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"TI1C FILE COPYQ

SRL-0002-TM AR-005-341

o DEPARTMENT OF DEFENCE

S• DEFENCE SCIENCE AND TECHNOLOGY ORGANISATION

SALISBURYI SURVEILLANCE RESEARCH LABORATORY

SOUTH AUSTRALIA

TECHNICAL MEMORANDUM

SRL-0002-TM

THE CALCULATION OF GROUND WAVE ATTENUATION IN THE HF BAND

USING PROGRAM WAGNER

DTIC R.M. THOMAS and A.O. ZOLLO

SELEC-1OCT 3 11988~

•÷s• D

Technical Memoranda are of a tentative nature, representing the views of theauthor(s), and do not necessarily carry the authority of the Laboratory.

S! .• ' ;,, c r' ;- -ur*:.z :elecso

Approved for Public Release

COPY No. 32 DECEMBER 1987

U . ___ I

UNCLASSIFI0D

AR-005-341DEPARTMENT OF DEFENCE

DEFENCE SCIENCE AND TECHNOLOGY ORGANISATION

SURVEILLANCE RESEARCH LABORATORY

TECHNICAL MEMORANDUM

SRL-O002-TM

THE CALCULATION OF GROUND WAVE ATTENUATION IN THE HF BANDUSING PROGRAM WAGNER

R.M. Thomas and A.O. Zollo

SUMMARY

We p-:esent computational test results from a doubleprecision version of the FORTRAN program 'WAGNER'. Thepotential value of this integral equation technique is itspurported ability to model propagation losses overtwo-dimensional paths through irregular and inhomogeneousterrain, However the numerical integration algorithm canbe affected by poor convergence and inaccuracy,part:.culrrly at frequencies above the MF band. We haveinve:stigated these properties in terms of selected keyparameters and have derived empirical criteria governingconvergence and physical accuracy. We find thatcalculations of basic transmission loss using WAGNER aresubject to significant limitations at HF frequencies asICthe terrain becomes irregular and as the conductivity anddielectric constant of the ground both become smaller, ZpE1', /On the other hand, the shadow loss due to an obstacle maybe reliably calculated by WAGNER on the assumption thatshadow loss is independent of ground electricai constants,thus permitting the use of dummy values of conductivityand dielectric constant to ensure that the physicalaccuracy criterion is satisfied. t -

DSTOAPOSTAL ADDRESS: Director, Surveillance Research Laboratory, -des

PO Box 1650, Salisbury, South Australia, 5108.

UNCLASSIFIED

SRL-0002-TM

TABLE OF CONTENTS

Page

1. INTRODUCTION 1

1.1 The program 2

2. TEST TECHNIQUES 3

3, RESULTS 3

3.1 Convergence 3

3.1.1 Elfect of path length and frequency 33.1.2 Effect of terrain gradient 43.1.3 Effect of ground ele:trical constants 4i.1.4 Convergence criterion 4

3.2 Accuracy 5

3.2.1 Effect of path length 53.2.2 Effect of terrain gradient and frequency 53.2.3 Effect of ground eiectrical constants 63.2.4 Accuracy criterion 6

3.3 "Pathological" behaviour 6

4. DISCUSSION 7

5. CONCLUSION 8

REFERENCES 10

LIST OF FIGURES

1. Calculation of basic transmission loss for the path given by Ott(figure 1, reference 1) 11

2. Convergence behaviour for 20 km path over smooth spherical Earth 12

3. (a) Maximum path lengths and step sizes for convergence at a givenfrequency (b) Maximum frequencies and step sizes for convergenceover a path length 13

4. Relationship between maximum terrain slope ind maximum frequencyfor convergence at a step size of 100 m 14

5. Accuracy of WAGNER for path with 500 m high hill, compared wlIh .knife-edge estimated loss 15

6. Dependence of accuracy on ground electrical consta.,E 26

7. Maximum frequency for accuracy in terms of Pro-ud electricalconstants and terrain slope 17

"YZ 8. Comparison with observation of diffarert Galculations of shadowloss 18

AM-i

- 1 - SRL-0002-TM

1. INTRODUCTION

Ott(ref.1,2) has formulated an integral equation technique for the calculationof ground wave propagation losses ovcr paths characterised by irregularterrain and varying electrical ground constants (conductivity and dielectricconstant). The calculation is performed by step-wise numerical integrationalong the transmission path of the sum of a c.rect ray and a ground-reflectedray, and is coded in the FORTRAN program 'WAGiER'.

