNCON2R program itself requires a controlcard (fig. 11). In addition, the DATA statement variable (CL)requires a specification of the contour levels that will beplotted (see app. B). An optional DATA statement variable(LABELS) can be used if labels are desired (see app. B). If the

SYNCON2R plot is satisfactory, the gridded bathymetry is loadedon the random-access storage devi-e via the loading program(SYNBLOCK), fig. 7).

Before a block of gridded data can be loaded on the random-access storage device, the dev-ice must be primed With a trafficdirector program (SYNTABLE, fig. 7). SYNTABLE is a predetermined"look-up" *able, which gives SYNBLOCK basic information that isneeded to place a block of gridded data in its proper address onthe device. Using the MSQLOC area number as the key, the tablesupplies the relative address, the actual block size to betransmitted, and a file key or name. The file key indicates byname in which file in the storage device a particular block ofdata is to be placed. Zn example of the "look-up" table printoutis given in table 1. In the DATA statement N is equal to thenumber of MSQLOC areas now on the "look-up" table. The relativeaddress is the physical location from the beginning of the fileof the first word of the data block. The actual block size is thequantity of storage required to contain the data plus theidentifica9-ion groups and is an even multiple of 32 (Aiken, et al.1970). The storage requi.-ement for the actual block size ispredetermined and is listed in table 2 by hemisphere latitudebands, which include the overlap.

Using the "look-up" table from SYNTABLE on the random-accessstorage device, a block of gridded bathymetry can now be loadedby SYNBLOCK. The punched deck of gridded data is preceded bytwo header cards. The first card contains the number of sets tobe loaded and the second card, one for each set, specifies theMSQLCC area number and the column and row information obtainedfrom table 2 (see app. B for exact card formats). The DATAstatement N is equal to the number of MSQLOC's presently on the"look-up" table. SYNBLOCK then looks up the file, the relativeaddress, and the block-size information from the preloaded tablefor each MSQLOC area and places the data in its proper location.An identification group containing the following is placed at theend of the data block:

19

N M NCL MM NN XA YA XG YG

A-*R[A Rl-*Rl+[R I00 0

I 5 9 13 17 21 31 41 51 61

1 FORMAT (5 I 4, 4 F 10.0)

-R = RIGHT JUSTIFIED =FLOATING POINT REQUIRED

N = number of columns of input dataM = number of rows of input dataNCL = number of contour levelsMM = row's maximum array sizeNN = column's maximum array sizeXA = 1.0 = minimum number of rowsYA 1.0= minimum number of columnsXG = x axis width of plot in inchesYG = y axis height of plot in inches

FIGURE 11. SYNCON2R CONTROL CARD FOR CONTOUR PLOTTING

20

SYNBAiPS DISK FILE LOCATOR TABLE

MSQLOC RELATIVE SIZE OF FILEADDRESS BLOCK KEY

211 0 3936 E08C212 3936 3936 E08C213 7672 4000 E08C214 11872 4000 E08C571 15872 4064 E08C572 19936 4064 E08C573 24000 4128 E08C574 28128 4128 E08C931 32768 4256 E08C932 37024 4256 E08C933 41280 4448 E08C934 45728 4448 E08C

1291 50176 4704 E08C1292 54880 4704 E08C1293 595Q4 4928 EO8C1294 65536 4928 E08C1651 70464 4928 E08C1652 75776 5312 E08C1653 81088 5824 E08C1654 86912 5824 EOBC2011 98304 6464 E08C2012 104768 6464 E08C2013 112096 7328 E08C20114 119424 7328 E08C

TABLE I. EXAMPLE OF "LOOK UP" TABLE FROM SYNTABLE

21

0 0 O O C%0 Or-44U ~ 1-1- . 0 - %

Cu

J -4

0% 0 4

V)

0 -u L

0 0.

~ E0

uj 0

0. 0

000

U) 0I U) NO N o 0~

0 04 %0to cW L C m n 0 co m cn222

NUM = actual size of storage block

ICOL = number of columns of array

IROW = number of rows or array

MSQLOC = Marsden Square Locator area number

IDAY = day that data re placed in storage

MONTH = month that data were placed in storage

IYEAR = year that data were placed in storage

LOCATE = relative address

This completes the structuring phase of SYNBAPS. Thepunched cards of gridded bathymetric data are loaded on magnetictape with one MSQLOC area per file using a UTILITY program(Rozanski, et al. 1968). This magnetic tape is saved for backupto the random-access sto:age device.

B. Accessing Programs

The relationship between accessing programs is given in a flowdiagram in figure 12. The two accessing programs are SYNBAPS1 andSYNPLOT (app. C). The request, in the form of control cards, issubmitted to the SYNBAPSi program (fig. 13). The formats for thisrequest may be either all "BEARINGS" or all "POINTS" or can bea mixture of both, as long as the number of beams is correctlyindicated for each set (the variable NOOFBM).

With the exception of SYNGRID, only a brief explanation ofthe program's operation was given in the structuring phasediscussion. Because SYNBAPS1 and SYNPLOT may be used by others,they will be described in more detail.

Figure 14 contains a more detailed program flow diagram ofSYNBAPSI. When a request is submitted to SYNBAPS1 the firstoperation is to call in the SEAARCH subroutine to generate thegreat-circle path to be followed by the profile. SEAARCH usesboth the direction solution of the great circle, subroutineGCDIST, and the indirect solution GCPATH (Chang, 1969A and B) tocreate a latitude, longitude, forward bearing, and range foreach nautical-mile point from the beginning to the end of aprofile. In addition, subroutine MSQFQ is used to calculate theMSQLOC area for each of the points. SEAARCH then creates a rangesearch table of only those points that start a profile, enteror exit a MSQLOC area, or terminate a profile. This table isprinted out and also placed in COMMON.

23

USERREQUEST

PO OFNRANGEVDS.ORAGEPT/P TEOUT

~RAG PLOT COMPUTER. DPT

IOF RESULTSI

OI PROFILING

FIGURE 12. SYNBAPS ACCESSING PROGRAMS FLOW DIAGRAM

24

OF REU "' "p~~ ~~O PROnFm m -•-- •:' IrLNG -II l I ..

