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A ~STRAL MODEL1v

VOLUME II:

SOFTWAARE IMPLEMENTATION

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THE ASTRAL MODEL Distry, tiw/

VOLUME II: Availability Codes

SOFTWARE IMPLEMENTATION Awailan~d/orDist

"peoia

I SAI-79-743-WA

ON • January 1979

Prepared by:

Science Applications, Inc.

L, S. Blumen

3 C. W, Spofford

Prepared for:

Long Range Acoustic Propagation Project

NORDA Code 600

NSTL Station, Mississippi

Prepared Under Contract No. N00014-77-C-0502

I SCIENCE APPLICATIONS, INC.

8400 Westpark Drive, McLean, Virginia 22101Telephone 703/821-4300

S 29082-21227 'Id_9 0 8i•i•F:• •

I

U CONTENTS

Page

1 1 INTRODUCTION 1-1

BASIC MODEL DESCRIPTION 2-1

2.! r-1ogram DRIVER 2-6

2.1.1 Subroutine ENVIN 2-92.1.2 Subroutine PARIN 2-102 1.3 Subroutine RCVIN 2-112.1.4 Subroutine TRAKIN 2-122 1..5 Subroutine TLOUT 2-13

2.2 Subroutine ASEPTL 2-142.2.1 Subroutine INITAL 2-162.2.2 Subroutine RCVR 2-182.2.3 Subroutine COMPSI 2-20

2.2.3.3 Subroutine PSIRCY 2-22

S2.2.3.2 Subroutine SURLOS 2-232.2.3.3 Subroutine EIGEN 2-24

2.2.3.3.1 Function HUP 2-262.2.3.3.2 Function HDN 2-302.2.3.3.3 Function AIRY 2-31

2.2.4 Subroutine SECTON 2-332.2.4.1 Subroutine TRACE 2-342.2.4.2 Subroutine PERIOD 2-362.2.4.3 Function BTMLOS 2-372.2.4.4 Subroutine NEWMOD 2-37

2.2.5 Subroutine SLOPE 2-382.2.6 Subroutine AMPDP 2-392.2.7 Subroutine MARCH 2-40

2.2.7.1 Subroutine COMPDW 2-422.2.7.1.1 Subroutine

DELPSI 2-432.2.7.1.2 Subroutine

COUPLE 2-44

2.2.7.2 Function NEWDW 2-442.2.7.3 Function NEWBC 2-452.2.7.4 Subroutine PHIBL 2-452.2.7.5 Subroutine RCOMP 2- 162.2.7.6 Subroutine DBTOIN 2-472.2.7.7 Subroutine INTSUM 2-472.2.7.8 Function DONE 2-48

I

II

CONTENTS (Cont.)

Page

1 2.2.8 Subroutine TLFINT 2-492.2.9 Subroutine SMOOTH 2-50

I 3 INPUT AND OUTPUT 3-13.1 Stand-Alone I/O 3-1

3.1.1 Input 3-13.1.2 Output 3-6

3.2 ASEPS I/O 3-16

3.3 Suspended Receiver Option 3-27

REFERENCES R-1

UIII!IIIUI

I!i

II

Section 1

Introduction

I This volume documents the computer code of the

ASTRAL model whose physics and supporting mathematics are

described in Volume I.* The purpose of this volume is to

provide a bridge between the physics/mathematics of the model

and the computer listing of the code. Section 2 describes

the overall program flow and the functions of each of the

routines. Section 3 describes the program input and output

with examples.

I This model was designed to be both a stand-alone

model with its own driver controlling input and output as

well as a callable subroutine whose input and output are

handled entirely through common blocks. To avoid recomputing

certain water-mass and near-field bathymetry information,some parameters, once computed, are saved for subsequent

3 tracks in common blocks which must be made available in

subsequent calls by use-ts of the subroutine capability.

I .Details of this dual approach are also contained in Section 3.

3 Spofford (1978).

I-

II

I Section 2

Basic Model Description

The following subsections delineate the individual

components of the ASTRAL model. The program can be concep-

tualized as a multi-leveled structure (Figure 2-1). The

outer level, which is driven by routine DRIVER, consists of

all parametri'.c input routines (ENVIN, PARIN, TRAKIN, RCVIN),

the basic control for the ASTRAL model (ASEPTL), a routine

which smooths the transmission loss output (SMAOOTH), and a

routine for output of results (TLOUT).

The next level is composed of the major components

of the ASTRAL model itself. The routines which comprise this

second level are: INITAL, RCVR, SECTON, SLOPE, AMPDP, MARCH,

TLFINT, and SMOOTH. The routines in this level, in turn,

invoke other levels of execution (e.g., SECTON calls sub-

routine TRACE, which in turn calls subroutines PERIOD, BTMLOS,

and NEWMOD).

A flow diagram (Figure 2-1) has been provided to

facilitate conceptual understanding of the sequential nature

of the execution of the model. Some license has been taken

with the composition of the flow dlagram: in the situations

3 where a single subroutine is invokea by a nurp'--• of other

routines, the common module is depicted in all places where

it is actually used (e.g., subroutine SMOOTH occurs in two

places in the flow diagram).

Figure 2-2 shows the flow within the ASEPTL sub-

routine and between the subsequent levels of subroutines.

2-1

I S/ pC., -

00

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2-24

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Blocks are meant to denote routines whose names are indicated

in capital letters. In a few more complicated routines some

of the internal flow is indicated. Figure 2-3 identifies all

subroutines and common blocks which they use.

III

IIIIIIII

I 2-4

I

I '~OMMON BLOCK_ _ZZ >ZU

* Z ~. - ~ a. L ci> 4

Z DRIVERJT rn::D:*@0Oe0* 00

ENI 0 .0

PARIN 0* @

TRAKIN

ASEPTL 0 0 0 * 00

SMOOTH 0 0 00 0

INITAL * 0 0 1 0 0 000 0 1 0 0 0

RCVR 0 0* *IICOMPSI 0 0 00

PSI RCY

SUP-LOS

EIGEN 0 0 FHONI ~ ~~~ ~~HUP - ------- - - - - - - - --

AIRY

SECTON 0 000 0

TRACE 0 0 00 0 0

PERIOD 0.0

SLOPE 0 0 600 0 00

AMPOP 0 0 10 0

MARCH 0 0 0 0 1 le

3 ~~~~~~~DELýSlCOUPLE - 1 0*

NEWOW 010Ol

NEVW8Cj

PHIOL 0 I

1 DTOIN - 0i> 1 1

rDONE

Figure 2-3. Conaiion Block Utiliziation

2-5

II

2.1 PROGRAM DRIVER

I Program DRIVER is, as its name implies, the driver

for the program. DRIVER establishes the main common blocks

used by the program. Additionally, it calls several sub-

routines which perform a variety of utility functions. The

subroutines called by DRIVER are as follows:

Subroutine Formal params. Param. desc. Sub. desc.

ENVIN none reads and printsenvironmentalinput parameters

PARIN none reads and printsother parametricinput (e.g., ranges,source depth, etc.)

RCVIN NTRACK track number reads and printsreceiver input

TRAKIN none reads and printstrack input

ASEPTL none driver for ASTRALmodel

TLOUT none prints results (viz.,TL ao a function ofrange, depth, andfrequency)

I Each of the aforementioned subroutines will be dealt with in

greater detail in later sections of this volume.

I

U 2-6

I

mm

The overall flow of the program through DRIVER is

as follows:

I 1. Environmental parameters (e.g., number ofprofiles, number of points per profile, the

sound speed profiles themselves, etc.) are

read in. A summary of these inputs is then

3 printed. (ENVIN)

2. Parametric inputs for the specific problem

to be solved (viz., number of range points,

maximum range step, source depths, frequencies,

and the maximum number of modes) are read in.

A summary of these inputs is then printed.

(PARIN)

3. Data for each receiver (viz., number of tracks,

receiver depth, and near-field bathymetry) are

read in. A summary of the receiver input is

then p'rinted. (RCVIN)

I 4. For each track specified in part 3, track

parameters (viz., number of environments,

maximum range, immediate track slope, and

near-field bathynietry irdex) are read in andI printed. (TRAKIN)

3 5. Subroutine ASEPTL, the driver for the actual

ASTRAL model, i13 invoked.

I 6. Transmission loss, as a function of depth,

frequency, and range is printed in matrix form.

(TLOUT)

I 2-7

7. Steps 4 through 6 are repeated for each track.

8. Steps 3 through 7 are repeated for each

* receiver.

The option exists for both raw ana smoothed trans-

mission loss curves to be printed. Use of the raw printout

option is controlled by the vaiue of the logical variable

DEBUG(3). If DEBUG(3) is .TRUE., the transmission loss

curve is first printed as raw data, then smoothed, and printed

again. If the value of DEBUG(3) is .FALSE., the raw data is

smoothed before printing, and then printed.

2

I2-

I |

II

2.1.1 Subroutine ENVIN

I Subroutine ENVIN is called from the main program

driver (DRIVER). It is responsible for reading the environ-

mental input parameters. Subroutine ENVIN calls no other

subroutines; once it has been executed, control returns to

* the main program driver.

The following variables are established by sub-

I routine ENVIN:

Variable Description Common

NPROFS number of profiles or water masses local var.

NZC(20) numb#.. -*÷ points in each profile /ENVS/

IFPAE(20) logical variable which indicates /ENVS/whether an environment has beenpreviously processed; initiallyset to .FALSE.

ZE(25,20) depth points for each profile (ft) /ENVS/

CE(25,20) sound speed points for each profile /ENVS/(ft/sec)

WVHTE(20) wave height (ft) corresponding to /ENVS/each water-mass area

Subroutine ENVIN prints the environmental input

parameters in summary form.

2I

2-9

I

II

2.1.2 Subroutine PARIN

Subroutine PARIN is called by the main program

I driver. It reads the parametric inputs specific to the

problem to be analyzed. No other subroutines are called

by subroutine PARIN; once it has been executed, control is

returned to the main program driver.IThe following variables are established with a

call to subroutine PARIN:

Variable Description Common

NRMAX maximum number of range points /RANGES/(< 400)

DRMAX maximum range step (nmi) /RANGES!

NZS number of source depths (< 3) /SRCFRQ/

NF number of frequencies (< 6) /SRCFRQ/

ZS(3) source depths (ft) /SRCFRQ/

F(6) frequencies (Hz) /SRCFRQ/

I ?MAX maximum number of modes (< 25) /PRCENV/DEBUG(5) logical variable controlling /STATUS/

optional output

Subroutine PARIN prints a summary of the parametricinputs before returning control to the main driver.