References 1 and 2 presented example calculations at frequencies between I and10 MHz showing results which are consistent with those obtained usingalternative methods. Generally favourablL comparisons with selectedexperimental measurements were also presented in references 3 and 4,indicating the reliability of the technique. The technique is however subjectto certain qualifications, for example:

(a) the teclhique is spatially to-dimensional and treats only propagationalong the great circle path betwe3n two antennas, neglecting side- andback-scattered radiation;

(h) care must be taken to ensure that the integration step length isiuffLoiently small to enable the solutien to converge; however too small artep length will lead to excessively large prcgram execution times:

(c) a frequency-coupled limitation exists on th- maxi-num gradient of pathterrain which may be tr3ated accurately; tnis "heuristic uncertaintypr~nciple"(re2.1) is given as

jy'j f < 10

where y' is the gradient and f is the frequency in MHz, and shows that agradient of 0.25 sl.ould return acclratek loss calculations throughout the HFband up to a iuaximum frequency of 40 M}Hz;

(d) accuraty can be machine dependent, with small wordlength machinesincreasing the susceptibility to round-c.ff errors unless double-precisionfloating point arithmbtic is used.

(c) computations are subjezt to poorly understood numerical instabilityunder .ertain conditions.

However, the potential advantages of the technique appear to outweigh thedisadvantages. Within the constraints of the *'heu:istic uncertiintyprinciple" it .hould be possible to treat a path havLng an irbit,:ery terrainprofile and include variations in ground ele-triral constants, for examp~eacross a coastline. Reliability in such a cal,.ulation could permit asignificant reduction in the need to perform propagation experiments in thefield, with consequent savings of t-ie, expense an' manpower. While theresidue series eapansion method(ref.3.6) provides a reliable and qui~h meansof calculating losses o',er smooth, homogeneoui. terraiii it is unable t-,)accommodate terrain irregularities, in contrast to WAGNER.

Alternative techriques for the esiimaticn of losses due to terzoinirregularities are based on knife-edge 4 iffraction. Bullinjton(ref.71presents a chart. from which it is possible graphically to estimate theattenuation caused by c single knife-edge located betweea two antenian in freespace, Its adaptation to the case of a single knife-edge on the surfact of asmooth spherical Earth has resulted in a :hart which gives the shadow lcs- ofthe obstacle with respect to qmooth, sphericai homogeneous Earth ground wale

SRL-0002-TM - 2 -

propagation, and has been verified experimentally(ref.8). Multipleknife-edges are not accommodated, however, and must be treated by othertechniques, such as WAGNER.

We point out that wbile e hill may be conveniently modelled either by aGaussian profile or Ly a knife-edge for ths purpose of calculating waveattenuation, results differing by several decibels are likely to be obtainedfrom the two methods, particularly in close proximity to the hill. However,the results of Ott(ref.l) indicate that such discrepancies diminish withdistance and become unimportant at distances exceeding on the order of 5 timesthe l/e full width of the hill. We therefore believe that with thisqalificatior, compariscns between Gaussian and knife-edge profiles may bumade.

1.1 The program

The mathematical details concerning the integral equation for ground waveprcpagation over irregular and inhomrogeneous terrain have been described byOtt(ref.l,2) and will not be repeated here. The solution to the resultinglinear Volterra integral equation is solved by the method of Wagner(ref.9),whence the ritlc of the computer program. This solution involvessubdivision of the transmission path into steps of the order of awavelength in size and a summation in signal strength over all subintervalsalong the path. The techniques involved in obtaining the numericalsolution are zon-tiivial and at this time a formal error analysis of theprocedure apparently has not been made. It is certainly beyond the scopeof this report. Consequently the user of WAGNER faces a lack ofinformation on such matters as the convergence properties of the techniqueand the accuracy with which it models transmission losses, particularlywithin the HF band.