NOOFBM NCARD

NOOFBM =number of proftiles of NWARD type to be processed

AMIN ALONG AEID8M ALAT& AN JALMINI BS DD

1 9 12 16 IS21 2527 ".747

1 FORMAT (A6, 2X, 2((F3.0, F3.0), lX, Al, IlX), 2 F 10.0)

L+-= LEFT JUSTIFIED -.*R=RIGHT JUSTIFIED = FLOATING POINT REQUIRED

AMIN ALON4G AE BMIN BLONG BEID ALAT IAN JALMINJ1BLAT IBN I LMINJ

L4- ff R+Rl !R1 R Rl4Rl !R1 R

I 9 12 16 18 21 2527530 3436 59 4345

2 FORMAT (A6, 2X, 4(F3.0, F%3.O, IX, Al, IX))

FOR NCARD ='POINTS"

IDBM =unique proifile I.D. (alphanumeric)ALAT =degree of latitude - start pointAMIN = minute of latitude - start pointAN, BN =hemis~here irndicator, N or SALONG =degree of longitude - start pointALMIN = minute of longitude - start pointAE, BE = hemisphere ind~cator, E or WBS, = beoring from start point for "BEARING" cord onlyDD = maximum range from start point for "BEARING" card onlyBLAT =degree of latitude - end pointBMIN = minute of latitude -end pointBLONG = degree of longitude - end pointBLMIN =minute of loi-aitude -end point

FIGURE 13. SYNBAPSI PROFILE REQUEST CONTROL CARD

25

z zSo 0

o __j rz

zl

0.0Cooz

2126

Subroutine MINCON is called in to calculate the startingpoint for the profile within MSQLOC in minutes from the lowerleft corner. MINCON uses the function AMP to calculate themeridional parts for the latitude component. The mathematicalfoundation for AMP is given in Thomas (1964) and in U.S. NavalOceanographic Office (1962).

Subroutine RHUMB is called in to calculate, using AMP, therhumb line bearing through the MSQLOC area. A rhumb line isused here because the subroutine BATHY can only interpolatealong a straight line. The rhumb line approximates a chord ofthe great-circle path cna Mercator chart with the maximum deviationfrom the great circle at the approximate midpoint of that chordin the MSQLOC area. This deviation varies from zero to amaximum of about two nautical miles depending upon the great-circle path orientation. Maximum deviations occur in east-westpaths in high latitudes, but are considered a necessary trade-off for the system's overall speed of operation.

The random-access storage device is queried by the subroutineLOOKUP, which passes through the SYNTABLE to find the file keyand the relative address of the MSQLOC area, then extracts theactual block size and the column and row information. Theseparameters are used by the subroutine BATHY to extract griddedbathymetric data for the MSQLOC area.

From subroutine BATHY the subroutine GRIDBLK calls in thegridded data. Subroutine BATHY determines which quadrant therhumb line will pass through so as to maximize the number ofintersections for interpolation. This quadrant will determinewhether or not the columns or the rows will be the independentvariable for tl"1 cubic spline. The quadrant arrangement isshown in figure 15.

If the rhumb line falls in quadrants 2 or 4, the directionof the first interpolation is along a column and the independentvariable is the distance from the origin along the column to theintersection of the rhumb line. If the rhumb line falls inquadrants 1 or 3, the interpolation will be along a row and theindependent variable then is the distance from the origin alongthe row to the intersection with the rhumb line. At the inter-section a value is interpolated by the cubic spline using thegridded data values along that column (or row) as the dependentvariable.

When all the values have been interpolated at each inter-section, the values now become the dependent variable while thedistance along the rhumb line from the start of the profilebecomes the independent variable. The cubic spline is used oncemore to interpolate the final profile values at distances

27

• I -

5' CELL

DIRECTION OF FIRSTINTERPOLATION

I I

• ~PROFILE •u

t rORIGIN

9LI,.NE..

N• sow ,1 001- 1-.

/ ~3_ _....._ _ I _ _._

-- MSQLOC ORIGIN

FIGURE 15. QUADRANTS FOR SUBROUTINE BATHY

28

corresponding to every meridional part along the rhumb line tothe end of the MSQLOC area. An example of this rotation isgiven in figure 16. When a profile for a MSQLOC has beengenerated, BATHY calls the PUNOUT subroutine to put the MSQLOCprofile data on a temporary magnetic tape. MERFIX and AMP areused by PUNOUT to calculate the rhumb line distance in meridionalparts and set up a scaling factor. The parameters are used byPUNOUT to adjust the profile generated by BATHY, which is inmeridional parts versus depth, to a profile which shows nauticalmiles versus depth by linear interpolation. Only when theseoperations are complete is the MSQLOC profile data written onthe temporary magnetic tape and the next MSQLOC area or the nextprofile processed.

Each segment of a profile represents a single MSQLOC area.When the individual segments are written on the temporary magnetictape the depth is in the same units as in the gridded data baseand the range is in nautical miles from starting point withinthe MSQLOC area, which in each case is zero. At the end of theSYNBAPSI program the temporary magnetic tape is rewound. Theprogram SYNPLOT then reads this tape either on the same or asubsequent run. As each MSQLOC profile segment is read intoSYNPLOT it is linked in sequence to the other MSQLOC areas toproduce a great-circle profile. If geometric conversion to otherdepth units is required, it is performed at this point.

When the great-circle profile is complete, it is punchedout on cards and the profile is plotted. This process isrepeated for as many profiles as desired. Although the formatfor the punched profile cards is fixed at eight depth-versus-range points per card, the profile-plotting format is veryflexible. This flexibility is attained through a control cardfor SYNPLOT, the format for which is given in figure 17. Generally,whenever SYNBAPS1 cannot find a MSQLCC block of gridded data onthe random-access storage device or the plotting dimensions arenot set for minimal limits (fig. 17), the processing will haltat that point and skip to the next profile, allowing the job runto continue while an error message is printed out.

The profiles generated by SYNBAPS are intended as input tolong-range, acoustic propagation models. Although not necessarilyaccurate to geophysical or geodetic standards, the sytheticprofiles are interpolated to the accuracy required by the models.A depth value is interpolated at each nautical-mile point fromthe starting point to the terminus of the profile along agreat-circle path. Latitude and longitude values are roundedto the nearest minute, and the range is rounded to the nearestnautical mile.

29

N FINAL PROFILE VALUES FROMDEPTH 2ND. PASS OF CUBIC SPLINEVALUE AT 1 MERIDIONAL PART INTERVALS

N -14DEP VAR. IST. PASS INDEP. VAR. 2ND. PASSOF CUBIC SPLINE OF CUBIC SPLINE

FIUR 1. ROILE EXTRACTION F 2MNRDDE DAAPASE

INDER VAR. I ST. PASSOF CUBIC SPLINE

5' CELL

*--ORIGGIN

FIGURE 16. PROFILE EXTRACTION FROM GRIDDED DATA BASE

30

R 0 1 UNIT YLTH CONVERT

"1 11 I 21 28 31 41 ,51

100 FORMAT(2 F 10. 0, A 7, 3 X, 2 F 10. 0)

L4- z LEFT JUSTIFIED 9 =FLOATING POINT REQUIRED

R x axis scaling factor, nautical miles per inchD y axis scaling factor, meters or fathoms per inchIUNITS = label for y axis (x axis is always In nautical miles)YLTH = the total height of the y axis plot that will be displayed, the

maximum is 10 inches. This usually set as a multiple of D.Example: when plotting at 500 fathoms/inch, to'be able todisplay a profile that goes down to a depth of 4500 fathoms,YLTH would equal 9 inches. If not correctly set or if plotexceeds 13 feet on the x axis, that profile is omitted fromplotting. However, the cards are still punched.