2IIUn 2_i0

I

2.1.3 Subroutine RCVIN

Subroutine RCVIN is invoked by the main program

driver. It establishes input data for each receiver to beanalyzed. RCVIN calls no other subroutines; when execution

of RCVIN is completed, control returns to the main program

driver.

The following receiver variables are establishedwith a call to subroutine RCVIN:

Var able Dscr 'pt ion Common

NTRACK number of tracks Formal Param.

U. receiver -epth (ft) /RECVER/

FRSRCV ligical variable; set to .TRUE. /RECVER/

FRSNFB(8) logical variable; sek to .TRUE. /NFB/

I ZNFBZ(S) zero-range depth (ft) /NFB/

THNFB(8) slope angle (iad'ans, negative /NFB/dowvn): THNFB < -1.5 forsuspended receiver

RNFB(8) slope range (n-mL) /NFB/

IBCNFB(8) slope bottom class /NFB/

Subroutire RCVIN prints a sunmary of the receiver

inputs before returning control to t)'e main prugram dri-ýer.

I:-IIi

I

mm

2.1.4 Subroutine TRAKIN

Subroutine TRAKIN is called by the main program

driver. Its function is reading the data for each track.

No other subroutines are called by subroutine TRAKIN; once

its execution is completed, control is returned to the main

program driver.

m The following variables are established with a call

to subroutine TRAKIN:

Variable Description Common

NENV number of environment steps /ENVDET/(< 400)3 RMAX maximum range (nmi) /RANGES/

THBRC immediate track slope (rads)* /RECVER/

INFB near-field bathymetry index /NFB/for this track

INDEX(400) index for water mass in each step /ENVDET/

IBC(400) FNWC 1-5 (reset to 1,3,4) bottom /ENVDET/class for each step

RENV(400) beginning range (nmi) of new /ENVDET/Senvironment or step

DEP(400) depth (ft) of this step /ENVDET/

m Subroutine TRAKIN prints a summary of the trackinputs before returning control to the main program driver.

*THBRC - 1.5 rads for a suspended receiver

2I1 2-12

I!

2.1.5 Subroutine TLOUT

Subroutine TLOUT is called by the main program

driver to produce, in table form, the results of the ASTRAL

model. Subroutine TLOUT is called after the data for each

track have been processed. TLOUT is called with no formal

parameters, and calls no other subroutines.

The following information is printed with a call

to subroutine TLOUT. For a detailed description of output

see Section 3.

Variable Descr12tiOn

IEND termination code

IR number of range steps

zS array of source depths

F array of frequencies

For each range step:

I step number

RANGE(I) range

AMPM(IJK) TL for range step I (at range RANGE(I)) forK frequencies and J source depths

If the transmission loss profile is smoothed, sub-

routine TLOUT is called an additional time, after the smooth-

ing process has been executed.

2-13

mI

2.2 SUBROUTINE ASEPTL

The call to subroutine ASEPTL from the main program

driver invokes the actual ASTRAL model. Subroutine ASEPTL

serves as the driver for the subroutines which comprise the

ASTRAL model and establishes the necessary common blocks.

The flow of subroutine ASEPTL is indicated in Figure 2-2.

Calls are made from subroutine ASEPTL to the following

m subroutines:

Formal Description ofSubroutine Parameters Param. desc. subroutine

INITAL none ---- initializes all internalvariables

RCVR INDEX(l) sequential initializes parameterswater mass for new receiver (in-index cluding its profile)

computes receiver angleand coupling for eachmode

I SECTON INDEX(l) computes slope-conversionMUP(IINFB) mode index effects on each modeATUP(I,INFB) accumulated the receiver couples to

intensityloss

SLOPE MUP(IINFB) adjusts for effects ofATUP(1,INFB) immediate slope

AMPDP RNFB(INFB) range to end computes direct pathof slope intensity using

spherical spreadingand two incoherentpaths

MARCH DPNFB depth at march solution out inrange RNFB range

TLFI,,f none ---- converts intensity totransmission loss

SMOOTH none smooths raw trans-mission loss curve

2-14

I

II

i Additional information concerning the individual subroutines

called by subroutine ASEPTL follows.

i

IIIii

IIi

-- 2-15

II

2.2.1 Subroutine INITAL

The call to subroutine INITAL from subroutine

ASEPTL causes the initialization of all variables and arrays

internal to the ASTRAL model. The following parameters are

directly affected by a call to subroutine INITAL:

Variable Description Common block

Bottom loss parameters defined

THCRIT(5,3) critical angle (deg)

BLZER(5,3) loss at minimum grazing angle(dB)

THXX(5,3) angle at which loss becomesconstant

BLXX(5,3) bottom loss at THXX (dB)

FBRK(4) break frequencies (Hz)

Bottom loss angles and bottom loss by frequency class computed

THC(6,5) critical angle /BOTTOM/

BLZ(6,5) bottom loss at zero grazing /BOTTOM/angle

THX(6,5) first angle at maximum loss /BOTTOM/

BLX(6,5) loss at angle THX /BOTTOM/

DBLDTH(6,5) bottom loss slope (dB/rad) /BOTTOM/

VLOSS(6) volume loss (dB/nmi) at each /VOLOSS/frequency

Logical variables for control of processing

IFALL Indicates all modes attenuated /FINISH/below threshold; signals endof processing (.F.)

IEND values 0-5; termination code /RANGES/for run (0)

IFMDN(25) indicates end of mode processing /FINISH/(.T.)

IFDONE(6,25) indicates end of processing mode /FINISH/for each frequency (.T.)

2-16

I

CommonVariable Description Block

Mode variables zeroed

I PHIRC(6,25) mode amplitude /PHIRlCV/

Tolerance levels

DBCONV conversion factor to dB re 1 yd /CONV/TLMAX maximum transmission loss /CONV/

AMPMIN minimum amplitude (corre- /CONV/spontding to TLMAX)

PHIMIN minimum Eigenfunction /CONV/amplitude

DZMINl minimum width for an eigenfunc- /CONV/tion

ATTMAX maximum attenuation /CONV/

Angle increments

NA] number of angles at DTH1 /MODANG/

NA2 number angles at DTH2 /MODANG/

DTH1 angle increment for first NAl /MODANG/angles

DTH2 angle increment for next NA2 /MODANG/angles

TLTOL maximum TL change (for /TLSM/* smoothing)

REPS range tolerance (smoothing) /TLSM/DEPS fractional depth tolerance /TLSM/

(smoothing)RSMAX maximum range window for /TLSM/3 smoothing

Optional debug printout is available by settingthe value of DEBUG(2) to .TRUE. Subroutine INITAL calls noother subroutines; once its execution is completed, controlreturns to subroutine ASEPTL.

2-17

m

1 2.2.2 Subroutine RCVR

m For each new receiver (FRSRCV=.TRUE.), subroutine

ASEPTL calls subroutine RCVR. RCVR is called with one formal

parameter, INDEX(l), the index of the water masses at the

receiver.

Subroutine RCVR performs any necessary parametric

changes occasioned by the new receiver. The sound speed at

the new receiver is determined by linear interpolation.

Additional data, including the index of the first mode withwhich the receiver couples and the angle at the receiver for

each mode are also computed.

m The following variables are affected by a call to

subroutine RCVR:

Variable Description Common

THR(26) angle of each mode at receiver /RECVER/(+ radians)

DSTHR(25) solid angle of each mode at /RECVER/receiver

MMIN index of first mode receiver /RECVER/couples to

FRSRCV logical variable indicating /RECVER/presence of new receiver;set to .FALSE. at end of sub-routine RCVR

Subroutine RCVR calls subroutine COMPSI, which

determines the new mode parameters. The call to subroutine

COMPSI is of the form:

CALL COMPSI (IX,PHINF(l.IX))

1 2-18

4e

I

where

I IX = INDEX(l) See above

PHINF(1,IX) array of Eigenfunction valueswithin COMPSI the mode/frequency/source-depth dependencies areincluded in a three-dimensionalarray equivalenced to PHINF(1,IX)

Additional information concerning subroutine COMPSI follows.

Once execution of subroutine RCVR is .completed,

control is returned to subroutine ASEPTL.

I

I

2-1

III

I 2-19

I,

II

2.2.3 Subroutine COMPSI

Subroutine COMPSI computes the mode parameters

for each new environment. COITSI may be called either by

subroutine RCVR or by subroutine MARCH. It is called with

two formal parameters, as follows:

3 CALL COMPSI (IX, PHINF(1,IX))

where

IX index of water mass of interest

PHINF(1,IX) array of Eigenfunction values

Initially, the sound-speed minimum is determined.

From that, the phase velocities are computed (see Volume I,

3 Section 2.3.4). A call to subroutine PSIRCY generates, for

each mode, the phase integral, range period, upper and lower

turning point depths, and upper and lower turning point

gradients (subroutine PSIRCY will be discussed in ditail in

the next subsection). The call to subroutine PSIRCY is as

follows:

I CALL PSIRCY(NCZE(1 ,IX),CE(i,IX),CH(M, IX),PSIZ(M,IX),RCYCZ(MIX),ZLrP(14, IX). ZDN(M, IX),GUP,GDN)

where

I NC no. of points in current sound-speed profile

3 ZE(1,IX) depth of first point on profile (ft)

CE(1,IX) sound speed of first point onprofile

CHM(, IX) phase velocity (ft/sec) of mode Nfor environment IX

I2-20.I

II

PSIZ(M,IX) phase integral (sec)RCYCZ(MIX) range period (nmi)

ZUP(M, IX) upper turning point depth

ZDN(M,IX) lower turning point depth

GUP upper turning point gradient

GDN lower turning point gradient

Surface loss is the next parameter to be established.

At present, zero loss is assumed for all angles, frequencies,

and wavehs-ghts. This is currently done within subroutine

COMPSI; however, once an expression for surface loss is

available, it can readily be implemented in subroutine

3URLOS, which is currently inactive.

In the evert that su.routine SURLOS is utilized,

the calling sequence is as follows:

I CALL SURLOS (STHSRF,WVHTE(IX),NF,F,SURFLS(1,M, IX))

whe re

I STHSRF sin(surface grazing angle)WVHTE waveheight (ft)

NF number of frequencies

F frequency array (Hz)

SURFLS(1.I., IX) surface loss returned (dB/bounce)M mode number

3 IX environment number

Subroutine COMPSI next calls subroutine EIGEN,

which computes depth-unnormalized eigenfunctions for the

source. The call to subroutine EIGEN is as follows:

CALL EI GEN (CM(,. I X), CS, ST11SRF, ZUP(13, I X). ZDN(•1, I X), GUP, GM. CZS.