Our version of WAGNER was originally coded in single-precision but has beenconverted to double-precision to reduce round-off errors., Named W5D, it iscompiled under VAX FORTRAN version 4.5 and runs on the HF Radar DivisionVAX 8200 under the operating system VMS version 4.4. We have tested theprogram for the case presented in figure 1 of reference 1, that is, a

frequency of 1 4Hz, ground conductivity of 0.01 S mi1 , dielectric constantof 10, an otherwise flat path of length 15 km containing a Gaussian hill ofheight 1 Im located at a distance of 5 km from the transmit antenna. Theintegration subinterval cr step size used in reference 1 is not specifiedbut our work employed s step size of 100 m. The antennas are verticallypolarised and located ad, ground level. The resulting basic transmissionloss is graphed as a function of distance along the path in figure l(a).ASreement with reference I is excellent, validating our version of theprogram at this frequency in the MF band. Note that the data inreference I are pr-tsented in terms of the amplitude attenuationfunction (f) with respert to twice the free space field which is related tothe amplitude basic transmission loss Lb at wavelength X, between isotropic

antennas separated by a distance x, a(-cording to

S= 2f

Our calcu'&tions are presented in ter,,s of basic transmission loss indecibels (dP). Lossb• ere reprrsented by negative .aumbers. The executionzine require* to prodice the rosults of figure 1(a) was 250 s. In general,execution time varies aa the square of the number of integration steps.We point out that at 15 km the shadow loss resulting from the hill is about-10 dB with respect to smooth, sphec¢cal Earth propagation, in excellentagreement with the graphical estimate from refcrence 8. However if we move

- 3 - SRL-0002-TM

out of the MF band into the HF band we encounter problems. Figure l(b)shows results for a frequency of 10 MHz, all other parameters remainingunchanged. It indicates that the shadow loss of -10 dB at 1 MHz has at10 MHz been transformed into a gain of +41 dB. Since in this case theknife-edge technique graphically predicts a shadow loss of -18 dB, it isclear from the discrepancy of 59 dB that WAGNER has broken down.

2. TEST TECHNIQUES

Our initial attempts at applying WAGNER to real terrain at HF frequenciesproduced resalts such as figure 1(b) which were obviously in error. In viewof the difficulties involved with a formal error analysis it was decided -r-arry out an "experimental" study of the intervals in certain key parametersfor which the results of WAGNER could be relied upon. The aim was to developempirical or heuristic "rules of thumb" which could be applied to predictwhether a proposed calculation would be successful ot not.

The key parameters selected for thlis study were integration step size,frequency, path length, terrain slop,,, ground conductivity and dielectricconstant. The question of the reliability of any calculated result has twoaspects. Firstly it is necessary to know whether the calculation has arrivedat the convergence limit in the mathematical sense. Since the program doesnot iterate on the integration step size by testing the ditference betweensuccessive loss calculations, it is not possible to know "a priori" how farany given result deviates from its convergence limit. Secondly, successfulmathematical convergence of an algorithm does not necessarily produce acorrect answer from the physical viewpoint. It is therefore necessary tocompare each convergent solution with the loss estimated using an independentmethod for example the residue series expansion algorithm, in the case of asmooth Earth, or the graphical knife-edge method in the case of a singleterrain obstacle. Thus we aim to produce two criteria, one describing theconditions necessary for convergence and the other similarly specifyingphysical accuracy.

Both convergence and accuracy were mapped at regular grid points in the spaceof the integral equation's key parameters, Calculations of basic transmissionloss were carried out with uniformly spaced integration steps ranging down insize from 1000 to 10 m, at frequencies between 1 and 30 MHz, path lengths from10 to 100 km, terrain gradients from 0 to 3, ground conductivities from 0.001

to 0.1 S m'1 and dielectric constants from 1.1 to 100.

Two types of terrain were employed, a smooth spherical homogeneous Earth ofeffective ridius factor equal to 4/3 and a single Gaussian hill based on theterrain of figure 1 but permitting variable hill heights and ground electricalconstants. Note that the maximum gradient of terrain is given in this case by

MR- approximately 10" times the hill height in metres.

3. RESULTS

3.1 Convergence

3,1.1 Effect of path length and frequency

Basic transmission losses were calculated ovet a rxaoth spherical Earthat path lengths L 10, 20, 50 and 100 km using integration step sizesAx ranging from 1000 m down to 10 M. A ground conductivity

0.003 S m 1 and dielectric constant K = 3 were used at each of thefrequencies f 2, 10, 20 and 30 MHz. The results for L = 20 km are

SRL-0002-TM -4-

given in figure 2 in comparison with the residue series expansionresult. It is evident that at 2 MHz a step size in excess of 1 km isadequate for convergence, while at 30 MHz the required step size hasshrunk dramatically to only 10 m.

