The Movement of Barchan DunesMeasured by Aerial Photogrammetry

HERMAN J.FINKEL,

Dept. of Agricultural Engineering, Technion,Israel Inst. of Technology, Haifa, Israel

ON THE sOlithern coast of Peru, in thePampa de La Joya, sand dunes of the

barchan type o.ccur extensively. The barchanis ~ crescent-sh'j}ped formation with a parab­alOld plari',.. It 1!.a;s-.,§harp cusps or horns poi n t­ing in the ditls~fiiJ~,.of the prevailing wind.The windwardi~pe is gentle (about 10°),and the leeward slope is a concave surfacestanding at the angle of repose of the sand(about 32°). (Se'e Figure 1.) These barchansare distributed by the hundreds over an areaof about 50 kilometers length and 15 kilom­eters width. They ai'e .characteristic of anopen, relatively ftanles.ertwhich is absolutelyfree from moisture ai{d"v.egetation, and whichis swept by a relatively' constant, unidirec­tional wind blowing from an unlimited sourceof sand. The barthans in this area vary inheight from less than one meter to aboutseven meters. They are continually in motionin the direction of the wind, due to the rollingof sand up the windward slope and over thecrest. This increases the angle of the leewardslope (or slip.face, as it is called) and causesan immediate shifting forward of the sanduntil the stable angle of repose is re-estab­lished. Thus the entire body of the dunemoves forward over the hard, stony pave­ment of the desert as though it were an inde­pendent, living organism. The rate of forwarddisplacemen t of the barchans is a function ofthe grain size and density of the sand, thevelocity of the wind, and the dimensions ofthe barchan. This has been the subject ofmuch theoretical study.!

The movement of these dunes is, however,of more than academic interest, since thePampa de La J oya is the site of a projectedirrigation scheme to convert 3,500 hectaresof desert into agricultural land. Shiftingdunes in this area represent a serious hazard

! See, for example, Bagnold, R. A., "The physicsof blown sand and desert dunes." Methuen andCo., London, 1954.

FIG. I. Typical Barchan of thePampa de La Joya, Peru.

to the water distribution canals, as well as aninsurmountable obstacle to cultivation. Be­fore undertaking the design of large-scale andexpensive measures for the control of thesedunes, either by stabilization or eradication,it was necessary to gather data on the physi­cal behavior of the barchans. 2

Among the many factors studied, the for­ward rate of motion of the barchans was para­mount. Since the area is desolate and com­pletely uninhabited, there were few land·marks and no personal observations whichcould give any reliable indication of thechange in position of even a single barchanover the years. It was only known that boththe highway and railroad line which traversethis pampa have expensive maintenanceproblems in keeping their rights-of-waycleared from the continually encroachingsand. Under these conditions the use ofphotogrammetry seemed indicated.

The entire desert had been flown in 1955by the Servicio Aerofotografico Nacional ofthe Peruvian Air Force (hereinafter referrecl

2 This work was carried out by the author underthe auspices of the Food and Agriculture Organiza­tion of the Un ited Nations, wi th the coopera tionof the Peruvian government.

. ED. NOTE-The movement of dunes is also considered in a comprehensive paper that treats par-tICularly of the geologic characteristics of barchans in southern Peru. See Finkel, H. r., 1959, Jour. Ceol.,Vol. 67, No.6, pp. 614-647. .

439

440 PHOTOGRAMMETRIC ENGINEERING

angles to the wind direction) varied from 10to over 65 meters. This width, when plottedagainst the crest height for each barchan, wasfound to have a linear relationship expressedby the equation

where W is width and H is crest height, inmeters. This had a highly significant de­gree of correlation. By chance, however, ofthe 45 barchans which had been measured onthe ground only 19 appeared on the plani­metric map plotted by multiplex. The hori­zon tal displacements of these 19 were meas­ured by calipers to an accuracy of 0.1 milli­meter, representing a distance of 1.0 meter onthe ground. This displacement, when plottedagainst the crest heights of the dunes as actu­ally measured in the field, gave a set of pointsto which a reci procal function was fi tted bythe method of least squares, having a coeffi­cient of curvilinear correlation of 0.71, whichin this case was significant. This functionwhen converted to units of annual displace­ment, resulted in Table 1.

1t was believed, however, that the sta­tistical sample of 19 dunes might not havebeen sufficiently large enough to support theconclusions. The remoteness and desolation

to as SAN). This flight was at a very highaltitude and the scale of the photographs wasapproximately 1 :60,000, but due to theclean, dry, desert atmosphere, the pictureswere very clear and each individual barchanwas sharply outlined. Fortunately part of thesame area was rephotographed by SAN in1958 to the scale of 1: 20,000 and with excel­lent results. (See Figure 2.) Ground controlhad been established and marked with largestone crosses which were identifiable in bothsets of pictures.