XPHINF(l,1 IM)

2-21

,Iwhere

CS = CE(1,IX) sound-speed at surface

CZS sound-speed at source depths

XPHINF(1,1,M) array of Eigenfunction values(treated by EIGEN as 2-dimensionalarray on frequency/source-depth)

Subroutines EIGEN, SURLOS, and PSIRCY will be discussed

subsequently.

Subroutine COMPSI returns control to subroutine

. ASEPTL upon completion of execution.

2.2.3.1 Subroutine PSIRCY

Subroutine PSIRCY computes mode parameters for

each new environment. PSIRCY is invoked by a call from

subroutine COMIPSI. Computations are made for each layer

in the sound speed profile, and are dependent on the computed

value of the gradient at each point. The gradient value

soecifies whether or not the point in question is a turning

point. For a non-zero gradient, the range period and the

phase integral of each mode in the new environment are

adjusted.

Uue The following variables are affected by a call

to PSIRCY:

Variable Description

PSIZ(M,IX) phase integral (sec) of mode M forI environment IX

RCYCZ(M,IX) range period (nmi)

ZUP(M,IX) upper turning point depth

2-22

II

Variable Description

ZDN(M,IX) lower turning point depth

GUP upper turning point gradient

GDN lower turning point gradient

For a complete treatment of the methodology involved in

the computations, see Volume 1, Section 3.2.2.

I Subroutine PSIRCY calls no other subroutines; once

its execution is complete control is returned to subroutine

COMPSI.

3 2.2.3.2 Subroutine SURLOS

Subroutine SUPLOS computes surface losses in dB

per bounce for each specified frequency. At present, sub-

routine SURLOS returns a value of zero for all surface

losses. This can easily be modified with placement of an

appropriate expression for surface loss in the subroutine.IThe following variables are affected by a call

3 Ito subroutine SURLOS:

Vari able Description

ISTHSRF sin(surface grazing angle)

WVRTE waveheight (ft)

NF no. of frequencies

F frequencies (Hz)

3 SURFLS(I,M,IX) surface loss (dB/botnce) mode Menvironment IX

xetoSubroutine SURLOS calls no other subroutines; once

execution is completed, control returns to subroutine COMPSI.

1" 2-23

I

I

2.2.3.3 Subroutine EIGEN

Subroutine EIGEN is called by subroutine COMPSI to

compute depth un-normalized source eignfunctions. These

eigenfunctions are functions of the upper and lower turning

point depths, upper and lower turning point gradients, source

depth, and frequency.

Geometric limits on intensity and the corresponding

diffraction-limit angle are initially set. Then, for each fre-

quency, the lower turning point scale factors and limits of

diffraction (e.g., minimum angle before diffraction limits

intensity, caustic limit on intensity, and depth scale factor)

are determined. A check is made to determine whether the

mode is totally internally refracted (RR) or refracted at

depth and surface reflected (RSR). Based on this informa-

* tion, appropriate calculations of the upper turning point

scale factors and diffraction limits are made.

-I It is then determined whether the upper and lower

turning point regions overlap. If overlap exists, the

I region of overlap is defined, and a linear interpolation

between the upper and lower caustic limits on intensity is

performed.

Subroutine EIGEN utilizes functions HUP and HDN

to compute the values of the eigenfunctions associated with

the upper and lower turning points, respectively. Functions

"HUP and HDN use Airy functions to compute the eigenfunctions

of the upper and lower turning points in the following manner:

2I 2-24

I

I•Ih h (-aUP(Z -zup))/2 Ai (- (-U -z

hup cUPI Ai2 (0) (If Z- O) Ai(O) .)

IAi 2 (a dn(Z - z dn))Shd =h Ai-

dn Cdn Ai2(0)

1 where hc = caustic limit of intensity

Ai = Airy function

a = depth scale factor

Zup/dn = upper/lower turning point depths

Z = source depth

Functions HUP and HDN are discussed in more detail subse-

quently. For an in-depth treatment of the methodology

involved in the development of the source eigenfunctions,

see Volume I, Section 3.2.2.

3 Function HUP is invoked by subroutine EIGEN in

the following manner:

SH(J) HUP(ZS(J),ALUPHCUPZUPHG(J),TH3(J),THUP3)

where ZS(J) = source depth

ALUP = depth scale factor = aup = 1.77/AZup

HCUP = caustic limit of intensity = I/up

3 ZUP = upper turning point depth

1HG(J) = geometric intensity limit = 1/tan(O U)

I 2pI 2-25

:II

TH3(J) e3;e = angle at source depth Z of the ray- equivalent s

THUP3 = -up3; eup = minimum angle permitted before

diffraction limits intensity

A flow diagram of subroutine EIGEN is shown in Figure 2-4.

2.2.3.3.1 Function HUP

Function HUP computes the eigenfunction value

associated with the upper turning point. The parameters

"necessary for upper turning point eigenfunction computation

are:

HUP(ZS,ALUP,HCUP, ZUP,HG,TH3, THUP3)

where ZS - source depth

ALUP = depth scale factor

I HCUP = upper caustic limit for intensity = 1/6UP

ZUP = upper turning point depth

HG = geometric intensity limit

TH3 cube of angle e at source depth ZS of the rayequivalent

3THUP3 = up = (3/4)g UP/f

The upper turning point eigenfunction H(J), is computedas follows:

II

1 2-26

.i

I

ISubroutine EIGEN

I es KZ÷21Tsin6

loop on source depths

geometric intensityFhgin 0Ic ,o •°s = :°ud speed atyes c > source depth

phase integrali oof current mode

I end loop on source depths

loop on frequency I8dn =f frequencyI• dn ' (- .5caf)

gdn

I ldn - 1.77/Az dn

z dn 'M Zdn- " ZdnIh cdn ' 1/8 dn

I 0

IFigure 2-4a. EIGEN Flow

i

I 2-27

II

-I

eu .u0

O.p -,1. 7 /A3..

Atp - Z p ) -5c

Iloop on source noove

,A upper turning point

I o H(J) - ""l (zO ,hR) o elap o reghion

3 -, A

ino jj.j) * .O.J..h )

U Z

Mend sourlcw loop , I3 HUd loop on s o urce depth-- 9o6

3 Figure 2-4b. u -IGEN Flow (Cont.)

i 2-28

I

II.

add in surface-image interference

loop on source

PHI = H(J)

| no

ir 0| no

III 0

no

PRHASE =FKZ * F z s

3Yes 2

PHASE'( < t PH IT2 PHI *SIN (PHASE)

no

end source loop

u end frequency loop,

I Figure 2-4c. EIGEN Flow (Cont.)

I ! 2-29

I

H(J)(=uh = h [ ZUP)up cup 2Ai2(0) (if z$O Ai 2 (O)

* where Ai = the Airy function

For a more detailed treatment of the methodology involved, see

Volume I, Section 3.2.2.

2.2.3.3.2 Function HDN

U Function HDN computes the eigenfunction of the

lower turning point. HDN is called from subroutine BIGEN

in the following manner:

I H(J) =HDN(ZS,ALDN,IHCDN,ZDNHG,TH3THDN3)

I where ZU source depth

ALDN • depth scale factor

HCDN = caustic limit of intensity v 1/0

ZDN • lower turning point depth

HG M geometric intensitv limit

TH3 =cube of angle 8 at source depth ZS arequivalent

THIN3 P 0dn (3/4)gdn/f

The value of the eigenffunctiol of the lower turuing poLatH(J), is computed as follows:

I =Ai 2(adn( - dn)(J) =hdn =A 2(O)

Cdn Ai (0)

where Ai = the Airy function.

I 2-30

II

For a more detailed treatment of the related methodology,

see Volume I, Section 3.2.2.

I 2.2.3.3.3 Function AIRY

I Function AIRY produces normalized, squared Airy

functions. AIRY is called from functions HUP and HDN.

Ai2 (-X) -4.0 < X < 1.77

Ai 2(0)

AIRY(X) =0 X <(-4.0

172(~ X> 1.77

For -4.0 < X < 1.77, Ai(X) is approximated by where

CX is interpolated from tabulated values of C(I) and

CI = 2log/o Ai(O) I=1,31C(I)~ ~~A = 11o|"I-11•) I13

3 The range of I corresponds to a range of -X from -2.0 to

4.0 at intervals of 0.2. This function (or more properly

1/AIRY) was originally used and documented in FACT (Baker

and Spof ford, 1974).

I Function AIRY is called in the following manner:

From Function HUP:

3 AIRY(A*(Z-ZT))

Ii 2-31

II

where A = depth scale factor = aup

Z = source depth

I ZT = upper turning point depth

From function HDN:

AIRY(A*(ZT-Z))

where A = depth scale factor a dn

Z = Source depth

ZT = lower turning point depth = dn

III

IIII

I

II

2.2.4 Subroutine SECTON

SECTON treats the near-field bathymetry (NFB)(if it has not been treated before) by tracing (in TRACE)

all ray equivalents which reach the receiver, over the

near-field bathymetry. It sets up 2ertain parameters for

TRACE and cycles through the angles (both up- and down-

going). The following variables are affected by a call to

TRACE:

Variable Description Common

FRSNFB Logical flag indicating first /NFB/

time this sector is seen(set = .FALSE.)

5 DRDCMY Derivatives of period, Zup, Zdn /DRDCM/DZPDCM with respect to phase velocityDZNDCM for routine PERIOD

MUPDN(2,25) Mode number after NFB for each Formalmode MP(J) for up (first index Parameter= 2) and down (first index = 1)ray at angle THR(M)

ATUPDN(2,25) Accumulated attenuations Formal(intensity reductions) per Parametermode and angle after NFB

The call to TRACE is

CALL TRACE( IX,M,ZRTH, ZNFBZ, THNFBRNFB,IBCNFB, MUPDN(I,H),ATUPDI (I,M),TANBETSINBET, COSBET)

U where

I IX = water-mass index

H = mode number

TH = initial ray angle at receiver

Ii 2-33

II

ZNFBZ = extrapolated NFB depth at range zero

THNFB = NFB slope angle

I RNFB = max range of NFB

IBCNFB = NFB bottom class

MUPDN = new index

ATUPDN = accumulated (intensity) losses

TANBET = tan(THNFB)

SINBET = sin(THNFB)

COSBET = cos(THNFB)

SECTON calls TRACE (which calls PERIOD, BTMLOS and NEWMOD)

and returns control to ASEPTL.

