THE KINGDOM OF MOROCCO - ASPRS

1 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING June 1999657 COLUMN Grids & DatumsTHE KINGDOM OF MOROCCOThe contents of this column reflect the views of the author, whois responsible for the facts and accuracy of the data presentedherein. The contents do not necessarily reflect the official viewsor policies of the American Society for Photogrammetry and Re-mote Sensing and/or the University of New Roman province of Mauritaniawas invaded by Muslims in the 7thcentury AD, leading to the foundingof the present country of MOROCCO asan independent KINGDOM in the 9thcentury. Later centuries saw occupa-tion by the Portuguese, English, Span-ish and French.

2 In 1912, two protector-ates were established: French MOROCCO ,on the Atlantic coast which includedmost of the present country and Span-ish MOROCCO on the Mediterraneancoast. In recent years, the kingdomhas annexed much of the former Span-ish Sahara. The geodetic history of theentire country is a combination ofSpanish and French influences. Thecoordinate systems of MOROCCO areamong the more difficult to compre-hend and unusual in the entire first-order Frontier Triangula-tion of Spanish MOROCCO was attachedto Spain by measurements of theInstituto Geogr fico y Catastral deMadrid in 1923-1929. It was composedentirely of one meridional arc and wasoriginally referenced to the MadridDatum on the Struve ellipsoid.

3 Thiswas locally computed on the BeniMeyimel Gauss-Kr ger TransverseMercator Grid of 1923 that was ad-justed in the late 1950 s to the Euro-pean Datum of 1950. Station BeniMeyimel on ED50 is: fo = 35 45 North, lo = 5 41 West of Greenwich. The local SpanishGrid origin for Puerto de T nger (Portof Tangier) was at Faro (Lighthouse)de Malabata where: fo = 35 48 North, lo = 5 44 West of Green-wich. Neither of these Grids had falseorigins. The same triangulation arcwas later completely recomputed withrespect to the namesake of the capitalof the former Spanish MOROCCO , theT touan Datum of 1929 where: Fo =35 35 North, Lo = 5 19 West of Greenwich.

4 The azi-muth to T touan South West Base is:ao = 231 44 .There were two types of classicaltriangulation in French MOROCCO . Theoriginal triangulation, the Recon-naissance Triangulation, was startedabout 1910 and covered a major por-tion of the country. It was accom-plished by Topographic Engineers at-tached to French Foreign Legiontroops engaged in the conquest of Mo-rocco. The work was done on a yearlybasis to satisfy military needs, and theofficers in charge did their own com-putations. Errors were cumulative be-cause values for the last 2 or 3 primarystations were accepted by the extend-ing party the following season.

5 Thework was accomplished in approxi-mately 40 different portions, and wasnot as well coordinated as the previ-ous 50 years worth of French efforts inadjacent Algeria. The ReconnaissanceTriangulation is referenced to theAgadir Datum of 1921 where: Fo = 30 25 North, Lo = 9 37 Westof Greenwich. The origin is the mina-ret of a mosque in the 16th century Portof Agadir. The solar azimuth toSignaux de Founti is: ao = 109 19 36 . A subsequent Polaris observation(2 pointings) was not French North African ellipsoi-dal Bonne projection was used for theReconnaissance Triangulation, andthis Grid continues to influence map-ping systems in North Africa to thisday.

6 Proper computation of these Gridcoordinates must be performed fromthe series form of the equations formillimeter accuracy. Texts that sug-gest the universal use of spherical for-mulae with the equivalent authalic ra-dius and latitudes are wrong! TheLatitude of Origin (fo) = 35 06 North,and the Central Meridian (lo) of zerodegrees from Paris corresponds to 2 20 West of Greenwich. TheFalse Origin is 100 kilometers for bothEastings and Northings. This Grid hasperplexed novice cartographers (andmany old pros ) for decades. Evenmore confusing, some implementa-tions of this Grid display no False Ori-gin. The active use of this Grid wasterminated in 1942, but it continues toconfound, as I shall explain second type of French triangu-lation commenced in 1922, and isknown as the Triangulation R guliere(regular triangulation).

7 This work wascarried out entirely by TopographicBrigades of the Service G ographiquede l Armee (Army Geographic Ser-vice), sent from Paris to MOROCCO . Allcomputations were performed in R guliere Datum of 1922 is basedon the origin at the astronomic stationMerchich 1921 (south of Casablanca),where: Fo = 33 26 North, Lo= 7 33 West of azimuth to station Mohammed ElKebir is: ao = 46 52 (fromsouth), and the ellipsoid of referenceis the Clarke 1880 where: a = 6,378, meters, and 1/f = Dur-ing the same era, of 7 baselines thatwere measured for the classical trian-gulation, Ber Rechid and Agourai werelocally adopted as temporary datumorigins.

8 The Ber Rechid 1920 Datum isdefined where: Fo = 33 17 North, Lo = 9 56 West of azimuth from North Base to SouthBase is: ao = 169 34 . The geo-detic definition of the Agourai Datumseems to be lost, but it may exist some-where in Rabat or Paris. The remainingbaselines of the R guliere Datum of1922 included Marrakech, Guercif,Taroudant, Bon Denib, and Sidi BenZekri, where sidi is an Arabic term ofobeisance, similar to my lord. In the1950 s, the Army Map Service(AMS) found the R guliere classicaltriangulation to be intrinsically Lambert (partially conformal)Conic projection is used for theR guliere Datum of 1922, and this Gridalso confounds cartographers to thisday.

9 There are two original zones: forZone Nord, the Latitude of Origin (fo)= 33 18 North (or 37G where 100 grads= 90 ), the Central Meridian (lo) = 5 24 (6G) West of Greenwich, and theScale Factor at Origin (mo) = For Zone Sud, the Lati-tude of Origin (No) = 29 42 North, theCentral Meridian (lo) = 5 24 West ofGreenwich, and the Scale Factor atOrigin (mo) = The FalseOrigin is 500 kilometers for Eastingsand 300 kilometers for Northings forboth zones. The formulae used withthis Grid have a long and lurid historydating back to the 19th century, cour-tesy of the French way of doing the 19th century, France wasthe center of cartographic research inthe mathematics of map projection table computationswere performed by hand, all formulaewere commonly truncated past the cu-bic term to ignore infinite series termsconsidered at the time, too small towarrant the extra effort.

10 For instance,the Lambert Conformal Conic projec-tion was used only to the cubic termin the formulae for the tables of the CONTINUED ON PAGE 658 CLIFFORD J. MUGNIER658 June 1999 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSINGCOLUMN CONTINUED FROM PAGE 657developed meridional distances. This resulted in FrenchArmy projection tables that have become part of the arcanelore of computational cartography. This secret has been ex-plicitly detailed in the French literature for a century, but ap-parently ignored by readers of English-only papers. StandardLambert formulae will not work for MOROCCO , and the use offully conformal formulae will yield computational errors thatexceed 15 meters!