By using a multiplex projector, SANplotted the correct positions of over 100barchans on a sheet of 'low-shrinkage acetatepaper to a scale of 1: 10,000. The entireplanimetric outline of each dune was indi­cated. This was done for both flights on thesame sheet using different colors to distin­guish the 1955 from the 1958 positions. Partof this sheet is shown on Figure 3. It wasimmediately obvious that the barchans ad­vanced at varying rates, with the smallerones having a greater forward displacement.In the field, the complete dimensions of 45barchans had been measured by use of stadiaand a theodolite. These formations varied inheight from one to almost seven meters. The,Yidth across the horns (measured at right-

W = 10.3 H + 4.0 (J)

Fu;. 2. Aerial photograph of the 1958 flight (enlarged frolll the original 1: 20,000 scale photography),showing sonIC of the Barchans in the area studied. Courtesy of Servicio Fotograrico Nacional, Peru.

MOVEMENT OF BARCHAN DUNES MEASURED BY AERIAL PHOTOGRAMMETRY 441

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1,?90 71

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DISPLACEMENT OF DUNES IN THREE YEARS

FIG. 3. Displacement of dunes in three years.

:.:.D 0

161

of the desert of La Joya, as well as the scarci tyof field parties, made obtaining additionaldirect height measurements difficult and ex­pensive. Consequently, it was decided tomake additional use of photogrammetry.

On the composite plot shown partly in Fig­ure 3, calipers were used in measuring thewidth across the horns of 75 additional bar­chans. Since the average width was about 37meters an accuracy to one meter was con­sidered sufficient. From these scaled widthsthe crest heights of the dunes were calculatedby the tested relationship expressed in equa­tion (1). These derived heights of dunes wereplotted against the forward displacement inthree years, as measured on the compositeplot of Figure 3. The procedure previouslyused for the 19 barchans was then applied todata of these 75 dunes, and a reciprocal func­tion was fitted; this finally led to the resultspresented in Table No.2. It was encouraging

to find that the forward displacement of the75 barchans, whose height was calculated in­directly from the photographs, did not dif­fer greatly from that of the 19 barchans whoseheight was actually measured in the field.The results for the sample of 19, however,proved to be statistically significant, whereasthose for the sample of 75 proved to be highlysi[!,nificant.

A different technique might have been ap­plied to this problem, namely, the determi­nation of the crest heights of the 75 dunes bystereoscopic methods. This was not adopted,however, because the 1: 20,000 scale of the1958 pictures could, at best, have given anaccuracy of only two meters for dune heightdetermination by stereoscopic methods. Plan­imetric measurement on 1: 10,000 scale en­largements, of the width across the horns.was, on the other hand, done to a grou nd­equivalent accuracy of one meter which rep-

TABLE 1

ANNUAL DISPLACEMENT or 19 BARCHANS ACCORDING TO HEIGHT OF THE CREST

Crest Height (meters)

A llnual Displacement (meters)

1.0

30

2.0

22.6

3.0

18.1

4.0

150

5.0

13 .0

6.0

11. 3

442 PHOTOGRA¥MET~I<;: EN§tNE~RING

. "TABLE 2'

,\NNUAL DISPLACEMENT OF 75 BARC:HANS ACCORDING TO THE HEIGHT OF THE CREST

Crest Height (meters) 1.0 2.0 3.0 4.0 5.0 6.0 7.0Average3.67

;/ nnual Dis!)Iacement(meters) 32.3 22.0 16.8 14.5 12.2 11.5 9.2 15.4

------

resen ted an accuracy of one- ten th meter lfi

the calculated height of the dune crest.The results of these determinations of the

forward speed of the dunes as a function ofthe crest heights were compared with thetheoretical speed as calculated from the aver­age velocity of the prevailing wind and thesand grain size according to the formulae ofBagnold. The agreement between these theo­retical rates and those determined by aerialphotogrammetry was surprisingly close.

MASS DISTRIBUTION OF THE BARCHANS

As there are hundreds of barchans scatteredover the Pampa de La Joya, it was consideredpossible that their pattern of distributionmight not be completely random, but insteadwas the orderly consequence of certain lawsof dune movement. Here again, aerial pho­togrammetry was the key to solving thisproblem. That portion of the pampa whichhad been re-flown in 1958 was chosen for thisphase of the investigation. Use was made ofthe flight index-sheet as a simple, uncon­trolled aerial mosaic to the scale of approxi.mately 1 :30,000. This was sufficiently largeto show clearly all of the barchans in the area,although of insu fficient size for measuringtheir size. (See Figure 4.) The area of themosaic was then ruled off in to rectangular co­ordinates laid out on the azimuth of 152°,which was the direction of the prevailingwind as determined in the field by the orien­tation of 45 barchans. The rectangles repre­sented 1,000 meters in the direction of thewind, and 200 meters at right angles to thewind. The number of dunes which fell withineach of these coordinate rectangles was thencounted, and this density (per area of 20hectares) was taken as the parameter ofbarchan distribution over the area.