2.2.4.1 Subroutine TRACE

TRACE traces rays from the receiver to the end

of the near-field bathymetry. The flow of TRACE is shown

in Figure 2-5. Numbers in parentheses correspond to FORTRAN

statement numbers. The following variables are defined by

a call to TRACE:IVariable Description Common

m Mc Zero mode number, -0 if Formal

ray terminated Parameter

AT(6) Accumulated losses at Formaleach frequency (in Intensity) Parameter

3 TRACE calls BTMLOS, PERIOD and NEWMOD as follows and returns

control to SECTON.

2m 2-34

I

Z'me4ý o InrmnPosil

IýRfeto Ryb yl

Yer 10

Ic(ýueRfecinPrmtr

DiIayDnRelctI

I.!FigureYe 2..(lwof 00ou) e RCYe

2-35eLose, ec

(20)IRnt

1 (1) BTMLOS(IBCNF,J,GAMMA)

where BTMLOS returns -the dB loss per bounce and:

IBCNF = Bottom Class Index for NFB

-I J = Frequency Index

GAMMA = Grazing Angle

(2) PERIOD(I,%CT,PNEW,ZUPNEW,ZT)

where

I = Water-mass index

CT = phase velocity

PNEW = period (CT)

SZUPNEW = upper turning-point depth (CT)

ZT = lower turning-.-Aint depth (CT)

I (3) NEWMOD(CT,I-14P)

where

CT = phase velocity

TI I = water-mass index

HP = mode index (CT)

2.2.4.2 Subroutine PERIOD

H IPERIOD is called by TRACE to determine the rayperiod (PNEW) and upper (ZUP) and lower (ZDN) turning points

corresponding to phase veloci.ty CTILDA in water mass IX:

2-36'I

III PERIOD( IX,CTILDA,P, ZUP, ZDN)

It uses the processed environmental water-mass data inI /PRCENV/ to linearly interpolate in RCYCZ(CM),ZUP(CM),ZDN(CM).

To speed up the calculation, the derivatives of each function

with respect to CM have been computed external to PERIOD

(in SECTON) and passed through /DRDCM/. When the ray turnsI deeper than the last mode the period is extrapolated

assuming a pressure gradient profile from the surface to

infinity. If CTILDA < CM(M = 1), the first-mode values areused. PERIOD calls no subroutines and returns control to

j TRACE.

2.2.4.3 Function BTMLOS

Function BTMLOS computes the bottom loss (dB) ata given frequency for a mode (ray) incident on the bottom

at a given bottom grazing angle. The bottom loss is constant

for grazing angles less than the critical angle or greater

than the angle of maximum loss. Between these limits, the

I bottom loss varies linearly.

1 2.2.4.4 Subroutine NEWMOD

NEWMOD computes the new mode index, MC, corres-

ponding to phase velocity, CTILDA, in water mass IX:

I NEWMOD(CTILDA, IX, MC)

It compares CTILDA with CM(MIX) and sets MC = first M forwhich CM(M, IX) > CTILDA. If CTILDA > CM(MMAX,IX), LC =MMAX. NEWMOD uses processed environmental data from /PRCENV/,

calls no subroutines, and returns control to TRACE.

I 2-37

S2.2.5 Subroutine SLOPE

:2; Subroutine SLOPE is called from subroutine ASEPTL.

It takes the near-field bathymetry data which has beenwmodified by subroutine SECTON and performs the followingfunctions :

1. Determines which modes propagate after the

near-field bathymetry adjustment.

2. Computes the amplitude for each mode at

the specified range.

3. Sets limits on the modes established in

Part 1.

4. Sets logical variables (which had been

initialized to TRUE in subroutine INTIAL)

to FALSE where modes still propagate

The following variables are directly affected by

the action of subroutine SLOPE:

Variable Description Common

IFMDN(25) Logical variable set to .FALSE. /FINISH/* mif modes still propagate

IFDONE(6,25) Logical variable set to .FALSE. /FINISII/if modes still propagate

PHIRC(6,25) Accumulated attenuation /PHIRCV/

Ml Index of 1st propagating mode /MODEMS/(after NFB)

?42 Index of last propagating mode /?AODEMS/(after NFB)I

Subroutine SLOPE calls no other subroutines.

22-38I

2.2.6 Subroutine AMPDP

Subroutine AMPDP computes the direct-path intensity

at a range of 1 nmi with spherical spreading and two incoher-

ent paths (see Volume I, Section 2.2.2). The following

values are affected by a call to subroutine APDP:

Variable Description Common

Range(R) Range at which TL computed /RANGES/Range(l) set to 1.0 if IEND=3.Range(2) = MAX (RNFB,2)

AMPM(R, Z ,f) TL(R,Zs,f) dB re 1 yd AMPM(I,Zs,f) /TLINT/S set to intensity at Range(l)

IR No. of range steps in TL(R); set = /RANGES/1 if •END = 3, otherwise set = 2

Subroutine AMPDP is called from subroutine ASEPTL with 1

formal parameter, RNFB(INFB), the range to the end of the

slope in NFB sector INFB.

Subroutine AMPDP calls no other subroutines; once

execution is completed, control returns to subroutine ASEPTL.

2IIIII 2-39

I

I

2.2.7 Subroutine MARCH

Subroutine MARCH propagates the model solution out

in range (see Figure 2-2). The first environment is des-

cribed by near-field bathymetry. Once the near-field bathy-

metric solution has been determined, a new water depth is

introduced. MARCH calls subroutine COMPDW, which makes any

parametric adjustments necessitated by the change in water

depth. An intensity is then determined by a call to sub-

routine INTSUM. If it is determined that the solution is

complete (see discussion of function DONE) control returns

to subroutine ASEPTL. If not, the next environment is

assimilated. In the event that the new environment is the

first, the environmental index (KENV) is determined before

proceeding.

Once KENV has been determined, a new depth, bottom

class, and water mass index are assigned. If a new water

mass has been encountered which has not been previously

processed, COM)SI is called to compute basic mode parameters

(see Section 2.2.3). Checks on whether the new depth or

bottom class differs significantly from its previous value

are performed by functions NEWDW and NEWBC, respectively.

A change in water depth or water-mass index forces changes

in source mode parameters, which are modified to include the

-3 depth by a call to COMPDW. If either the water mass or

depth changes, and any significant bottom-reflected modes

are still propagating (as determined by NEWBC), new bottom-

loss rates are computed in subroutine PHIBL. The rangeincrement, number of steps and losses per range increment

are then determined by a call to RCOMP. Once these param-

eterk have been established, intensity within a region is

m computed at each specified range step by subroutine INTSUM.

22-40

I

mI

The following calls are issued by subroutine MARCH:

Parameter SubroutineSubroutine Parameters Description Description

COMPDW FIRST Logical vari- Resets source modesable .TRUE. for new depthfor NFB

DEPNEW Depth at newrange

IXNEW Sequentialwater-massindex

PHINF(l, EigenfunctionIXNEW) values

function DEPNEW New water Logical functionNEWDW depth determines whether

DEPOLD Old water or not a signifi-depth cant depth change

has occurred

function IBCOLD Old bottom Logical functionNEWBC class index determines whether

IBCNEW New bottom or not a change inclass index bottom class has

occurred

COMPSI iXNEW Sequential Computes modewater mass parameters for newindex environment

PHINF( 1, Eigen functionIXNEW) values

PHIBL IBCNEW New bottom Computes bottom lossclass index rates for each mode

and frequencyRCOMP KENV Environment Determines number of

index range steps, rangeNR Range step increment

numberDR Range incre-

men t

INTSUM none Attenuates and sumsmodes for a givenrange step

function N Range step Logical functionDONE index determines whether

run is done

I3 2-41

II

2.2.7.1 Subroutine COMPDWISubroutine COMPDW has two basic operating modes.

3 If FIRST = .TRUE., it treats the receiver by initializing

the eigenfunctions at the end of the near-field bathyr,.try,

adjusting them for finite depth, and computing the indices

of the first surface and bottom-reflected modes as well

as the initial phase integrals (PSIMR).

On subsequent calls (FIRST = .FALSE.) the source

is treated with phase integrals (PSIMP) computed and new

mode indices MP(M) determined by adiabatic mappinig through

subroutine COUPLE.

For both source and receiver, the surface loss,

bottom-grazing angle, and eigenfunction values at the source

are computed.

The following subroutines are called by subroutine

3 COMPDW:

3 Formal ParanmeterSubroutine Parameters Description

3 DELPSI DEPTH New depth

ZDN L. ;er turning point depth

ZUP Upper turning point depth

PSIZ Phase integral of mode M(infinite ocean)

PSI New phase integral (finiteocean)

RCYCZ Range period of mode M(infinite ocean)

RCYC New range period (finite ocean)

THBMD Bottom grazing angle

MBOTP Index of 1st BR mode (new)

M Current mode index

2-42

III

In treating the source (FIRST = FALSE.) the mode coupling

is determined by:

I Formal ParameterSubroutine Parameters Description

COUPLE MPP Max number of modes used tocover PSI

MSURF Index of 1st surface reflected* mode

MBOTP Index of 1st BR modePSIMR Receiver phase integral

PSIAP New source phase integral

MPP Coupling index

The following parameters are then computed for

* both source and receiver:

3 THBM(M) Bottom grazing angle

RCYCM(M) Ray/mode cycle distanceZDNH(M) Lower turning point depth for

ray traceSFLSNM(N,M) Surface loss/nmi

PHIM(J,N,M) Depth normalized eigenfunction

3 Subroutine COMPDW then returns control to subroutine MARCH.

2.2.7.1.1 Subroutine DELPSI

Subroutine DELPSI adjusts the phase integral, range

period, bottom grazing angle and index of the first BR modeto account for changes in depth.I

If the current mode is not bottom reflected, the

bottom grazing angle is set to 0.0. The phase integral

and the range period remain unchanged and control is returned

3 to subroutine MARCH.

I 2-43

I

When the current mode is bottom reflected, a new

bottom-grazing angle is computed. It is then used to com-

pute a new phase integral and range period.

For a description of the call to subroutine DELPSI,see the preceding discussion of COMPDW. Subroutine DELSPI

calls no other subroutines.