CONVERT the data base is uncarrected for speed of sound in sea water.For fathoms the assumed standard is 800 fathoms per second, formeters it is 1500 meters per second. To convert from fathomsto meters CONVERT = 1.8750, from meters to fathoms CONVERT =0.533---3. If no conversion needed CONVERT = blank or 0.0.

FIGURE 17. SYNPLOT CONTROL CARD

31

.. |• = MW

The great-circle subroutines are based upon a sphere21,600 nm in diameter and can have a maximum error of 20 nmover a distance of 1 hemisphere (about 11,000 nm). Thisamounts to an error of about 2nm/l,OO0nm of range. F~orprofiles of 1,000 nm or less this error is insignificant inpropagation model applications, but it could be important atvery long ranges. The magnitude of this error depends uponthe difference in shape between the sphere and the oblatespheroid and on the method of path generation. Greater accuracycan be obtained by usinma geodesic where the error is 1 m inlatitude, longitude, and range and 0.035 sec. in bearing withina hemisphere (Thomas, 1965 and 1970).

Within each MSQLOC area there is a difference between thepath followed by the great circle and the actual path along whichthe depths values are interpolated (fig. 18). Because SYNBAPSilatrequires a straight line along which to interpolate depth values,a rhumb lincs between the first position entering a 5-degree squareand th n last position before leaving the square is used insteadof the curved great-circle path. For all great circles thatfollow a meridian or the equator this difference is zero. Forall other directions, the maximum difference is located at theapproximate mid-point along a rhumb line within 5-degree square.Under the most unfavorable condition of high latitude and aneast-west orientation, this difference rarely exceeds 2 nm.

Preliminary estimates of the accuracy of the interpolateddepth values in the profile plane are - 15 fm. This assumes thatthere are no positional errors in the great-circle path in thehorizontal plane. A completed data bank, including regions ofsmooth to rough topography, will be needed before full erroranalysis can be undertaken.

C. Status Program

Program SYNSTAT queries the random-access storage devicethrough the S)ýTABLE for a listing of the identification groupfrom each MSQLOC gridded daca block. This listing includes thefile key as in the following example:

ACTUAL DATE ADDED TOFILE RELATIVE BLOCK NO. OF NO. OF RANDOM-ACCESS

MSQLOC KEY ADDRESS SIZE COLUMNS ROWS DEVICE

1. 1291 E08C 50176 4704 63 74 18 April 1972

2. 1292 E08C 54880 4704 63 74 19 April 1972

All MSQLOC gridded data blocks or selected ones can be listed.They are selectable through SiNSTAT control cards as shown infigure 19.

32

MAXIMUM ERROR ATMIDPOINT ABOUI 2 N.M.

I&Iw

I-4.J

50

SQUARE

LONGITUDE

FIGURE 18. DIFFERENCE BETWEEN RHUMB LINE AND GREATCIRCLE PATH WITHIN A FiVE-DEGREE SQUARE

33

ITYPE NUM

1 8 15

10 FORMAT (A7, I 7)

L

D. CDC 3800 System Subroutines and Functions

The subroutines used to open the file, position, read, andwrite on the CDC 813 permanent disk are on-line COMPASS languageroutines provided by the Naval Research Laboratory, ResearchComputation Center Staff (Aiken,et al., 1970). These subroutinesare DKOPEN, DKLOCATE, DKREAD, and DKWRITE. The subroutine DATAis an off-line COMPASS language routine that retrieves the integerday, month, and year from the computer's internal clock (Houston,1969). The function TIMELEFT is an on-line COMPASS languageroutine that retrieves time marks from the computer's internalclock. It is used to time various phases of the structuring andaccessing programs operation (Shannon, 1968).

The )n-line plotting subroutines PLOTS, PLOT, LINE, SYMBOL,and AXIS are FORTRAN language routines. With the possibleexception of LINE and AXIS these routines are part of the standardCalcomp plotter package (Gossett, et al., pending).

Most o- the previously mentioned subroutines and functionsare unique to the NRL CDC 3800 computer system. However, theseroutines have counterparts on any large computer system, and.their replacement should pose little or no problem.

PROFILE OUTPUT

Two adjoining MSQLOC areas, 1291 and 1292, in the westernNorth Pacific Ocean were selected to test the computer programand were digitized, structured, and placed on the random-accessstorage device. The location of five test profiles along rhumblines, subsequently shown in figures 21, 22, and 23, are indexedin figure 20. The contour chart used as an index chart showsonly part of the contour data that will input to the data base;therefore, the test profiles show a slight difference in detail.Figure 21, a profile through both MSQLOC areas, shows that thelink point between two data blocks is undetectable. This 530-nmprofile was generated in 7 seconds.

In figure 22, composed of three profiles A, B, and C, adashed line is superimposed on each profile. The dashed linesare profiles hand drawn by a bathymetrist, and the solid linesare the computer profiles- All the profiles used the same database. Although the general shapes for both types of profiles arethe same, the cubic spline profiles show details between thecontour levels that would otherwise be lost if not captured by thesurface of gridded bathymetric data. This is especially true inthe more steeply sloping areas because the cubic spline considersdata adjoining the profile path. The three profiles in figure 22show the system's ability to start a profile inside a MSQLOC area.Figures 22A and 22C show profiles that terminate in gently sloping

35

;DtAOD r

I,-In

- 8-

~/ (I\ q, ~ L

36 J

FATHOMS

-j-

4-

(0 0

1

~ § -\ SHATSKIY RISE

(A) _

N oSN

-7NSHATSKIY RISE

wE

SHATSKIY RISE -

(C)__ _ _ _ _ _ _

FIGURE 22. CUWIC SPLINE VS MANUAL PROFILES

38

FATHOMSo 1000 20= 00 40

IEz

LU.

> z00 LU

LiLLjU

I-U-

zz

o 100,0 2=0 3= 00

O0

3z

00 0W-

U,-

20Mmw3=40

FATHO0

-39

areas, and figure 22B shows a profile terminating on the upslopeside of a seamount in the next area to the north. Figures 22Band 22C show that the cubic spline can follow both convex andconcave submarine topography equally well.