These results are more conveniently shown In figure 3 which reprerentstwo orthogonal planes through the 3-dimensional space of step size,frequency and path length, showing the boundary of ;he volume within

Swhich the oasic transmission loss has converged to within i d1flFigure 3(a) indicates an approximately inverse relationship Detween pathlength and step size for a given frequency, while figure 3(b) indicatesan approximately inverse square relationship between frequency and stepsize. We can therefore state an empirical convergence criterion in theform

Ax < kX2 (1)

where ), is the wavelength in metres, Ax is in metres and L is in km, andthe constant k is yet to be found.

3.1.2 Effect of terrain gradient

Real terrains exhibit slopes which vary from approximately zero for flatground to very large values fjr almost sheer cliff faces. Largegradients wL.' not normally be associated with Gaussian hills sincemechanical stability considerations are likely to ensure that overgeological time-•caies the slopes of hills would settle towardsequilibrium values of fairly modest size, say 0.5 or less. In spite ofthis, we have found it convenient to examine the influence of terraingradient over a large range of values by making use of idealisedGaussian hill geometries and assuming that similar slopes will havesimilar effects on the performance of WAGNER, regardless of the type oftopography involved. This appzoach follows the lead of Ott(ref.2).

The geometry employed for this study was based on that used for figuze 1but with the Gaussian hill height varied up to a maximum of 3000 m,corresponding to a maximum gradient Iy'j -3. Figure 4 relates valuesIy'I, and X which just produce convcrgence with a step size Ax = 100 m.A quadratic curve which conveniently fits the data points isdescribed by

S= 18 (81y'1 2 - 21y'l + 1) (2)

3.1.3 Effect ,F ground electrical constants

It was found that the parameters grou:nd conductivity o and dielectric

constant K have a negligible effect on convergence.

3.1.4 Convergence criterion

We may use equation (1) to write the condition for convergence as

X> Lt-x f(lY'l) g(-,k),

I - 5 - SRI-0002-TM

where the function g is identically unity (Section 3.1.3) and thefunction f equals unity for a slope of zero. For non-zero slopes,comparison with equation (2) shows that k = 4.6 and f = 81y'1 2 -21y'1+l.If we conservatively adjust k downward to k = 2, providing a safetymargin of about a factor of 2, we arrive at our convergence criteriongiven by

Ax < 2X2L'(81y'J2 - 21y'I + 1)-' (3)

where Ax required integration step size in metres

S= wavelength (10 < X • 30C m)

L = path length (0 i L , 100 km)

yII= maximum value of terrain slope along the path(0 : ly'l 5 3)

Being an empirical result, equatton (3) holds only approximately withinthe tested parameter volume and cannot be guaranteed to hold elsewhere,

3.2 Accuracy

The existence of mathematical convergence is no assurance of physicalat~curacy. Therefore we varied parameters within the constraints ofequation (3) in order to investigate how closely the convergent results ofWAGNER agreed with basic transmission losses calculated by alternativemethods, namely the residue series expansion for smooth Earth propagation,and the graphical knife-edge technique for single-hill terrains.

*- 3.2.1 Effect of path length

It was found that for smooth spherical Earth propagation, WAGNER alwaysSccnverged to within 0.1 dB of the value of basic transmission loss

predicted by the residue series expansion. This result appeared to holdeverywhere within the same vclume of parame'.er svaee as was used for theconvergence study. in particular, path length variations appeared notto affect the accuracy of the final result, provided convergence hadbeen achieved.

3.2.2 Effect of terrain gradient and frequency

Figure 5 shows how the accuracy of WAGNER varies with frequency in theF case of a 500 m high hill located 5 km from the Tx antenna along a total

path of 15 km, with a = 0.01 S m-1 and K = 10. Thc convergent values otbasic transmission loss are plotted and comparea with the loss forsmooth spherical Earth terrain and with the eddition of the shadow losspredicted by the knife-edge graohical technique. It is evident thatthere is agreement up to a maximum frequency of only about 2 MHz andthat above 5 Mf{z WAGNZR incorrectly predicts a ohadow gain with respectto smooth spherical Earth propagation, rather than a shadow loss.