2.2.7.1.2 Subroutine COUPLEUSubroutine COUPLE computes the indices MP at the

source corresponding (thru PSI) to modes M at the receiver,

plus indices of the first surface reflecting mode and the

first bottom reflecting mode. Subroutine COUPLE is called

by subroutine COMPDW (for parameters in call see COMPDW

* description).

The following variables are modified by a call to

subroutine COUPLE:

MP Indices corresponding to M

MBOT Index of first bottom reflectingmode

MSRF Index of first surface reflectingmode

2.2.7.2 Function NEWDW

pIh Function NEWDW is called by subroutine MARCH in

an effort to determine whether a significant change in water

depth has occurred. The function returns a value of .FALSE.if the last mode was not bottom reflected and will not become

bottom reflected (new depth .GT. depth of last mode). Checks

are also made to determine whether the first bottom reflected

2-44

I

Sm mode becomes non-bottom reflecting or the last non-bottom

reflected mode becomes bottom reflected. In the event that

there are some bottom reflected modes, a check is made to

determine whether the change in water depth results in a3 change in phase sufficient to necessitate changes in the

mapping.

1 2.2.7.3 Function NEWBC

I Logical function NEWBC is used by subroutine

MARCH to determine whether or not a significant change in

bottom class has occurred. If the index of the 1st bottom

reflecting mode is outside the range of the modes being3 considered or the new bottom class index is the same as the

old bottom class index, no significant change in bottom

class has occurred, and function NEWBC returns a value of

.FALSE.. If these conditions are not satisfied, function

NEWBC returns a value of .TRUE., which then prompts sub-routine MARCH to call subroutine PHIBL to modify allnecessary bottom loss parameters.I__m__ _ _ __ _ _

2.2.7.4 Subroutine PHIBL

Subroutine PHIBL is called by subroutine MARCH,

conditionally dependent on the presence of a new bottom

class. PHIBL computes the bottom loss (in dB/mile) foreach propagating mode/frequency combination. Subro4tine

PHIBL tests to ascertain whether bottom loss calculations

are necessary; if so, it determines whether a particular3 bottom loss has been previously calculated. If not, sub-

routine PHIBL invokes function BTMLOS to compute the actual

bottom loss. Function BTMLOS is called in the following

manner

2-45

III

BTMLOS(IB,N, THBM(M))

where

IB = new bottom class index

N = frequency index

THBM(M) = bottom grazing angle of the modeIThe value returned from function BTMLOS is then divided by

the mode (ray) cycle distance to yield the bottom loss

in dB/mile which is then stored in array BLOSS(6,25). For

a description of BTMLOS see Section 2.2.4.3.

2.2.7.5 Subroutine RCOMP

Subroutine RCOMP is called by subroutine MARCH

to determine the number of range steps, the range step

increment, and the attenuation/mode/step. A tentative

3 calculation of the range step increment is made equal to

the length of the current environmental step. If this value

is less than or equal to the maximum permitted range step,

the no. of range steps is then set equal to 1. If this

value is greater than the maximum range step, more than

I one step is required, and a new range step increment is

computed.IThe attenuation/(mode/step) is then calculated

3 with a call to subroutine DBTOIN, in the following form:

3 CALL DBTOIN(DR)

where DR = range step increment

Control is then returned to subroutine MARCH.

2-46

m

2.2.7.6 Subroutine DBTOIN

Subroutine DBTOIN determines the total attenuationarising from volume, surface, and bottom losses for each

propagating mode and frequency combination. This total

attenuation is expressed as an intensity reduction factorfor each range-step increment. These values are stored in

array ATTENR(6,25) in common block /ATTENS/.

2.2.7.7 Subroutine INTSUM

Subroutine INTSUM attenuates the amplitude ofeach mode by the loss factor calculated by subroutine DBTOIN,

and sums the product of the (attenuated) amplitude and the

source eigenfunction value, dividing by the range. The

minimum transmission loss is computed and logical variables

indicating the end of processing are set if appropriate.

The following variables are affected by a call

to subroutine INTSUM

m PHIRC(6,25) Attenuated mode amplitude /PHIRCV/

IFDONE(6,25) Logical variable indicating mode /FINISH/is fully attenuated at frequencyM (.TRUE..)

AMPM(400,3,6) Transmission loss (intensity re /TLINT/I yd)

IFMDN(25) Logical variable indicating end /FInISH)of mode M processing (.TRUE.)

IFALL Logical variable indicates end /FINISH/of processing (.TRUE.). All modesattenuated below threshold

TLSUM Minimum TL (over frequencies) /CONV/

I Control returns to subroutine MARCH.

I 2-47

I

I

3 2.2.7.8 Function DONE

Logical function DONE returns a value of .TRUE. ifcalculations in subroutine MARCH should be terminated,

setting the termination code for the run (IEND):

IEND End Code Description DONE

0 Processing not completed .FALSE.

1 Maximum range reached .TRUE.2 Maximum number of range points reached .TRUE.

3 All modes attenuated below threshold .TRUE.

4 Approximation of transmission loss .TRUE.exceeds maximum transmission lossvalue TLMAXI

Control is returned to subroutine MARCH, which then allows

continuation or termination of processing. Once MARCH

returns control to ASEPTL and the final transmission loss

is computed in TLFINT, an additional setting of the end

code is possible. Specifically, if for all frequencies and

ranges beyond some range short of the maximum range the

loss exceeds TLMAX, the TL array is truncated and IEND is

set to 5.

IUIIII 2-48

IN

mI3 2.2.8 Subroutine TLFINT

Subroutine TLFINT converts total loss intensities

to transmission loss in dB re I yd with the maximum possible

transmission loss equal to TLMAX (an input value specified

in subroutine INITPL). The conversion is done in place in

array AMPM(400,3,6).

The following variables are modified by a call to

subroutine TLFINT:

Variable Description Common

AMPM(400,3,6) Loss (intensity) converted to /TLINT/

loss in dB re 1 yd

IR No. of range steps in TL(R) /RANGES/

IEND Termination code set 5 /RANGES/m (see DONE)

m Subroutine TLFINT calls no other subroutines; onceits execution is completed, control returns to subroutine

m ASEPTL.

1 2-49

I

I2.2.9 Subroutine SMOOTH

Subroutine SMOOTH causes the current transmission

loss curve to be evaluated for discontinuities and smoothed

where appropriate. A call to subroutine SMOOTH may be issued

either from the main program driver (DRIVER) or from the

driver for the ASTRAL model (ASEPTL).

Discontinuities in the transmission-loss curve may

arise from changes in water mass, changes in water depth,

or neither of the above. A discontinuity is operationally

defined as a change in transmission loss which exceeds a

specified Uolerance level. Once the presence of a dis-

continiuty has been established, one of the above reasons

is identified as the source of the discontinuity.

3N A discontinuity arising from a change in water mass

is treated by defining a transition region which extends from

the middle of the previous water mass to the middle of the

current water mass but no greater than 150 rmi in length nor

closer than half way to the nearest discontinuity on both sides.

As a simulation of a continuous change in water mass, all

transmission loss values between these two selected end-

points are linearly interpolated in range between the point

defining the transition region.

Discontinuities which arise from a change in

water depth are made to approximate a more continuous

change in water depth by isolating the point which reflects

this discontinuity. The point is then linearly interpolated

in range between the two points inrm-ediately adjacent to the

discontinuity.

2

1 2-50

II

in the event that neither of the two aforementioned

conditi.ons are identifiable as the cause of the discontinuity,

no smoothing is performed. For a more complete discussion of

the methodology involved in the design of the smoothing

algorithm, see Volume I, Section 3.2.4.

The sequence of execution of the call to subroutine

SMOOTH is d&;endent on the value of the logical variable

DEBUG(3). If the value of DEBUG(3) is .TRUE., the follow-

ing sequence of events occurs:

1. Subroutine ASEPTL causes execution of the

ASTRAL model.

3 2. Subroutine TLOUT is called by the main program

driver. Raw transmission loss points as a

function of range, depth, and frequency are

printed.

3. Subroutine SMOOTH is called by the main pro-

gram driver. The points printed in step 1

are inspected for discontinuities.

3 4. Subroutine TLOUT is again called by the main

program driver. Smoothed transmission loss

points as functions of range, depth, and

frequency are printed.

m In the event that the value of DEBUG(3) is .FALSE.,

1 1. Subroutine ASEPTL causes execution of the

ASTRAL model.

m 2-51

I..

II

2. Before returning control to tie main program

driver, subroutine ASEPTL issues a call to

subroutine SMOOTH.

3. Control is returned to the main program driver,

which then calls subroutine TLOUT. The

smoothed transmission loss points (only) are

* printed.

Subroutine SMOOTH is called with no formal param-

eters. SMOOTH issues no calls to other subroutines.

II

" "--I

IIII

1II

2-52

I

3 Section 3

Input and Output

1 The ASTRAL Model was designed to function in two

distinct operating environments. For most users, it is a

stand-alone propagation loss model requiring card (or disc)

input and printed (or disc) output. The I/O operations

of ASTRAL in this mode are described in Section 3.1.

3 In the FNWC operating environment ASTRAL is only

a portion of the overall ASEPS system. As such its I/O

3 is handled entirely through common areas and ASEPTL is

called directly with the DRIVER, ENVIN, etc. routines

omitted. The operation of the model in this mode is des-

cribed in Section 3.2.

* IIn order to avoid redundant calculations several

areas of processed data are defined for subsequent use on

3 other runs. These need not be of concern to the external'

user; however, their intelligent utilization by "stacking"

3 !multiple runs may offer significant running time savings.

- They are the concern of the ASEPS program since they must

be made available to ASEPTL on subsequent calls, and certain

logical variables must be set indicating that the precom-

puted data are or are not available. Details of this struc-

ture are reserved for Section 3.2.

1 3.1 STAND-ALONE I/O

13.1.1 Input

Table 3-1 summarizes the user's input run deckwith appropriate format statements and variable descriptions.

33-1

I

'H VI

4)

(A) Pe 4C -

0a) ntoV r-4 )-)02a-) '--1 ' -%

C1~4 4110 CO W C*H (D 0 D

10S- 0 0)9 P 0 c -, 2o

z - 'H 'hD ;-4 (D -) 0n 4l-1 0 flfU

0- 0r- z-- 0 04 ) 0 -H a) r.