Figure 23 shows two mirrx-image profiles, which illustratethe profile repeatability along the same path in either direction.Profile A was run from west to east, then profile B was run fromeast to west, both along the same path.

FURTHER MODIFICATIONS, ADDITIONS AND OTHER APPLICATIONS

The first modification to SYNBAPS will replace the great-circle subroutines, GCPATH and GCDIST, in the accessing phasewith geodesic subroutines, GEODIST and GEOPATH. The argumentlist for the new routines will be the same as for the greatcircle routines. The second modification will replace the contourchecking program, SYNCON2R, in the structuring phase with asmoother contour plotting program. A third modification willattempt to increase the overall efficiency (speed of operation)by simplifying the programs. One example is to use bufferingstatements when writing and reading on the temporary magnetictape.

An additional program to operate on the SYNBAPS output willbe an updated automatic depth correction routine based onMatthews' sound velocity correction tables. This will permitthe use of depth values either corrected or uncorrected forspeed of sound in sea water.

An additional version of SYNBAPS1, the accessing program,called SYNBAPS2 is be'ng considered. This program will generateeight radial profiles simultaneously from one point to the edgeof a MSQLOC area or an irregular chart area. This output couldbe useful for profile evaluation of site locations where greaterdetail is required. In addition, SYNBAPS1 can be merged with theNODC Ocean Station Data file to produce a composite plot of thebottom profile and selected sound velocity profiles along agreat-circle path. Extending this concept one more step willproduce profile plots of various acoustic environmental parameters,such as depth to the axis or bottom of the deep sound channel, bymarrying SYNBAPS to an appropriate oceanographic data file orfiles. The number of possible combinations of oceanographic datawith the depth data using SYNBAPS is almost infinite.

A system similar to SYNBAPS, but using land topography,could be applied in radar terrain studies and weather patternmodels requiring elevation data.

40

SUMMARY AND CONCLUSIONS

The SYNBAPS data base was designed to meet the specificand immediatu need for bathymetric profiles for acousticmodeling. However, properly used, it offers many applicationsbeyond its preliminary designs.

Often in naval planning as well as in naval operations,

speed is as important as accuracy when information is needed.SYNBAPS is not ideally suited to hydrographic charting becausesome high-frequency information is lost, but it provides veryrapid responses. SYNBAPS has these additional features:

* Only data points are stored in the data bank,

* The locations of data points are logically structuredon a Mercator projection by 5-minute intersections,

* Random access to the data is by large blocks (5-degree square),

* The data bank is updated by replacing blocks of data,

* The size of the data bank is fixed once it has beencreated for any ocean area,

* Classified survey data, in chart form, can be incor-porated in the data base with no compromise ofsecurity,

a Highly compacted forms of the accessing program andthe data bank can be used on shipboard.

41

LIST OF REFERENCES

Aiken, E.L., Denton, D.L., and Shannon, D.P., 1970, 813 diskfile subroutine package: U.S. Naval Research LaboratoryMemorandum Report 2104 or Computer Bulletin 19, Washington,D.C.

Chang, D., 1969A, A FORTRAN subroutine for locations and bearingsat given distances from a starting point along a great circlepath: U.S. Naval Research Laboratory Computer Note 33,Washington, D.C.

, 1969B, A FORTRAN subroutine for the great circle distancebetween two points and bearings at the points: U.S. NavalResearch Laboratory Computer Note 32, Washington, D.C.

Davis, T.M. and Kontis, A.L., 1970, Spline interpolation algorithmsfor track-type survey data with application to the computationof mean gravity anomalies: U.S. Naval Oceanographic Office,Technical Report 226, Washington, D.C.

Gossett, D.E., Hill, S.L., Houston, J..H., Kroesh, J., Rogers,G.H., Ulrich, J.T., and Williams, M., (pending): 3800 Calcompplotter subroutine package, U.S. Naval Research LaboratoryMemorandum Report or Computer Bulletin 3, Washington, D.C.

Houston, J.H., 1969, 3800 Computer integer date request subroutine:U.S. Naval Research Laboratory Memorandum Report 2008 orComputer Bulletin 10 Washington, D.C.

Thozanski, T.L., Burgess, J.G., Gossett, D.E., and Shannon, D.P.,1968, Computer utility program: U.S. Naval Research LaboratoryMemorandum Report 1935 or Computer Bulletin 1, Washington, D.C.

Shannon, D.P., 1968, 3800 Computer timeleft function: U.S. NavalResearch Laboratory Computer Note 5, Washington, D.C.

Thomas, P.D., 1964, Conformal projections in geodesy and carto-graphy: U.S. Dept. of Commerce, Coast and Geodetic Survey,Special Pub. No. 251, 4th edition, 142 p., Washington, D.C.

,_ October 1965, Mathematical models for navigation systems:U.S. Naval Oceanographic Office, Technical Report 182,including figures and tables, 142 p., Washington, D.C.

1970, Sdreroidal geodesics, reference systems, and localgeometry: U.S. Naval Oceanographic Office, Special Pub.No. 138, 165 p., Washington, D.C.

42

L... . .: . p. , , : ~ l II I I I I I

U.S. Naval Oceanographic Office, 1962, Tables from AmericanPractical Navigator Bowditch: U.S. Naval OceanographicOffice, H.O. Pub. No. 9 Tables, Washington, D.C.

U.S. Naval Oceanographic Office, 1969, Bathymetric atlas of thenorthwestern Pacific Ocean, U.S. Naval Oceanographic Office,H.O. Pub. No. 1301, Washington, D.C.

U.S. Naval Oceanographic Office, 1971A, Bathymetric atlas of thenorthcentral Pacific Ocean, U.S. Naval Oceanographic Office,H.W. Pub. No. 1302, Washington, D.C.

U.S. Naval Oceanographic Office, 1971B, Bathymetric atlas of thenortheastern Pacific Ocean, U.S. Naval Oceanographic Office,H.O. Pub. No. 1303, Washington, D.C.

43

BIBLIOGRAPHY

American Standards Association, 1966, USA Standard vocabularyfor information processing, X3.12 - 1966, United States ofAmerica Standards Institute, New York, N.Y.

Baker, B.B., Jr., Deebel, W.R., Geisenderfer, R.D., Editors,1966, Glossary of oceanographic terms: U.S. Naval Oceano-graphic Office, Special Pub. No. 35, 2nd edition, Washington,D.C.

Bhattacharyya, B.K., 1966, BiLcubic spline interpolation as amethod for treatment of potential field data: Geophysics,v. 34, p. 402-423.