This result and those of similar calculations for hills up to 3000 a inheight, corresponding to terrain slopes Iy'I up to about 3.0, indicatethat accuracy is governed by a condition of the approximate form

ly't f < 1 (4)

-- _ • i• • • • ••j •--- • -'• • -''•-''•'" - •,. • - _ A-

SRL-0002-TM - 6 -

where f is the frequency in M11z. This contrasts strongly with the"heuristic uncertainty principle" proposed by Ott (see section 1 above).Whereas Ott's result for ly'I = 0.25 predicts accuracy up to a maximumlimiting frequency of 40 MHz, our equation (4) limits this maximumusable frequency to only 4 MHz.

3.2.3 Effect of ground electrical constants

Figures 6 and 7 present the results of a study of tite effect of groundconductivity a end dielectric constant K on the accuracy of the integralequation solution. Figure 6 is drawn in terms of shadow loss (or gain)versus frequency for different choices of the ground constants and for aterrain slope of 0.25, It shows that WAGNER agrees best with theknife-edge prediction over the 1 to 30 MHz frequency interval when theground constant values are highest. In particular, for the low valuesof ground constants applicable to the Alice Springs region

(c = 0.003 S m' 1 , K = 3), a terrain slope of 0.25 can be accuratelymodelled up to a maximum frequency of only 2 MHz. Calculations foradditional terrain slopes resulted in figure 7, showing the maximumfrequency which can be accurately used as a function of the groundconstants.

In general, a and K vary roughly in proportion to each other accordingto ground conditions and we find it convenient to treat the product oKas a single key parameter. Plotting its square root as in figure 7permits the data to be represented on a more compressed horizontalscale. The results of figure 7 indicate that the maximum frequencywhich can be used in order to obtain accurate results is inversalyproportional to the terrain slope (in agreement with equation (4)) andapproximately proportional to the fourth root of the product oK.

3.2.4 Acr.uracy criterion

The above results lead to an empirical accuracy criterion given by

ly'l f (oK)" 1.8 (5)

In the Alice Springs region we may have typically ly'l-0.25,

0-0.003 S m'1 and K-3, implying that accurate basic transmission lossresults can be obtained up to a maximum frequency of only about 2 MHz.In this case therefore, WAGNER cannot be used to calculate basictransmission losses at frequencies in the HF band.

Alternatively, equation (5) shows that at a frequency of 10 MHz in theAlice Springs region, accuracy can be assured only for terrain slopesless than about 0.06 or an elevation 7hange of 60 m over a distance of1 km. Thus our version of WAGNER appears to be limited to lowfrequencies and gentle terrains, if basic transmission loss is to becalculated with acceptable accuracy.

3.3 "Pathological" behav.oui

While the results described above are disappointing in terms of possibleapplications of WAGNER in the HF band, they nevertheless indicate a smoothand regular variation with : espect to the key parameters, Howeveroccasional sharp departures frcm this predictable behaviour have beenobserved. For example, in the case of smooth spherical earth propagation

at 10 MHz, with a = 0.003 S m', K = 3, L 100 kin, and Ax = 100 m, the

S& - 7 - SRL-0002-TM

calculated basic transmission loss appeared to be converging as expected.However further reduction of the step size to 5 m surprisingly prrduced asharply divergent result for distances in excess of 50 km. Additirnalreduction in step size then led to a recovery with convergence finallybeing achieved for Ax = 20 m.

The user is warned of the possibility of occasional rare occuriences ofthis type. One safeguard is to always examine the trend of the basictransmission loss as a function of distance along a path, lcoking forirregular behaviour.

4. DISCUSSION

The results of Section 3 above show that even when a calculation by WAGNER ofbasic transmission loss has converged to a stable value, the result remainssubject to a severe physical accuracy constraint which renders our version ofWAGNER almost useless in the RF band. This is particularly so when the groundelectrical constants have low values, as In the case of the arid desertenvironment surrounding Alice Sprin,.s.