IH 0) 2 0 0 02

F4 0 0 E

to-47-

E-4i

IICd,

-z W z V. N -Ll i

1 $-4:j~ N

3-2

-a.~ 0 rqH 'a

0 0 * 4-)C r. >-

0. ed .,q 0 *14 a)R

0 0) -H 4-). 4- 0-r4 U4

>) a 0 W0a) 0 2 *H) C) 0 XeC.H > a 4 04 0-a) W 4-)

a) a CR 04a)H 0)v2"bi 0 -0 4J02

Q)" 0 cd-M"0Cd $-4 ka Q) 02

kC (). ) 02c) 4- 0 k co ~ ~ ~ 9 >e- 04- 00 a) 4JR> a~.0 ,-

0.. P..- L 4-) 0) z *HQ

kR co 00~C k '0

00 Cd 4-) )~ 4) 0d41> ()0 0 "1o, ILI 4-4 0Cd k D H k -b.0 H cd C E

"024 0 E $q 'o 04- 0J04) r. k- a) 000 r la 0 cd a)

'0 02 (D ~ .0 0 C2

cz 10 ý4 E

-a'112

4-) E C r4 LOL

Z0 4 44 P4 0-a P0 1-

CC.)I- Z r-i

1--4

I0CO)

41"-4

bd 0

C.))

3-3

I

Figure 3-1 shows the flow of input in terms of the four input

routines and ASEPTL. The input has been structured to allow

3• the user to consider a basic "ocean" of up to 20 profiles.

(ENVIN) for a specific set (PARIN) of source parameters

(depths/frequencies) and control parameters (NRMAX - typically

400, DRMAX - typically 30 nmi, and MMAX - typically 25 modes).

A receiver is then introduced (RCVIN) at a parti-

cular depth surrounded by up to 8 near-field bathymetry

3 sectors of varying point-slope-range-reflectivity descrip-

tions. An arbitrary number of tracks from this receivrer may

be considered as described (TRAKIN) in terms of their

corresponding NFB sector, the immediate slope at the receiver,

a maximum range, and up to 400 environmental regions of

arbitrary length along the track., consisting of different

water-mass (profile) indices, bottom classes, and depths.

The initialization for the receiver is performed

once for all such tracks and as each NFB sector is encountered

for the first time the mode-conversion effects are computed

3 once and saved for subsequent (not necessarily sequential)

runs. Similarly as each water mass is encountered for the

first time the infinite-ocean eigenfunction data are com-

puted and stored for later use. The track from a given

receiver may encounter and re-encounter any water masses in

any order. Similarly, different tracks may encounter NFB

sectors in any order.IOnce all NTRACK tracks are processed, a new receiver

3 may be considered with entirely new NFB and track characteris-

tics. For these tracks processed data will still be avail-

able for any water masses encountered which were encountered

for previous receivers.

1 3-4

III.

BEGIN

ENVIN

Input all WaterMass Data

IPARINInput Source Dataand Key Parameters

IRCVIN

Input Receiver and NFB

Data and # Tracks forReceiver

I LFoo 7Pon Number of Tracks

TRAKIN

Input Track Data:S# Environmental Regions,Max Range, Immediate Slope,NFB Sector, and Region Data

'....Execute ASEPTL and Output TL-----

IFigure 3-1. Overall Input Flow.

3-5I

Figure 3-2 is a copy of a typical run deck for

a short run. An option has been provided for debugging

purposes which can generate considerable output from within

the ASEPTL routine (and lower-level routines). In normal

execution ASEPTL produces no output other than an execution

time. The debug options are normally all set = .FALSE.

The output which each generates is described in the following

subsection.

3.1.2 Output

In normal execution (no debug printout) thefollowing information is printed by the indicated routines:

Routine Information

ENVIN Number of points per profileProcessed Status (should be all.

.FALSE.)Profiles with index and wave-height

PARIN Number of Range PointsMaximum Output Range StepSource DepthsFrequenciesNumber of Modes (max)Debug Flags

RCVIN Number of TracksReceiver DepthNFB Parameters

TRAKIN Number of Environmental RegionsMaximum RangeImmediate SlopeNFB IndexTrack Region Summary3 Index, BC, Range, Depth

ASEPTL Execution Tirre for this Track

TLOUT EndcodeNumber of Range StepsTransmission Loss Matrix

3-6

m

4T 4 77 60 1ron. 5100.

Ir,070. 50qn 50?0, 1"00. 5010. 30000011nO •6, 190Ono 510p,

0O0 30.03 4

Inn, 400, 80025. 1001 200. 400.

25

3 4A00.3600, 41n0.-0.05 -0.140, ?V.

3 1

non.023 0 * 3 016 .

SI 3 •00 1 14000,

2 1 V000 19O00.0m2 1 5,n00, l•Onn.

3 3 700A 1P000.3 4 p00. 15000.S 4 A?0. *no * Note - all "tracks" from

? 4 830. 2n a given "receiver" mustC; have same SVP at range 0.

IC~n. n.I IjC.A. I. 15

2 nO. 1iAnt) °6

m "3 n0.• 18000,1 • 'I00, 17n00f.

1 5 O

m' 3 o. 1sO0.2 >4 00, 15nOn.I ' 3?0. 180nn.

(Separator Card Indicating that new RCVR data follows would go here)(New RCVR data would go here)

I Figure 3-2. Sample Input

Im 3-7

IFigure 3-3 is a copy of the output generated by the run

deck of Figure 3-2.

I The value of the logical variable DEBUG(J,J=I,5)

controls the extent of the output generated by a run of the

ASTRAL Model. The minimum amount of output occurs when allvalues of DEBUG(J) are set to .FALSE..

The effect of a level 1 trace (DEBUG(l) = .TRUE.)

is best seen by a description of the output which emanates

from the individual subroutines.

I Subroutine Results

ASEPTL Prints messages tracing progressI through modules called by ASEPTL

RCVR Angles at receiver for each mode

COMPSI Water mass index,for each mode: phase velocity,upper and lower turning pointdepths, phase integral and rangeperiod, and the eigenfunctionvalues for each frequency-source-

i depth combination

SECTON For each propagating mode:angle at receiver, mode indicesfor slope-converted rays,accumulated intensity losses

SLOPE Mode limitsfor each mode and frequency:accumulated attenuation

HARCH Environmental indexPrevious and current bottom classindices, depths, water massin dices

Status of bottom class, water mass,depth, and any modules which makeparametric adjustments

iCOUPDW Sequential water mass index,

depth, and location; also, indicesof 1st surface reflected and 1st BR

I 3-8

U

cC.

c c

c4-)

I0cc ccccc cccocc

t-~~C- L-M l

c 0~ C y c C

cC c

c ccc cccc

z I

c. a C . *

Q cc c4.)

cc c 66oc 0 ..-:ý :

N c~l.

N. C .CC gc~

c Q -C

3 3-9

IIi I

II

JFt't TP. i T ( I r

IT yijnr v i i,r i); ?IV nFP,-1 1 0* 1f•. ! lfn fl.

1 " nno !)n. flgl.i 1 1 0nn. 1"o'ff.I, I Silo. 1,0•An ,.

• "! 700. riflflo.A. 1' 4 '•fl0*, 1c, Nlflo

7 A P. ?fl n ApfA.AI A al) . PfOP(I,

A' F FYcfiITrl, TI11F f(cFCrifllSn ) 1.177

IIII

Figure 3-3. Sample Output (Cont.)

III3 3-10

I

TO I'--, I ( It' I tic r

I (Pw

I 1.00 (,u. 7 o.4.1 14&.7 1.4.7 A4.7 1.4.7 #-4.7 64..7 4.4.7 6.4.7 6.4.7 44(.7

7 1A0.0A0 f) 4 ), O. s (a)A* Q;) . P* 2 A4*7 An.%) ( . 41. . . 7, 94.h (41.3 9) f?

,A.1~ "A? 0? *A 07 *. P0 1 .0 9 4.13 Q? .. 4 'UP . 01.0'1,. 91 .* 9P..? 9 ).#; 1)4.h

C;I ~A 09, '. :0 04.0 00,.7 4A* Lc; 1 ,RQ4U .* t7 .hIA .A* 04,4 '#4.h 46.4 9A 41

A 713A. IQcfl n7*3 10*4. 4r,7 ~. i 4 1" f,.47 . 07, O, 0 10- 0 " 9.4 104.0

I1 . I I 0A 1fA1 qo1 if.4UP. 6 0 1~ .;*1 0 16.1f, 1A3.7 L(,14)f ~~ 101Iq.0q% .7(A.3 10On.7CA~ . p () 17.q 4 .1 -C 4 ~1 01 -S.3A0. D 10.7 06.79 111.. (ai 4 QR.R .1)3 107.1

P-c .?)tAcU7 n. 19.AIA 1) .3 A? 1 (13 10.4 io. 1 11n4.0 101'.7 t-10.7 90.4 104.3 109.1

:,p 17. a ft 1?1.4 ~* 1 104.1 O. 104 0 Q. S. I 117n.4 )1 nA .)0N7*6101.3 10c... 1 104.11 PS7L..n 1?.1 104.7 IPO.4 1V40 17l,? Q. 0.C 1 03,. 7 11. 1?14. AU.]' 101.)701 1 o"; 1. 71"p -4 n .; A 1p7. II psi 110-4)n~ 0.3 139701c. 7 n. 1 Pk.a 1?.11 Q104 10?.! 107.1 113.0

17 '.1 ?~1 1 Piac7 1 .41I,.41 PS'.? 4PA.1 Ill.? jol.1 I iiu.r PI.O. 10041.704l.9 104.3 103.0

IC 4z71.1 11 P . 177. f4 14.?A~ 41A In,4 k I r1.a11&.! A 171.,A 107. 10?.. I107IA o.0 11P.1

I 1~ 4.:;? 17!. 1 10.0 1 ? 4. 1a.3 139,0 1 P-.9 Il. 110..?II 1ý.S I I P.- 101 .A-11,110, t..