Grim, P.J., Keller, G.E., and Barday, R.J., 1972, Computerproduced profiles of micro-topography as a supplement tocontour maps: International Hydiographic Review, v. 49 (1),

___1968, Initialization for the 3800 Calcomp plotter package:U.S. Naval Research Laboratory Computer Note 10, Washington,D.C.

Hunt, L.M., and Groves, D.G., Editors, 1965, A glossary of oceanscience and undersea technology terms, Compass Publication,Inc., Arlington, VA.

Pennington, R.d., 1965, Introductory computer methods and numericalanalysis: The Macmillan Co., New York.

U.S. Army topographic Command, 1969, DOD glossary of mapping,charting, and geodetic terms: 2nd edition, prepared for Dept.of Defense by Dept. of the Army, Corps of Engineers, U.S.Army Topographic Command, Washington, D.C.

44

GLOSSARY OF SELECTED TERMS

Accuracy The degree of freedom from error, thatis, the degree of conformity to truthor to a rule. Accuracy is contrastedwith precision, e.g., four-placenumerals are less precise thansix-place numerals; nevertheless aproperly computed four-place numeralmight be more accurate than animproperly computed six-place numeral.

Address (1) An identification, as representedby a name, label, or number, for aregister, location in storagn., or anyother data source or destination suchas the location of a station in acommunication network. (2) Loosely,any part of an instruction thatspecifies the location of an operandfor the instruction.

Algorithm A finite set of rules that gives asequence of operations for solving aspecific type of problem. It shouldhave the following features,(1) Finiteness, (2) Definiteness,(3) Input, (4) output, and(5) Effectiveness.

Alphanumeric Pertaining to a character set thatcontains both lettý.,rs arid numerals,and usually other characters.Synonymous with Alphameric.

Arleument list List of the formal parameters of asubprogram used as an explicittransfer of information to or from asubprogram.

Band (Latitudinal (and) Any latitudinal strip, designated by"accepted units of linear or angularmeasurement, which circumscribesthe earth.

Bathymetric Relating to the measurement ofocean depths.

Bathymetric chart A topographic map of the floor ofthe ocean.

45

Bathymetry The science of determining andinterpreting ocean depths andtopography.

Bearing 1. (general.) The horizontal angle ata given point measured clockwisefrom a specific reference datum to asecond point. Also called bearingangle.2. (navigational) The horizontaldirection of one terrestrial pointfrom another, expressed as theangular distance from a referencedirection. It is usually measuredfrom 000' at the reference directionclockwise through 3600. The terms,bearing and azimuth are sometimes usedinterchangeably, but in navigationthe former customarily applies toterrestrial objects an- the latter tothe direction of a point on thecelestial sphere trow. a point on theearth

Binary (1) Pertaining to a characteristic orproperty involving a selection,choice, or condition in which thereare two possibilities. (2) per-taining to the numeration system witha radix of two.

Binary Coded Decimal Pertaining to a decimal notation in(BCD) which the individual decimal digits

are each represented by a group ofbinary digits, e.g., in the 8-4-2-1binary coded decimal notation, thenumber 23 is represented as 0020 0011,whereas in binary notation, 23 isrepresented as 10111.

Block A set of things, such as words,characters, or digits, handled asa unit.

Block diagram A diagram of a system, instrument,computer, or program in which selectedportions are represented by annotatedboxes and interconnecting lines.

46

Cartesian coordinates Values representing the location of apoint in a plane in relation to twointersecting straight lines, calledaxes. The point is located bymeasuring its distance from each axisalong a parallel to the other axis.If the axes are perpendicular to eachother, the coordinates are rectangular;if not perpendicular, they are obliquecoordinates. This system is extendedto represent the location of points inthree-.limensional space by referencingto three mutually perpendic:ilarcoordinate axes which intersect at acommon point of origin.

COMMON Is a specification statement, usedduring compilation rather thanexecution as a convenient method forpassing values between main programand subprograms without mentioningthem as arguments.

COMPASS Control Data Corporation assemblylanguage for CDC 3000- and 6000-series computers.

DAT?. Is a specification statement, usedduring compilation rather thanexecution as a convenient method' forentering data value into referencedstorage areas.

Data Any representations such as charactersor analog quantities to which meaningmight be assigned.

Deck A collection of punched cards.

Dependent variable A fixed variable given as a functionof another variable, i.e., if y isgiven as a function of x, then, y isthe dependent variable.

Digitize (1) The conversion of graphical analoginformation or characters into digitalform, usually for the purpose of rapidmanipulation or storage by a digitalcomputer (2) to express data in adigital form.

47

Field In a record, a specified area usedfor a particular category of data,e.g., a group of card columns used torepresent a wage rate or a set of bitlocations in a computer word used toexpress the address of the operand.

File A collection of related recordstreated as a unit. Thus in inventorycontrol, one line of an invoice formsan item, a complete invoice forms arecord, and the complete set of suchrecords forms a file.

Fixed point Pertaining to a numeration system inwhich the position of" the point isfixed with respect to one end cf thenumerals, according to some convention.

Floating point Pertaining to a numeration system inwhich the position of the point doesnot remain fixed with respect to oneend of the numerals.

Flowchart A graphical representation for thedefinition, analysis, or solution of aproblem, in which symbols are used torepresent operations, data, flow andequipment.

Geodesic A line of shortest distance betweenany two points on any mathematicallydefined surface. A gecdesic line is aline of double curvature, and usuallylies between the two normal sectionlines which the two points determine.If the two terminal points are innearly the same latitude, the geodesicline may cross one of the normalsection lines. It should be notedthat, except along the equator andalong the meridians, the geodesic lineis not a plane curve and cannot besighted over directly. However, forconventional triangulation the lengthsand directions of geodesic linesdiffer inappreciably from corre-sponding pairs of normal sectionlines. Also called geodesic line;geodetic line.

48

Great circle A circle on the surface of the earth,the plane of which passes through thecenter of the earth.

Header card The first card or cards of a deck ofpunched cards containing identifi-cation of fixed information about thepunched cards of variable data thatfollow.

Independent variable A variable whose assigned value(s) arearbitrary when defined as a functionof another variable, i.e., if y isgiven as a function of x, then, x isthe independent variable.

Input (1) The data to be processed. (2) Thestage or sequence of states occurringon a specified input channel. (3) Thedevice or collective set of devicesused for bringing data into anotherdevice. (4) A channel for impressinga state on a device or logic element.(5) The process of transferring datafrom an external storage to aninternal storage.

Interpolation To determine intermedi•t• valuesbetween given fixed values. Asapplied to logical contouring tointerpolate is to ratio verticaldistances between given spot -levations.