However in many applications the total basic transmission loss may not be therequired variable. It may suffice to calculate only the shadow loss (relativeto smooth spherical Earth propagation) due to one or more terrainirregularities. Since shadow loss depends mainly on topography and verylittle on the electrical constants of the terrain, it may be possible tocalculate shadow loss by using "dummy" values of conductivity and dielectricconstant which are chosen to be high enough to ensure numerical accuracy(equation (5)). The program cold be run first for the terrain underconsideration and then for a smooth spherical Earth, and the first resultdivided by the second in order to obtain the shadow loss., If shadow lossdepands only on the frequency and on the geometrical dimensions of theobstdcle, a reliable result should be obtained, with the dummy groundconstants being self-cancelling. For the case of a sing)e obstacle thisresult should agree well with the graphical estimate using reference 8.In the. case of arbitrarily complex terrains WAGNER alone possesses thepotential to produce believable shadow loss results, subject to theconstraining equation (5).

We are able to demonstrate the usefulness of this approach. Figure 8 comparesthe shadow loss predicted by the knife-edge technique with two results fromWAGNER, firstly a single Gaussian hill approximation to the terrain andsecondly the actual terrain interpolated into intervals equal in size to thespecified integration step size Ax., The WAGNER calculations were carried out

for a dammy conductivity of 50 S mi and a dummy diclectric constant of 500.A]so shown are actual shadow loss data measured over this path. Thecalculations using the actual terrain profile agree best with the observationsat the lower frequencies but tend to overestimate the loss above 15 MHz. TheGaussian profile piedicts a frequency variation of shadow loss which is notmatched by the rather flat variation of the observations. The graphicalknife-edge estimates also fall away with frequency rather more rapidly than isactually measured, but are nevertheless in fair agreement. Application of the

H technique to other paths has also been generally successful(tef.8).

The above results indicate that shadow loss in the HF band may be reliablyobtained from WAGNER provided firstly that the otonvergence criterion issatisfied, and secondly that the accuracy criterion is satisfied by using highdummy values of ground conductivity and dielectric constant. That the methodproves to be satisfactory relies on shadow loss being largely independent ofground electrical constants.

SRL-0002-TM - - 8 -

5. CONCLUSION

In the absence of any reporced theoretical analysis, we have empiricallyderived heuristic criteria which govern the convergence behaviour and physicalaccuracy of Ott's integral equation approach to the calculation of ground wavepropagation losses over irregular and inhomogeneous terrain. We have foundthat for irregular terrain the existence of mathematical convergence does notnecessarily imply a physically accurate calculation.

The computer program WAGNER which implements the integral equation calculationhas been tested for homogeneous ground by varying selected key parameters overintervals pertinent to ground w~ve propagation work being carried out inconjunction with HF radar studies. These parameters and their test intervalsare as follows:

Integration step size (uniform) Ax : 10 to 1000 mFrequency f : 1 to 30 MHzPath length L : 10 to 100 kmTerrain maximum slope ly'I . 0 to 3.0

Product of ground conductivity (o K) : 101 to 104 S m"'and dielectric constant

The following heuristic critezia weze found to govern the mathematicalconvergence and physical accuracy of the calculated basic transmission less.

Mathematical convergence:

Ax < 2).2L '(8Jy'J 2 -21y'l + 1)"'

Physical accuracy:

ly'l f (oK)-i < 1.8

It is stressed that the empirical origin of these expressions means that theyare not unique and their validity cannot be guaranteed outside the testedparameter ranges specified above.

While our results confirm the usefulness of WAGNER in calculating basictransmission loss near a frequenzy of I MHz, they demonstrate serious accuracydifficulties at higher frequencies. In the case f = 10 MHz, Iy'I = 0.25,

a = 0.003 S m-1, K = 3 and L = 20 km, mathematical convergence way be achievedproided the integration step size A:- is reduced to about 100 m. On theHF Radar Division VAX 8200 running under the operating system VMS version 4.4and using VAX FORTRAN version 4.5, the execution time for this calculation isapproximately three minutes. Convergence is therefore not a difficulty exceptpossibly at the high extremes of terrain slope and patn lUngth when small stepsizes and hence a large number of steps are required. Since execution timevaries as the square of the number of integration steps such a calculation mayrun for many hours, but convergeuce will ultimately be reached. On the otherhand, physical accuracy appears as a much more eerious problem and basictransmission loss over the above path can be modelled by WAGNER to an accuracyof better than 3 dB only for frequencies below 2 MHz. The presence ot hills

- 9 SRL-0002-TM

of only modest size therefore effectively precludes the use of WAGNER for thecalculation of basic transmission loss in the HF band. This result does notappear to have been spelt out by the authors of previous reports dealing withWAGNER.