10 471.41 1 ,A 7 .4 I&A.7 143.4 11 107.04 11'.iI' f?`k. 107.0. 1 0;.4 10.Q 11!).7

71 r 117.14.IA!IP.? 1 6410.9 130.4 Ifls., 101.*P 117.1 1 P." 1 147.7 1011.4 1 21.117.1P>1) -P. 7 1) 1 Pn .7IP .",* 1417. 1443.74 AI, 10M. 117. % )3*. 1 I'. n; 30.4 I 1).? I ~ 1?3.Q

x2 .&.f~i0 la.1 1).7.!3 14-a&. r j~,n. Iiii.n io7.4 )I-.n , .:'1.it 1.-, 104.4 1. 1Ar 7110.7

s, 7 tA .A )~A. '0. 1 10 A 1,1.4 1 O I.7t 1107.0 11CM.:A I Pik. .1 1037 04.0 ý 1.0 10 I'0f ) . ft

Pit or.A . A t )L1 ,l ''.4 1 1.P I ?p.0t 179.7 1047 . 11 hl-.$ )I?.$- 1' .t. 11ý. 4 1 04 .0 1)* IfI.Q 1';01.-%

Figure 3-3. Sample Output (Cont.)

1 3-11

y~~4I~Fr'TAfrTK -,LIIPF (P'At's)

NF;) 1 101: v

FNV t0( ,ýFMT rlofkrKý CtIMPArIYTI jnfF W T n(, PrNV r

2 1 P; . 1%Pnon.rý 4fl0. j~nonn

4 1 1 tn. Affl 7llfl.

rAqF FyFriITTM) TImF (SFCt)NAS1

Iiue33 apl upt(ot

3I1

III

TcP041KIAT1Or1 rnrF IMI111PCW nF 94A4ItF rTFPr

TP T ism Ic; I .nt- I. ovq

7r(rT) Inn. 100. 10nn 100. 410. 460. 4nf . 40(n. ROn. Poo. Ann, goo.3FIFn (H7) ?'. 1100. POO? . 400. 7?. 100. Poo. 400. ?c,. 10., 200, 40n.

1 1.0A 6.4.7 At.7 AA.7 0; 4,T 0;47 T .7 A4.7 hln.7 64,T7 64.7 0.7 14074AA 0 1•n .• Q1, .17 04.7 44.A 41 . lo 4 ). , 4? 44.h C41 .15 Q1.r, Q4o0 q4I . .7 U1 .Q 4,fl 0 ,6 '6 97'Ah . M 11.0 C)6•., 071 , Q1.7 Q1. 036.4 97,44 ( . 1 - G,3 .• 0.2 go 1 . .I o• .4 '4,1 40 .Q* QS . T * ,1 . 99.4

AI 144.7. Q07.? f)-.c 100.4 107. 1 f.7.P 10 7.0 Io.1 03 .? I 7.n1? I •? l lnn 4 O .p 0 9,.:, 10 1. 1 103* 4. 0 A I A.I •n . 1,). lnH.4 A 07.0 .0 100. 13. n 103.6

A> ;A .n7 10.1 i 13 I.? 10 0.3 0A. 1 101,0 104.1 t Q1 0A 9.4 10 1,A 1104.A

Q'17 71.4 . c; 9 109.? 0 '.A IO. 310h 5 .? iQpo4lop.7 114.1 114.? lfl.- O .15. j(6.AI

I A ;1 ý •.14 10 0-1 1•1.1 4 107 114l.4 101.3n 10-40 07P 4, & IQ.Q 1 (4 3 ? 0 14.9 l17,npp';.? I I An.;.) I nt.1 (14 .1 0 14, ? 10% 1 1 1 . ? ! n0 .3 S 101,? 101.4 10303 10.1

11 b .7 1 On. 6 I • n j4o 1 04. 6 1. 0.. 10o .o In. tlo . 110 .lo InI.9 I1.7 109.6 11n.I

I• .•711n• I?.?11•• IR.•10'.? lfl,.1 1n".0 1?03 O.M 1114.0 104.9 Q, 1?12.t

-- 1 4; 7, 1 Q:3 1 i10.3 IP1 ' 101II.3 101. .4 11 )n.1l; .10 fl•.7 104.9 113 .A4 -• 7 14 11'J,.k 104.1 1 17. 134PR 107.4 1101.7 1111 III.' 104.7 1 01f. 107.3 110.9

il *3n.27 17.6 107.7 11-4 .? 1 43 107,9 1 0..,R 113.0

1i 07 1 4L- .1 .1 111.14 I t.0 I I P11 .4 10 4 .1 111•. ? I I *A . II.I 1f'.7 103 ?1 4 1070A 113.3

IA I71".Tl 11c;.- I I. IA 11 . ?? sA 104.1)e • 1 n441 09.I 4 1", )6.7 !101.4 1 (17,? 1107 7 114.I

7i s• ~ n f°' 11j.Q Ina.1 1119A I;nPI OP14n f 14. -I 10.U 14. 0 104.4 I• 1 0-4.A 1(19.9 1)74

I

I I 1 At .1Ic ) I

7fe.-k 71t,.? 1 0 .;1 6 1 n, I IIA.I 1 n 9 IA PIjt.0 1 ,f P . t Ia I?(I1 :.A.lp IM - i o 16 0 1n .o Io' 01 14.)IA; .P (P" Fiur 3-3 111A 110,17P.c .S)Iar-.'3109.1 Oupu '%.$on;t.)r 444IL0 1. 7'

"I "'lIl *I1 1u 1;- 7 1117 1n- " ' v, ;7111M ;Ifl, n* ýP*1Aqu r. 11 .1 I ; .1 1 'r 1 3-M 1 30 . f -I1 & In ýIn , I1 ,PIpIkc 4 1IJ4 f1 : 4 0 ~ . Q4 1M 4 1 . , ,1f4 7 1n,? lp % I7ý1

I MIII'i:Ip or FmV I Vo-M ..TI A

jlMAAFl1ATr TP'ArC qj~oirtjrv; Po~fNFpA Tmnrv

PM YMW) TpC lF-MV IIFP

1n 1. Istnnn.

i A ?('f. I 10 A 0fl?o n ,?l I A(Wnon

4 ?7nl. jjll

A 1 1; Inn0. )Poo0fl.

I Figure 3-3. Sample Output (Coat.)

3-.14

I

QF cl 'L T --4zI 3I4tt A3 vY

PH'lJiF~P A~F 04te'f '4TF0SL

I TP4N'44T Cc(ft, I Pc7ýP(FT 1nA. 1In. Inn. 100. 400. 4010. 40n. 40. A0. Pon .00 R RON. AO0.iFP n V 17) 7 . 100. POO, 400l. Pr,. I 0(. ?(p . 4on . 29;. lo00. Pno . 4no.

T (PI*A)I I nn 1. 7 A4.7 AL .7 A4.7 A4.7 IA4* . 7 Ah.7 6 4.7 A 4*70, 04.7 T 4.7

P 20.n0 04.4 P41.j 1 l- .? 134 . sil.q AAA • 4.• 1 $;A. A 1410.7 QA. 0 A. 1A00 104.I

S1 . 0.7 UP1.?, P7.A PP1.7 1 Aq7* 47. 7 107. MR4 rl AM 10 .7 P 7.4 P7.6 A7.0 . R S.A

4 73:1.11 40. 1.P . 0 (Op*. 91.4 R4.7 14P.1 Q• OP Q3* 10. O £0.6 RQol Qo.0 91.1r I A.ff Q4 J. -4. M 93.I 41'o 0*.7 Q .97 91,? Q1. o Q I. 1 91.' 0.0

fin (I7?7.? WO,3 979. 04.7 Q7,0 .P .1 7 CW6.? 1 , ; o7A .l 10.) Q4. 0 o

A4 1 7F,.0 An P. Q Q7,6 06.7 97.7 Q-,.P 04 . c 04 t, 47.4 944. 7 0-4.4 94.9 C)7 , rtj P20,A 1114. 2 1PP. A 09q,6 QP.:% 97.1 04,*0 -~ . p 0,0~ 95.11 Q4. I 9A. 3 99.?1(3s ?;'A Aft 117.31 A01.o1 I0* ~fk &Iol f. 14 0,4U 07.7 (47.7 107.-A Q . -4 94,3 q7*p )oQ*Q

I It PA A. An 1 -4 A I Cý )f7.Q 149A.)114 n .&InIC . 4A.5~ 97 10.60..

1P '477A lo. i Af 10-0 1I.3 1071411.3 ) )n.cý0.4 1 V.107.7 1110.7 I of* C 103.1l?. 101.0

1• , Inn. 107.1 1 n4.7 107. 1.? 1 0. nQ.1 IPA.n 103.) 1)7,0 0.7 0 44.r 101.8 1 1.';

gI f,-41 )1 .? A. P 1013. 0 .1 3 04,7 q14, .7in 10 1.7 101. 743i'.0% 1"0.c Q3. 01.1 0. 1)4.10

77 71.71. '01.7 )I n044 PI .7 10..P nP .% qtl.aIA I0.4b 100.7 10 100.9 1)0.,

__ 7T Onf). 1 * l.7 10 .;)•). ,. 10.",7 n I ,7 I 1 117.3 I OR. 100., 107. 4 l I1..?

-I

-I PP iý- .7gur IP.3-h. ;) 113 Q4. rpl Oupu (in0 Cont71.) Qq1n117511

I

I 3-15

-I

mSubroutine Results

mode (new receiver phaseintegrals, range period orcycle distance, bottom grazingangle) for propagating modes

RCOMP Environmental index, range steps,range increment

m A level 2 trace is instigated by setting the

value of DEBUG(2) = .TRUE. In this instance, debug output

m (module by module) consists of:

INITAL Frequencies, bottom parameters,volume loss, conversion factor,tolerance levels, angle incre-men ts

EIGEN Geometric intensities, Irequen-cies, adn, Zdn, hcdn, zup' hcup,aup, eigenfunction values

TRACE Details of ray trace

COMPDW Source depths, depth normalizedeigenfunctions

DBTOIN Attenuation for each mode-freq.combination

INTSUM For each mode, frequency, sourceattenuated mode amplitude,source weighting

Ii DEBUG(3) = .TRUE., a raw transmission loss

curvm is printed. This curve is then inspected for dis-

continuities and smoothed, if necessary (see section on

subroutine SMOOTH). The smoothed transmission loss curve

is then printed.

m DEBUG(4) and DEBUG(5) are, at present, inactive.

m 3.2 ASEPS I/O

All 1/O to ASEPTL is through labelled commons.

Your types of variables are passed:

I 3-16

I

1 (1) User Specified Input - used by ASEPTL but

m never modified

(2) User Set Input - logical variables set by the

I user to indicate a condition (environment or

near-field bathymetry sector) which has not

been encountered on a previous run. Once the

condition is treated in ASEPTL, ASEPTL will

reset the logical variable so that in sub-

sequent encounters processed, saved (see

Type (3)) data will be used rather than re-

computed

(3) Processed Information - generated by ASEPTL

and required by ASEPTL for subsequent treat-

Sments of either a given sound-speed profile,

receiver, or near-field bathymetry section.