Look-up table An index file or array(s) which isusually used to access a main recordfile. It contains the identifier (orfile key) and the storage address insequential or non-sequential order.It may also contain critical infor-mation.

MARSDEN chart A system introduced by Marsden earlyin the nineteenth century for showingthe distribution of meteorologicaldata on a chart; especially over theoceans. A Mercator map projection isused; the world between 90*l" and 80*Sbeing divided into Marsden "squares"each of 100 latitude by 100 longitude.

49

MARSDEN chart (Con.) These squares are systematicallynumbered to indicate position. Eachsquare may be divided into quartersquares, or into 100 10 subsquaresnumbered from 00 to 99 to give theposition to the nearest degree.

Mercator projection A conformal map projection of thecylindrical type. The equator isrepresented by a straight line true toscale; the geographic meridians arerepresented by parallel straightlines perpendicular to the linerepresenting the equator; they arespaced according to their distanceapart at the equator. The geographicparallels are represented by a secondsystem of straight lines perpendicularto the family of lines representingthe meridians and therefore parallelwith the equator. Conformability isachieved by mathematical analysis,the spacing of the parallels beingincreased with increasing distancefrom the equator to conform with theexpanding scale along the parallelsresulting from the meridians beingcepresented by parallel lines. Alsocalled equatorial cylindricalorthomorphic map projection.

Merge To combine two or more sets of itemsinto one, usually in a specifiedsequence.

Meridional part The length of the arc of a meridianbetween the equator and a givenparallel on a Mercator chart, ex-pressed in units of one minute oflongitude at the equator.

Offline Pertaining to equipment of devices notunder direct control of the centralprocessing unit.

Online Pertaining to equipment or devicesunder direct control of the centralprocessing unit.

50

~--~ ,~ - ---- - - - - --

sz:oraý. !-o an ex~ternal stor-age.

"" .' "2.Z n t - .h• * i2s se t es_. a

A .-ert. ical I sect ion of sur face ofthe ground, or r.,-e underlying s-trata,or both, along any fixed line.

rfir;3m Icit '."he smallest field (group) cI. uniquecontiguous characters or digits.

IPUrJOIh(' Cards (1) A card punched with a pattern ofholes to represent data. (2) A cardas in (1) before being punched.

P~ad ixA quantity whose successiveintegral powers are the implicit,Aultipliers of the sequence of digitsthat represent a number. For exampleif the radix is 5, then 143.2 means1 times 5 to the second power, plus4 times 5 to the first power, plus 3times 5 to the zero power, plus 2times 5 to the minus one power.

Random access (1) Pertaining to the process ofobtaining data from, or placing datainto, storage where the time requiredfor such access is independent of thelocation of the data most recentlyobtained or placed in storage. (2)Pertaining to a storage device inwhich the access time is effectivelyindependent of the location of thedata.

51

Real Time (1) Pertaining to the actual timeduring which a physical processtranspires. (2) Pertaining to theperformance of a computation duringthe actual time that the relatedphysical process transpires in orderthat results of the computation can beused in guiding the physical process.

Relative address Identifies a word in a subroutine orarray with respect to its position.Relative addresses are translatedinto absolute addresses by theaddition of some specific referenceaddress, usually that at which thefirst word of the routine or arrayis -tored.

Rhumb line A line of the surface of the earthmaking the same angle with allmeridians; a loxodrome or loxodromiccurve spiraling toward the poles in aconstant true direction. Parallelsand meridians, which also maintainconstant true directions, may beconsidered special cases of the rhumbline. A rhumb line is a straight lineon a Mercator projection. Also calledequiangular spiral; loxodrome, loxo-dromic curve; Mercator track.

Round off To delete the least significant digitor digits of a numeral and to adjustthe part retained in accordance withsome rule.

Routine A set of instructions arranged inproper sequence to cause a computer toperform a desired task.

Selection overlay A tracing of selected map sourcedetail compiled on transparentmaterial; usually described by thename of the features or detailsdepicted, such as contour overlay,vegetation overlay. Also called lift;pull up; trace.

Storage (1) Pertaining to a device into whichdata can be entered, in which it can

52

Storage (Con.) be held, and from which it can beretrieved at a later time. (2)Loosely, any device that can storedata. (3) Synonymous with Memory.

Synthetic Produced artifically; devised,arranged, or fabricated for specialsituations to imitate or replaceusual realities.

53

LIST OF ACRONYMS USED IN COMPUTER PROGRAMS

AMP- Function used in MINCON, MERFIX andRHUMB to calculate meridional partsfor the latitude component.

AXIS- Calcomp plotter subroutine toautomatically scale and draw axes.

BATHY- Subroutine which determines whichquadrant the rhumb line will passthrough, extracts the gridded dataand calculates the profile for eachMSQLOC area.

BURNS- See SYNCON2R

CALMA 485- (1) A large bed, graphical analogdigitizer manufactured by the CALMACorporation.(2) A processor program for (1) thatinitially scales the synthetic trankfrom charts.

CDC- Control Data Corporation

DATE- COMPASS off-line subroutine whichautomatically calculates an integerday, month, year from the computer'sinterval clock.

DAWHAT- See SYNCHEX

DKLOCATE- Subroutine which positions read/writehead at specified relative address.

DKOPEN- Subroutine which opens disk file.

DKREAD- Subroutine which reads blocks of datafrom the disk file in groups of 32words or larger.

DKWRITE- Subroutine which writes blocks ofdata on to disk file in groups of 32words or larger.

GCDIST- Subroutine used by SEAARCH for directsolution of the great circle.

55

Preceding page blank

GCPATH- Subroutine used by SEAARCH for indirectsolution of the great circle.

GEODIST- Subroutine for the direct solution ofthe geodesic.

GEOPATH- Subroutine for the indirect solutionof the geodesic.

GRIDBLK- Subroutine which calls in the griddeddata from the random access storagedevice for BATHY.

LOOKUP- Subroutine which "looks up" or extractsthe relative address, block size andthe column and row information for eachMSQLOC area from the random accessstorage device previous to passing thisinformation to BATHY.

LINE- Calcomp plotter subroutine to automati-cally draw a line as a function ofx and y.

MERFIX- Subroutine which calculates the rhumbline distance and sets up a scalingfactor for nautical miles along aprofile.

MINCON- Subroutine used to calculate the startpoint for a profile within a MSQLOCarea.

MSQFQ- Subroutine used to calculate in partthe MSQLOC area numbers for points onthe profile path.

MSQLOC- Marsden Square Locator Number (Marsdensquare system is a numbered, 10 degreerectangular grid of the world which issubdivided further into 5 and 1 degreesquares).