If it is desired only to determine the relative shadow loss at HF due toirregular terrain along the path, it is feasible to perform the integralequation calculation using unrealistically high ground electrical constants inorder to guarantee physical accuracy and then compare the result with thesmooth spherical Earth calculation carried out with the same parameters. Thedummy electrical constants effectively cancel themselves out in the processand therefore do not affect the derivation of the shadou loss. Thedemonstrated viability of this technique permits WAGNER to be used at HF forarbitrary multiple hills, which are not easily treated by the graphicalknife-edge technique.

Importantly, our condition on physical accuracy is in disagreement with thecondition given by Ott(ref.l). Whereas Ott's condition implies that terrainslopes of the order of 1 in 4 can be treated throughout the HF band up to amaximum frequency of 40 MHz, we find that our upper frequency limit is

actually 4 MHz, assuming a = 0.01 S m" and K = 10; the HF band is thereforeeffectively excluded from calculations of basic transmission loss unlesslarger values of a and K can be employed.

Finally, we emphasize that the results presented in this report were obtainedusing our double-precision version of WAGNER, locally known as W5D. It ispossible that more robust versions of WAGNER have evolved elsewhere. Everyeffort has been made to acquire versions currently in use in other parts ofthe world but without success. However this effort is continuing. Theauthors will be happy to supply a copy of WSD upon request.

5.

_t

MA

SRL-0002-T - 10

REFERENCES

No. Author Title

1 Ott, R.H. "An Alternative Integral Equation forPropagation over T,-egularTerrain, II".Radio Science, 6, '.29-435, 1971

2 Ott, R.H. "A New Method for Predicting HF GroundWave Attenuation Over Inhomogeneous,Irregular Terrain".OT/ITS Research report 7, Office ofTelecommunications/Institute forTelecommunication Sciences, Boulder,Colorado, 1971

3 Ott, R.H., "Ground wave Propagation overVogler, L.E. and Irregular, Inhomogeneous Terrain:Hufford, G.A. Comparisons of Calculations and

Measurements".US Department of Commerce, NTIA ReportNo 79-20, 1979

4 Hill, D.A. "HF Ground Wave Propagation overForested and Built-Up Terrain".US Department of Commerce, NTIA ReportNo 82-114, 1982

5 Bremmer, H. "Terrestrial Radio Waves".Elsevier, 1949

6 Forbes, A.M. "GWAVE - A Fortran IV Program forGround Wave Propagation over a UniformEarth, at Frequencies from VHF to SHF".WRE-Technical Note-1014(AP), 1974

7 Bullington, K. "Radio Propagation fundamentals".Bell. Sys. Tech. J., 36, 593-626, 1957

8 Thomas, R.M., "Measurements of HF Ground WaveHaack, G.R. and Propagation over Irregular Terrain",Golley, M.G. J. Elect. Electron. Eng, Aust., in

press, 1988

9 Wagner, C. "On the Numerical Solution of VolterraIntegral Equations".J. Math. Phys., 32, 289-401, 1953

10 Thomas, R.M. and "Estimation of Earth ElectricalHaack, G.R, Properties Using CW and FMCW Ground

Wave Propagation at HF".J. Elect. Electron. Eng. 7, 214-220Aust., 1987

S- 1i - SRL-0002-TM

TERRAIN PROFILE

S•2 3 4 5 6 7 8

(km)0

0. = 0.1 S Mi

-10 K = 10

Ax 100 M

-20

_ -30

Z -40 SMOOTH SPHERICAL EARTH

,-(a)• I MHz

-- 50

- Z-IRREGULAR TERRAIN-60

-70 ___

0 5 10 15DISTANCE FROM TX (km)

-20

2 -40U, AUI I'

Sz -60 o IRREGULAR TERRAIN

V) -80SMOOTH SPHERICAL EARTH

(-10IF (b) 10 MHzP- o -120

10 5 0o 15DISTANCE FROM TX (km)

Figure 1. Calculation of basic transmission loss for the path given by Ott(figure 1, reference 1)

I _ _ ___ _.___ _ _ _ _

SRL-0002-TM - 12 -

-60CONVERGENCE

-70 SMOOTH SPHERICAL EARTH

a 0.003 S m" K = 10 L = 20 km

-80

"• -9---"- ---- 0 -••-0-----------e--0-2 ~-90 - 2 MHz

RES:DUEo , .SERIESI -120(n

z< 10 MHz

-130 -

-1440

RESIDUE SERIES

30 MHz

-160I I 1I , 1 1 1 1 i, I10 100 1000

STEP SIZE (m)