The results are shown, schematically inFigure 5. The average density of the duneswas computed for each row parallel to thewind direction (called Xl) and for each tiertransverse to the wind direction (X 2), and re­corded in the margins of Figure 5. \\Thenthese average densities were plotted againstXl (measured northward from an arbitrary

starting point) and against X 2 (measuredeastward from a point of greatest dune con­centration, called the focus) a set of descend­ing curves was obtained to which both para­bolic and exponential regressions were fittedwith very high degrees of curvilinear correla­tion.

The conclusions drawn from this statisticalstudy of the barchan distribution were as fol­lows:

1. The barchans seem to form a focus of highdensity at the south, or upwind end of thearea studied.

2. From this focus, the average density decreaseswith the distance downwind.

3. The density also decreases in the crosswinddirection, starting from the focus.

4. The lateral spread of the dunes over thedesert also increases downwind from thefocus, although asymmetrically. There are farmore dunes to the right, or east of the focal­axis than to the west. (Su bsequent analysis ofthe prevailing winds failed to provide an ex­planation for this distorted distribution).

5, The total number of dunes in any kilometerstrip transverse to the wind direction remainsapproximately the same (within limits ofstatistical error). Consequently the decreasein dune density downwind appears to be theresult, primarily, of the lateral spreading ofthe same number of barchans over a progres­sively wider area.

These conclusions, together with those re­corded above in the tables of annual forwardmotion, aside from their general interest togeomorphologists, are of specific practicalvalue to the engineer who is charged with de­signing a program of sand dune control insuch an area.

DISTORTION OF THE BARCHAN SHAPE

Close examination of the air photos revealsthat in many of the barchans of the Pampade La Joya, the west cusp is noticeably longerthan the east. This has been confirmed byground measurements on a large number ofbarchans, where the average length of theeast horn was 0.85 of that of the west horn.This individual asymmetry might be ex­plained by the fact that the ground has agentle, but uniform slope to the west of abouttwo per cent. One would naturally expect the

MOVEMENT OF BARCHAN DUNE.S MEASURED BY AERIAL PHOTOGRAMMETRY 443

FIG. 4. Part of aerial flight index-sheet used as an uncontrolled mosaic, ruled off into rectangleswith coordinates parallel to and perpendicular to wind direction, for study of mass distribution of thebarchans.

moving sand to roll a bit farther on the lowerside of the slope, and thus elongate the romof the dune on that side, Accordingly itismore difficult to explain the general tendencyof the barchans, en masse, to drift noticeablytoward the east, or up the slope, as indicated inthe distribu tion studies described above. Pos­sibly the blowing action of the sand againstslightly rising ground encourages rather thandiscourages the formation of more barchans,regardless of the relative length of the Cl!Sps.This apparently paradoxical behavior isworth further study.

GEOLOGIC DATI~G BY BARCHAX

DISTRIBUTIOK

Another aspect of the aerial study of bar­chans, namely the dating of climatic changesin post-Quaternary time, has suggested itself,but has so far, defied a simple solution. It is

here mentioned to stimulate those readerswho may be geologists and mathematicians.There was evidently a period of great uplift­ing of the entire southern coast of Peru dat­ing from earlier than the Quaternary Period.(The present elevation of the Pampa de LaJoya is about 1,260 meters above sea level.)After the uplift there was apparently a changein the climate, toward greater aridity, and thesand began to be blown northward from thePampa de Clemisi; this is a large sand depositnear the coast, about 80 kilometers upwindfrom the first barchan, and lying at an ele\'a­tion of about 1,000 meters, The barchans arefirst formed at a poin t kno\\'n as H uagri andextend north\\'ard (the direction of the windmo\'ement) until they crash against the steepslopes of a mountain range kno\\'n as the Cer­ros de Caldera, o\'er 50 kilometers fromHuagri. The width of the barchan area in-

444 PHOTOGRAMMETRIC ENGINEERING

A B C 0 E G H M N 0 TarAL frIEAH

MEAN M 6.6 " 4.' 37 " 24 2.0 2~ l7 0.9 2~

TOTAL 96 105 116 74 55 59 65 55 82 57 29 1~7 2B

I f-8 L I----r- .......... II ..2

~ ~ '. 17 '8, "-- ,'''' 19 .,4 9 _ JI 8 I---s:::" -- . ~""""""".. 28 .,5 9 13_ 12 .. 986 10 _6 5 _, 24 .07 I--~"--