PLOT- Calcomp plotter subroutine which movespen in x and y direction.

PLOTS- Calcomp plotter subroutine whichinitiates plotter action.

PUNOUT- Subroutine which places each MSQLOCarea profile on magnetic tape.

56

RHUMB- Subroutine using AMP to compute therhumb line (approximation of a chordof a great circle on a Mercator pro-jection) bearing through an MSQLOCarea.

SEAARCH- Subroutine used to generate a great-circle path.

SPLICO.4- Subroutine used by SPLINE for cabicspline calculations.

SPLINE- Subroutine for the cubic splinealgor-ithro.

SPLINT- See SYNGRID

SYMBOL- Calcomp plotter subroutine which plutsalphanumeric characters and symbols.

SYNBAPS- Synthetic Bathymetric Profiling System.

SYNBAPSI- Accessing program which produces adepth range profile on uagnetic tapefor each MSQLOC area.

SYNBLOCK- Program which loads gridded bathymnetricdata into the random access storagedevice.

SYNCARD- Program which checks longitude of datapoints and depth values.

SYNCHEX- Program which track plots data pointson a Mercator projection at the scaleof the source manuscript.

SYNCON2R- Program which plots contours of thegridded data on a Mercator projectionat the scale of the source manuscript.

SYNGRID- Program which transforms synthetictrack line data into gridded bathy-metric data at seven points per card.This is the primary structuringprogram.

SYNPLOT- Accessing program which links togetherthe profiles on magnetic tape producedby SYNBAPSI for each MSQLOC area to plota great circle profile. This program isusually run linked to SY7BAPSi.

57

SYNSTAT- Status program which queries randomaccess storage device for listing offile key, relative address, blocksize, number of rows and columns anddate that data were added to storageand/or actual gridded data.

SYNTABLE- Traffic director program which suppliesrelative address, block size and filekey to SYNBLOCK for the accurate place-ment of blocks of gridded bathymetricdata on the random access storage device.

SYNTRACK- Progrm which outputs header, track,data ardA blank cards and conductserror checks. Input is a scaled datatape from the CALMA 485- processorprogram.

TIMELEFT- COMPASS on-line function which extendstime mark from computer's intervalclock.

UTILITY- Systems program which loads griddedbathymetric data cards on mangetictape.

58

APPENDIX A

Preparation of Charts for Digitization

The 5-degree square unit, around which the data base iscreated, has been explained in the "Outline of the System" andin figure 3, 4, 5, and 6. Paper copies of the contour charts,which are on a Mercator projection, are used to prepare thebasic manuscripts for digitizing. Sufficient overlap aroundeach 5-degree square is required to provide 5 minutes on allsides for the MSQLOC area and an additional 5 minutes on allsides for interpolation of the track input data (fig. 6): Themanuscript size is then at least 320 minutes by 320 minutesregardless of the chart scale. Ideally, the manuscriot shoulCconsist of one easy-to-handle document. However, because chartformats vary, this is not always nossibhe. A case in point isthe addition of large scale survey of a newly discovered searm1ountto a regional chart.

One method of handling this is to digitize the two chartsseparately, then, substitute the synthetic tracks from the newseamount chart for those in the corresponding section of theolder regional chart. A second method is to prepare a contourselection overlay for the seamount chart, photographically reduceit to the scale of the regional chart, make a print at that scale,attach the print to the regional chart and match the contours.This method also can be used with transparent media.

The smallest cell selected for SYNBAPS is a 5-minute (meridionalpart) square with a depth value at the four corner intersections.The s,'nthetic tracks of input depth points are usually taken at a5-minute spacing on a Mercator projection. In high frequency dataareas, additional tracks of data at l-, 2-, 3-,or 4-minute spacingcan be input so as to improve the four cell depth values. However,there is a limit to how much improvement can be made withoutlosing some of the high-frequency detail. One improvement woulduse a smaller cell size, but this makes random-access storage devicedata storage requirements very large. Thus, small features thatfall within a 5-degree cell can be lost to the data base,especially if they are not picked up at the input or structuringphase.

It is necessary to interpolate the beginning and end pointsfor each track in the overlap areas. This is not a requirementfor short tracks within the body of the MSQLOC area. Thesepoints may be visually interpolated by the analyst or by anexperienced digitizer operator. This interpolation need onlybe to the nearest 20 fathoms or about one-tenth the contourinterval.

A-1

The output from the SYNCON2R program is a contour plot ofthe MSQLOC area. Although this output is not a primary productof the system, it is used for checking and may be a usefulbyproduct as rough automated contours. Because of the 5-minutecell size and the nature of the interpolation scheme, largeflat areas tend to break up on the contour plot. This break upof contours is not an error in the data and does not affectthe profile generation. To improve the contour output aesthe-tically, the interpolation can be improved by adding contoursin key locations. In areas of rough topography this improvementwill not be necessary. The first example, around seamounts ora seamount group, is shown in figure A-I. Usually the addedcontour is placed outside the base contour to cutoff or terminatethe interpolation adjoining a fl..t area or to define the sea-mount base. The second example is for domes, rises, ridges ortablemounts (fig. A-2). Here the added contours are on the topof the structure in order to cutoff or terminate the interpolationon their flat or gently rounded summits. The third example isfor noses or spurs (fig. A-3). Although this feature is similarto those in figures A-1 and A-2, short disconnected contours maybe needed if the spur slopes are gentle. In all these examples,the track direction was assumed to be left to right.

The boundary condition is a special case of endpoint inter-polation. Whenever an island or continent is encountered, theze;ro contour or sea level is handled as shown in figure A-4.On the SYNCON2R program the zero-contour level should never beplotted, but the 1-fathom or 1-meter contour should be inter-polated to show the coast line. In profiling, the punched carddepth values after the first zero usually are discarded and theprofile terminated at that range.

A-2

____ 4--ADDED CONTOUR

9000

~ 04

CONTD OUR U--h

FIGURE~~~~~~~ A-I.f AD E ON O R O N E M O N S O

SEAMOUT GROU

A-31

S AUDED CONTOUR

//

0oo

ADDED CONTOUR

FIGURE A-2. ADDED CONTOURS ON DOMES OR RISES

A-4

&-ADDED CONTOUR

FIGURE A-3. ADDED CONTOURS AROUND A SPUR

A-5

TRACK

LLAN

100O AE

ALAN

APPENDIX B

FORTRAN Programs for

Structuring SYNBAPS

All programs and subroutines listed in this appendix aresubject to change without notice. Modifications within theprograms and adoption of the system for other computers willnecessitate major changes. The author should be contacted forthe most recent versions oc these progra ..