The user needs to do nothing with this other

than have it available

I (4) Output for the User - ASEPTL generated infor-

mation on propagation-loss for the user

The commons and variables described in Table 3-2 are all

that is relevant to the I/O process. The following notes

refer to the "Add'l Notes" column in Table 3-2.

1 1. This block contains input and computed receiver-

relevant data. When a receiver is being treated

for the first in a series of tracks, FRSRCVshould be set = .TRUE. (It will be reset to

.FALSE. in ASEPTL after processing.)

Im 3-17

I!

41

> 0 09.

c-oo h. 4' a 0 0

5. 0 v 4 >.o0 9. 0 ~

k4 v o x40 0 I 41 4 00l ; U. a 0 S 0 4 5.4

al0 0 tie 0 .C; 4 to 4

05'V 4 ' 0 0, .U

r.. 1. .0 a. 41900.40 0 .0 4)4 a - 0

V - ~ . Q 0 C -0 .

>0 sk 0 00 I.. Eba06- .4 0 44 4) 61 .0 0 4 s a a

co~~ 0.0 0 d94) to0 4'. U .0 A ' 00

q0 4 > .0 a a 0 16 ow at- 41o O>.4. 10 1.4 0 0 V 0 k0 .

caV 0 .' x0.4 4 U . A 05 00 fa aV

go 0 toa-44 0 0. N e4 1000 004. 00.4 to 0 .5.4-

0 Co. U)X

i E-4

00

U %1. "b

CO4 as

3I1

0 04 0

.m 00

k .b.. a W 0 . 4 0 tý A 4

0 VO 0.0 o

UC 41 .14 CO . 0 0 4-2

z - 0 0 0-

-7 Im IV NC . 0. 0)~ 03 '01 "455'0 v t)0 0. Om4

0 .0 0 v0 4 0 0 300 t

0 0 w xC .j t al 0 41

c 0. 60a

5-4 CO - 4C

01. 4) 4 ý 4 - -4

0 S. 0

m 0 Do0 0 00 4o. t.

x 009 a 2" ao 4) 0 0 cL 4)~ V- 4)6.64Ct.N

P4IIC3-1

Ie

NI l C

.4 0 0~

IN a .4

o 0 r D.V4 %4 9

A '04

aV

0 %4 41 .4 O -0 bo 441.s a W . 4:0iC

E .0

aa4 0

E-4~z

14hIm

3-20

II1 2. This common controls the near-field bathymetry

data (8 or fewer sectors) specified in terms

of the NFB slope intercept at zero range (not

necessarily the receiver depth), the slope

and its extent, and the bottom class on the

slope (with special option BC = 0 for perfectly

reflecting at all angles). Information for

this sector is computed and stored in /RCVNFB/.

I 3. This logical variable indicates whether (=.TRUE.)

or not (=.FALSE.) this is the first time this

NFB sector has been encountered. If it is,

the data in /RCVNFB/ will be computed and

FRSNFB set to .FALSE. If not the data will be

used.

4. This block contains corhputed receiver data

relevant to each near-field bathymetry sector

(the index dimensioned 8). MUP and ATUP are

treated internally (once INFB has been set)

as two arrays MUPDN (2,25) and ATUPDN (6,2,25)

through subroutine calls to avoid the CDC

* restriction on four-dimensional arrays.

3 5. This common contains the environmental de-

scriptors as they occur sequentially alongthe track. The track is divided into "envi-

ronments," I, beginning at RENV(I) and endingat RENV(I+l) except for the last one - I =

NENV which persists indefinitely - i.e., untilRMAX), A new environment occurs whenever the

water mass. depth, or bottom reflectivity

chatges.

II 3-21

I

1 6. INDEX(I) is the index in the water-mass arrays

in /ENVS/ and /PRCENV/ for this environment.

Note that the water masses may be in any order

in these commons. INDEX(I) controls their

m order along the track.

7. The variable dimensioned-20 - in this common

refers to a given water mass. When a water

mass is encountered for the first time a number

of properties of the modes will be computed

and stored in variables in /PRCENV/. When

this environment is encountered again these

stored parameters will be used.I8. IFPRE tells ASEPTL whether the mode properties

for this water mass are available (=.TRUE.)

or not (=.FALSE.) When a track is set up

for input to ASEPTL this should be set to

.TRUE. only if the corresponding mode infor-

mation is put into the corresponding parts

of /PRCENV/. ASEPTL will set to .TRUE. after

first processing.

9. This block contains the processed information

3 for each water mass (index dimensioned 20).

These data must be provided in the appropriate

location (INDEX(K) if IFPRE (INDEX(K)) =

.TRUE. Otherwise they will be computed.

m 10. This array is treated internally (for a given

value of INDEX) as a three-dimensional array

XPHINF (6,3,25) passed through sVbroutine calls

to avoid the CDC restriction on four-dimensional

3 arrays.

3 3-22

I

S11. This block contains the source depths and

frequencies for the TL computations. All

combinations (Zs*f) are computed. If Zs=O

two incoherent paths (at the surface) are

assumed for computing noise, equivalent to

60-foot incoherent TL(R). For future refer-

ence a shallow (-20 foot) coherent source

should probably be used but with modified3 surface ship source levels. The Zs=O result

should be appropriate to present source

-nlevels.

12. The user specified max range step between

computed values of TL(R) (suggested as -30

miles) will be used except for the first

range interval from 1 nmi to the end of the

nearfield bathymetry sector. Here the step

* might be larger.

13. The TL(R) computation might terminate beforeRMAX (due to loss of energy, etc.) but never

* beyond.

14. IEND will indicate the reason for terminating

the TL(R) computation as follows:

IEND Reason

1 4Max range (RHAX) reachedwithin 0.5 nmi

2 Max number of range points

(NRMAX) reached

3-23

I IEND Reason

I 3 All modes attenuated below

threshold

4 Upper-bound on best possible

TL exceeded (irreversibly)

5 Computed TL exceeds TLMAX

from last range on.

I The Input and Output from a user-oriented point of view are

summarized in Tables 3-3 and 3-4, respectively.

IIII

IIII

! 3-24

I

TABLE 3- 3

I NPUT SUMMARY

I ZRTEBRC

FRSRCV Set - .TRUE. First Time (ASEPTL sets - FALSE.)

If FRSRCV a .FALSE. Make Available

On RUIN, THR, DSTHR

3 ~ZNFBZ( INI'E)

THNFB( INF)

ENFEC INFB)I ~IBCNIB( INFB)

FRSNFB(INIFE) Set - .TRUE. For First Treatment of Sector

(ASEPTL sets a .FALSE.)

If PRSNPB(INFB) - .FALSE. Make Available3 MUP(l, INFB). ATUP(1, INFB)

INDE(I). 1.1, NE.N

RENV(I). DEP(I). IRC(I). 1-1. NENV

NZC(INDEX(I))

ZEJ.INDEX(I)). J-1,l. XZC(INWEX(I))

3 IVSTEC INDEX( I))

IFpRE(INDEX(I)) Set a .FALSE. For First Treatment of Water

Mass (ASEPTIL sets v RU.

I ~If IFP'RE a .TRUE. Make Available

MSURP( INDEX(MI --. SULFS( 1 1. ~NLZ J M)

IMS

ZS(K). Col -qzS

F(C). X-1.

3 3-25

TABLE 3-4

OUTPUT SUJMMARY

II*~I END

RANGE(I), I=1, IR

I ~AMJM(I,J,K), K~l, NP; J=1, NZS; I=I, IR

I

3.3 SUSPENDED RECEIVER OPTION

While ASTRAL is designed primarily for predictions

for bottom-mounted receivers, a suspended receiver over a

locally flat bottom may be invoked by proper setting of the

following input parameters:

"m ~In RCVIN

ZNFBZ Set to water depth at receiver

THNFB Set to < - 1.5 (e.g. -2.0)

RNFB Set to 2.0

IBCNFB Irrelevant

In TRAKIN

THBRC Set to < - 1.5 (e.g. -2.0)

By setting THNFB < - 1.5 the front-end ray trace is skipped

and the depth functions are computed assuming the water depth

is = ZNFBZ.

Note - this will over--ride the depth specified for the firstIenvironment (DEP (1)) in computing the loss at 2 nm. DEP (1)

will be used from 2 nm to the next depth change. By setting

THBRC < - 1.5 all modes are included. Note that THBRC is

used after the ray trace (which is done for all ray up- and

down-going ray-equivalents explicitly by skipping) to eliminate

ray-equivalents shallower than the assumed immediate slope.

Hence, for example if NFB = -2., but THBRC a 0.0 only the paths

leaving the receiver at positive angles will be included.

For a suspended reciever over a locally sloping

bottom, the local slope should be defined by ZNFBZ,THNFBZ,

etc., in RCVIN, and THBRC set < - 1.5.

3-27

Finally, there are instances when a receiver may

be bottom-mounted but the user wishes to include interface

effects. This may be done for some cases, approximately,

by use of the existing input options. If the receiver was,

in fact, at the zero-range depth of the near-field or local

slope (i.e. if ZR=ZNFBZ), then by suspending the receiver

a small distance above the slope (e.g. reset ZR to ZNFBZ -

10 ft. and set THBRC <- 1.5) paths downgoing into the

slope will be reflected immediately (with losses governed

by IBCNFB). This approach cannot be used if ZNFBZ is

substantially different from ZR. A preferable approach is

to add an effective vertical "beam pattern" at the receiver

(in terms of 6R) directly into the code in subroutine SLOPE.

This allows all the flexibility of the present approach plus

a receiver response independent from the near-field re-

flectivity.

3-28

Ii

i

REFERENCES

1. C. L. Baker and C. W. Spofford, The FACT Model, VolumeII, AESD TN 74-04, December 1974.

2. C. W. Spofford, The ASTRAL Model, Volume I: TechnicalDescription, SAI Report No. SAI-79-742-WA, January 1979.

ii

i

IiI

IiI

I

* R- 1

i

I Assistant Secretary of the Navy Commander(Research, Eng. and Systems) Naval Electronic Systems CommandDepartment of the Navy Naval Electronic Sys Command HdqrsWashington, D. C. 20350 Washington, D. C. 20360Attn: G. A. Cann 1 Attn: PME-124 1

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