_9_- 12 __ 5 ,- __ 2 ,_. ---".- _ 0 _0 I I 46 '"8 6 14 7 4 - _2 - I _L __ 0 0 4 6 .. ..9 L 9~ II. 10 5 9 7 5_ 4 4 2 ,

f--::4::- 77 .410 __ 1_ _ 10_ L. 7 4 5 L. _5_ 10 2 4 4 73 .." .7. 6 _ _ 7. __9 6 6 6 , 4 , 6 , 2 0 2 70 U12 2 -, - 1I L. 7 , 7 , , 2

_,0 2 2 2 56 37

" _2 . _ 4~

, 3 5 4 5 4 • 4 .L 3_ _0 I 50 "14 -~ 2 5 5 9 .5 , I 3 7 2 6 _ 5 -+- _l 58 ~9

15 __0_~-- 5 -, _5 6 I , , , I 2 4 0 41 27

16 2 - 3 2 __ 4 5 2 6 2 5 0 2 , 0 41 2717 1-- 5 3 I "- 3 _ 6 2 7 5 2 .- 5 _3 50 .8,18 ., 3 0 4 2 I 1 2 2 4 4 , I 28 2.119 t=.L 0 4 0 3 2 2 2 2 I 4 .•4 2 26 29

20 Q 0 2 2 2 2 2 I 3 0 2 0 17 I,'21 2 L. 0 I 4_ JJ. ----<-_.J~t=:1- ---'- - 24 2,0

22 L:L 0 .1 .3 3 3 - , _2_ _0_ 14 1,423 I 2 _2 4 3 __ 2 .4 _ _4 _ _ L_ 25 2,5

24 0 0 0 2 3 2 1 3 3 14 1,.25 1 3 3 2 2 • 2 _2 _. 2 23 2,62. 2 I 2 1 2 0 3 0 0 II 1.2

-~.",--27 I , 0 0 0 2 2 o . 3_ 9 1.028 _2 ~J. 2 0 I 4 3 I 0 14 1.629 0 1 I 0 2 3 2 2 0 11 l2'0 I _, 0 0 2 2. 2 I o . 9 1.0

'j31 __1- ____L __ 0 0_ 2 I 1 _1- __0_ 7 0,8

" 0 __ , . ~ ~0 3 3 I 0 9 1,0

'"33 0 7. 0 2 - _. 0 " 1.4

i;- ,~o~_"'~

34 0 2 .2 0 0- 4 0,835 0 I ~ - 1 I 5 1.0,. 0 0 4 . _0_ 7 1.437 0 0 1 .1 • . 0_ 2 Q4

'8 0 ,-- , 0 O. 5 1,039 2 , 2. .._ 3. ._._0___ 8 1,640 0 ~-

0 2 . 0 3 0641 5 2 ; II 2.2

42 • 2.0

FIG. 5. Mass distribution of Ban.:hans. The numbers represent the density of dunes in 20 Has.

creases somewhat irregularly to a maximumwid th of 10 to 15 kilometers.

The exact dating of the post.Quaternaryperiod of c1i matic change has not been estab·lished \\'ith great certainty, and is the subjectof some controversy among geologists. It ishere suggested that if a mathematical anal­ysis of the distribution of the barchans overthe entire area be made with respect to theirsizes. it may be possible to calculate the mini­m'ltm period of time required for the achie\'e­ment of the present configuration. These cal·culations would be based upon the knownrate of advance of the barchans of varyingcrest heights as reported in the first part ofthis paper, and upon the assumption that theregime of wind velocities has remained es­sentially the same as that reported in recentstudies by the author. 3 Furthermore, if thevolume of the dune material, amorphouslypiled up at the foot of the Cerros de Caldera

could be estimated, the known carrying ca·pacity of the \\'ind for this size of sand graincould be used to calculate the maximum pe­riod of time which might have elapsed sincethe climate turned arid and the sand began toblow. The author would be pleased to put hisdata at the disposal of any scientist who iswilling to tackle this intriguing problem, al­though further field and photogrammetricdata would probably have to be assembled.The first part of the problem outlined aboveis not unlike the problem of calculating theage of the universe from the known rates atwhich stars of different sizes are moving awayfrom each other. This analogy may offer apossible approach to the problem of barchandistribution.

3 Finkel, H. J. "The Barchans of Southern Peru".Tournai of Geology, Vol. 67, No, 6, November 1959,pp. 614-647,