B-I

z

0

_j4g

z 0

a 7

z mo- 0 U) 3r0"I- -ZO 0 x 0

>- t -ow'490 ot4-0- 0. 0i0 $ 3- 0 P- w U40

0.3- co Id uU) -O

c* C~0r 0 O 0 x de

4*4L0 0 0 Wr4 * Z.- -Mtn 0-W .x

0* 03E0U1-- - C r0 z u4

ODCr* '49 - W - W 1AIt le~ 49 01 X c (A 0 C

U0* .4) 0 z I. (A Id

49 Am"0 Q) *:ý 4 0 4L >-zx 7Z* O ý u ý 0 1.-- 0 1.-

.j 0* S49Il 0 0 49 z CL423 OZ W -1 0 LA - -- w* 4&.J W1 01 Cr c r Z i a c i

x 4* ilJz I- W cc tin 1. 0xr) (O* IA 4. )- W 1- -j I- 11W 0 )-aW

u ZZ W 41Z z.1 - in o;- XX0 W AW O 4cuxU w .o 1 0 .- 0. coZ3- -_

0 >-4 0L Z0 4 .4 z-z -40 M .o- ZLI Ij cW 4 D t A- C 0 Xd 0, 30 X= 0 aU) 4x U) 4r 0. ez C 0--t -Cfw 4- ) _-. Cy

0 CDO3 X 1.- 01-04 04a 011- 8I.13- P a- O- 4 I- *L CU4W ZC)- 1-

Vr 40 41 V) m M- &-0C M 4COr V LF W( I- 1.-.43-. 0)- P.Z V3WWl- 4X4Z C--- .Z mu.4 z O

0 x 49 C a ">> Id W IL - W.- &L WXC =.-C NCL 0 - WrI ar 1--Y-DI 03-4 M'U C4 -CW.-4.4 3*

3, - C4 k- C Z U) 490 =-( i--'- .9 A M40 9 0 49 a1 CL crE'I3b4~~3 M- mt r)

00 0010 0 u4 UU U jv V

0 Ob-Cr3- 0 ~' Cr B-2--r C'~L C'Ca0. .

z4 x

241 CLW0-U) U) *

CL - 0.

cr 0r

W49. LIJ&2 w

(n 0 LX0. 0-4 *u

_j W0. 4QcIL L xu ý

LL. (X Z4C O N-00-4

"* ZOD% 1.- 6.-00( X0I~ 003

-4 I -i- 4 *0.O- in.

x 440 1

z 0 IL Z k. U n

Oka Cl 0.0 X4 Z-0. 0- 00.vZ -4 4a * 0 f. O I.- j ~4I-- D UMf0% X' 0 3c a P LjIF a r Iw

04 -U 0 1-0 x Z f- 0- D ý 1 0- 0.. 1--* of V-0_j90 0

XI Z M o I.5- - o Zrb *-0xZ Z X I.IaX0

IA.0C

cD u

-w w 1-I-

0' 7 0 C 00% D z 40

x zw x OZ td

IM- LIa. m M'i CD* -WS.- 0 C

x 0 440 0.--L U) WI f~ i Iii

X Z* ui 4w - I) 0 Z

4mr Ir I Ix.5 A S J 04 _ xz

I.- 4 40t U-l .. Z-E 0 ( 0ýW ~ >.- 41C U) _j 31CS- Cin-

> ~ W 30 0W-~4I' J4Ix I.Zn C - Si. z 00' of.a

CD D0 =)z00 0 .W..- 4 0 -4 CL.1- 1- 0.N * z 4ix

a 4 D -. .- Z hOb U) .4 80 or4(* 1 2 4- - 4 .4 -COS(Z 4C z *4c ULZ s

0- 8-0 -Zi -) 44 8- 8- Z- MJ %a *- U.

LL. c -ao 0 0-a w- aJ -E-0o 4 xv £ t-- a. _WOIij 4w .- CrA 0TI.-U m i- I-A 4 Nw X Lo XOl Z. N -' 0 cc C 0C

U)4I M 0 wX -_ '0- .4 -M It D 0Cr - W U -9 . aI-- z 0 N

ca qx x 4 j*= 904 C

-- Or M X -t- B-4*- X

w 41

k w

V) 0

o M4-1 0 W

-j VC -4

OD V) 0 S

U) (1 0l* Ll all) 4)

z IhJ'0 z0.i4 0 CD 4 I W-3 ? * I- z

z *.-OX Z 9

-4 0* II.-4 - -

0C >.* OI0 91 - 1 -3-, 1- 44 .9- 41 . 0 . 4 f

LL 1-) =) 1- j- .Z IL ZwJ W z Lw = k"O I.- 4 WO In " - -q

0 D- 0 w 0 W U.40 -4+. 11) c0 41 4+ 3 T U3b *1 _j ;- I..

> 4* CC 1.C) Z I9- 1. 4W 14 8C <4 z ZW i&- - V42 -

z t-4 2I I-"-' z I..I4z-0 1.-* -: 1ý 0 w w " - a 4 O.- 0 )C, ý

-S 6- ZO.

0

-JoD

31CC

£3 4 -1.43 OC 0 u3- I CL fu W

CD 0 m

z0 0n x

CL w

a U 0 (D

z~z wo 0

Efl3-a u )tJ Ac

ZX 0- 4* 0 4a zr

0 0c *. 40

m- 00 u ;a- ,w o- x

0 L

Mir V-4 0 13- a -

4x 0 no -'a 0 0*k

0 )p 0 W . QU)

CL Cn 4 3-L tU) V- 0) WO 0MU ~ ~ ~ .4C %0 ý-4. "ft

so ZOW 0 3 'IaJ - Z -j*.- 'I.- 7.T _ JI -jX

U) ~~ ~L I- , U)+ (A 1- 0 X-4

'-'p W f&tL1 2C

LL7= y 141f 9- aj LL- OtL t- L

ft0 4 f 04 ON N-i r - - 40

B-6

a,.

T 0 0 0 j

U& f- -1)-0SC -0 - X

LCL 0 x* CD x $-

%"Ec L -j -1 -

I-' 4-u 0 0.0 0,4

I-~~~ -,-31-*0 .

in -l 0 c0 0. -. =r

41 0. ( 02 :0 21

0 Vo w fu ZO ZU-3 0- 4 0 0.1- m -,1 49

U) -J CD) ft" 4%tAt- CD Om O m 0 ) ) 0 -)&a VD v 0 40- (M I- I 1-cM.1 1P * I0 x - -Cc 0 04&0 00

M4- 4 4 -im -j m~ Zb4Cg - t- *c So Ix) 0- 4 0~ "

wD -- x P. wx **OW) 0 Jt * w a *# 0 A ~ cc