Figure 2. Convergence behaviour for 20 km path over smooth spherical Earth

- 13 - SL-0002-Th

CONVERGENCE TO WITHIN 1 dB

SMOOTH SPHERICAL EARTH

100 a = 0.003 S m"SK=3

z

0 f 10 MHz (a)

<

10 f f20OMHz 0

10 100 1000STEP SIZE (m)

30

(b)

S10 L 10km

LU L =20km

NN

I I . 5, , ,, -( , , ,. , ,,

S10 100 i000

STEP SIZE (ni)

Figure 3. (a) Maximum path lengths and step sizes for convergence at a givenfrequency (b) Maximum frequencies and step sizes for convergenceover a path length

SRL-0002-11 14 -

I[

1.5 CONVERGENCE

STiP SIZE 1 (O0 m

4{

1.0

0~00

05 0 15 ZO

FREQUENCY (MHz)

Figure 4. Relationship between maximum terrain slope and maximum frequencyfor convergence at a scep size of 100 m

- 15 - SRL-0002-TM

ACCURACY 500 m HILL Af 5 km ALONG15 km PATHa 0.01 K = 10

---- SMOOTH SPHERICAL EARTH

- GRAPH I CAL KNIFE-EDGE

0 WAG'ER

-40

-60 - "

S'-80 o

LnI GO

-140

-160 - II-1 2 5 I0 20

-k FREQUENCY (MHz)

SFigure 5. Accuracy of WAGNER for path with 500 m high hill, compared withKnife-edge estirmated loss

!Nx

SRL-0002-Th - 16 -

Iv'j = 0.25 L = 20 l�m

a 0.003

r.=3I

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0o 0

U,

KNIFE-EDCE

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10 30FREQUENCY (MHz)

Fi8ure 6. Dependence of eccuracy on ground electrical constants

-17 -SRL-0002-TM

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SRL-0002-TM - 18 -

PATH 5

a OBSERVATION, DAY 245, 1984(• WAGNER: TRUE PROFILE

WAGNER: GAUSSIAN HILLKNIFE-EDGE APPROXIMATION

0

-10 "I \

5 10 15 20 25FREQUENCY (MHz)

Figure 8. Comparison with observation of different calculations of shadowloss

SRL-0002-TM

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4 TITLE

THE CALCULATION OF GROUND WAVE ATTENUATION IN THE HF BAND USINGK__PROGRAM WAGNER

5 PERSONAL AUTHOR (S) 8 DOCUMENT DATE IDecember 1987

R.M. Thomas andA.0. Zollo 7 7. TOTAL NUMBER-i

OF PAGES 18

7. 2 NUMBER OFERREFERENCES 10K8 8.1 CORPORATE AUTHOR (S) 9: REFERENCE NUMBERS D

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Technical Memorandum 777991-1410002 1

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Defence Science and TechnologyOrganisation Salisbury

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15 DESCRIPTORS Co1puter 7rograms,118 ICOSATI CODES

a. EJC Thesaurus Ground wave propagation) 0046HTerms Attenuation I

Transmission loss

Sb Non -Thesaurus A ~Terms Wagner (computer program))

_• 17_J SUMMARY OR ABSTRACT ]V .(d this issecurOty classTied, the announ,'ement of this report will be similarl dassiied)

We present computational test results from a double precision version of the

FORTRAN program 'WAGNER'. The potential value of this integral equationtechnique is its purported ability to model propagation losses overtwo-dimensional paths through irregular and inhomogeneous terrain. Howeverthe numerical integration algorithm can be affected by poor convergence andinaccuracy, particularly at frequencies above the MF band. We haveinvestigated these properties in terms of selected key parameters and havederived empirical criteria governing convergence and physical accuracy.We find that calculations of basic transmission loss using WAGNER aresubject to significant limitations at HF frequencies as the terrain becomesirregular and as the conductivity and dielectric constant of the groundboth become smaller. On the other hand, the shadow loss due to an obstaclemay be reliably calculated by WAGNER on the assumption that shadow loss isindependent of ground electrical constants, thus permitting the use ofdummy values of conductivity and dielectric constant to ensure that thephysical accuracy criterion is satisfied.

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