PE_RS Grids and Datums June 1999

Document Sample
PE_RS Grids and Datums June 1999 Powered By Docstoc
					                                                                                                     ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○     ○   ○   ○   ○   ○

C O L U M N                                                                                       Grids & Datums

                                             THE KINGDOM OF MOROCCO
The contents of this column reflect the views of the author, who     plished by Topographic Engineers at-                        where: F o = 33° 26’ 59.672” North, Lo
is responsible for the facts and accuracy of the data presented      tached to French Foreign Legion                             = 7° 33’ 27.295” West of Greenwich.
herein. The contents do not necessarily reflect the official views   troops engaged in the conquest of Mo-                       The azimuth to station Mohammed El
or policies of the American Society for Photogrammetry and Re-       rocco. The work was done on a yearly                        Kebir is: a o = 46° 52’ 11.291” (from
mote Sensing and/or the University of New Orleans.                   basis to satisfy military needs, and the                    south), and the ellipsoid of reference
      The Roman province of Mauritania                               officers in charge did their own com-                       is the Clarke 1880 where: a = 6,378,
was invaded by Muslims in the 7th                                    putations. Errors were cumulative be-                       249.145 meters, and 1/f = 293.465. Dur-
century AD, leading to the founding                                  cause values for the last 2 or 3 primary                    ing the same era, of 7 baselines that
of the present country of Morocco as                                 stations were accepted by the extend-                       were measured for the classical trian-
an independent kingdom in the 9th                                    ing party the following season. The                         gulation, Ber Rechid and Agourai were
century. Later centuries saw occupa-                                 work was accomplished in approxi-                           locally adopted as temporary datum
tion by the Portuguese, English, Span-                               mately 40 different portions, and was                       origins. The Ber Rechid 1920 Datum is
ish and French. In 1912, two protector-                              not as well coordinated as the previ-                       defined where: Fo = 33° 17’ 41.6”
ates were established: French Morocco,                               ous 50 years worth of French efforts in                     North, Lo = 9° 56’ 02.05” West of Paris.
on the Atlantic coast which included                                 adjacent Algeria. The Reconnaissance                        The azimuth from North Base to South
most of the present country and Span-                                Triangulation is referenced to the                          Base is: a o = 169° 34’ 15.3”. The geo-
ish Morocco on the Mediterranean                                     Agadir Datum of 1921 where: F o = 30°                       detic definition of the Agourai Datum
coast. In recent years, the kingdom                                  25’ 25.0” North, Lo = 9° 37’ 48.06” West                    seems to be lost, but it may exist some-
has annexed much of the former Span-                                 of Greenwich. The origin is the mina-                       where in Rabat or Paris. The remaining
ish Sahara. The geodetic history of the                              ret of a mosque in the 16th century Port                    baselines of the Réguliere Datum of
entire country is a combination of                                   of Agadir. The solar azimuth to                             1922 included Marrakech, Guercif,
Spanish and French influences. The                                   Signaux de Founti is: a o = 109° 19’                        Taroudant, Bon Denib, and Sidi Ben
coordinate systems of Morocco are                                    36”. A subsequent Polaris observation                       Zekri, where “sidi” is an Arabic term of
among the more difficult to compre-                                  (2 pointings) was not adopted.                              obeisance, similar to “my lord.” In the
hend and unusual in the entire world.                                   The French North African ellipsoi-                       1950’s, the U.S. Army Map Service
      The first-order Frontier Triangula-                            dal Bonne projection was used for the                       (AMS) found the Réguliere classical
tion of Spanish Morocco was attached                                 Reconnaissance Triangulation, and                           triangulation to be intrinsically correct.
to Spain by measurements of the                                      this Grid continues to influence map-                           The Lambert (partially conformal)
Instituto Geográfico y Catastral de                                  ping systems in North Africa to this                        Conic projection is used for the
Madrid in 1923-1929. It was composed                                 day. Proper computation of these Grid                       Réguliere Datum of 1922, and this Grid
entirely of one meridional arc and was                               coordinates must be performed from                          also confounds cartographers to this
originally referenced to the Madrid                                  the series form of the equations for                        day. There are two original zones: for
Datum on the Struve ellipsoid. This                                  millimeter accuracy. Texts that sug-                        Zone Nord, the Latitude of Origin (f o)
was locally computed on the Beni                                     gest the universal use of spherical for-                    = 33° 18’ North (or 37G where 100 grads
Meyimel Gauss-Krüger Transverse                                      mulae with the equivalent authalic ra-                      = 90°), the Central Meridian (lo) = 5°
Mercator Grid of 1923 that was ad-                                   dius and latitudes are wrong! The                           24’ (6G) West of Greenwich, and the
justed in the late 1950’s to the Euro-                               Latitude of Origin (f o) = 35° 06’ North,                   Scale Factor at Origin (mo) =
pean Datum of 1950. Station Beni                                     and the Central Meridian (l o) of zero                      0.999625769. For Zone Sud, the Lati-
Meyimel on ED50 is: f o = 35° 45’                                    degrees from Paris corresponds to 2°                        tude of Origin (No) = 29° 42’ North, the
34.223” North, l o = 5° 41’ 09.5168”                                 20’ 13.95” West of Greenwich. The                           Central Meridian (l o) = 5° 24’ West of
West of Greenwich. The local Spanish                                 False Origin is 100 kilometers for both                     Greenwich, and the Scale Factor at
Grid origin for Puerto de Tánger (Port                               Eastings and Northings. This Grid has                       Origin (mo) = 0.999615596. The False
of Tangier) was at Faro (Lighthouse)                                 perplexed novice cartographers (and                         Origin is 500 kilometers for Eastings
de Malabata where: f o = 35° 48’ 47.7”                               many “old pros”) for decades. Even                          and 300 kilometers for Northings for
North, lo = 5° 44’ 57.0” West of Green-                              more confusing, some implementa-                            both zones. The formulae used with
wich. Neither of these Grids had false                               tions of this Grid display no False Ori-                    this Grid have a long and lurid history
origins. The same triangulation arc                                  gin. The active use of this Grid was                        dating back to the 19th century, cour-
was later completely recomputed with                                 terminated in 1942, but it continues to                     tesy of the French way of doing things.
respect to the namesake of the capital                               confound, as I shall explain later.                             During the 19th century, France was
of the former Spanish Morocco, the                                      The second type of French triangu-                       the center of cartographic research in
Tétouan Datum of 1929 where: Fo =                                    lation commenced in 1922, and is                            the mathematics of map projections.
35° 35’ 41.493” North, Lo = 5° 19’                                   known as the Triangulation Réguliere                        Because projection table computations
19.545” West of Greenwich. The azi-                                  (regular triangulation). This work was                      were performed by hand, all formulae
muth to Tétouan South West Base is:                                  carried out entirely by Topographic                         were commonly truncated past the cu-
a o = 231° 44’ 50.67”.                                               Brigades of the Service Géographique                        bic term to ignore infinite series terms
      There were two types of classical                              de l’Armee (Army Geographic Ser-                            considered at the time, too small to
triangulation in French Morocco. The                                 vice), sent from Paris to Morocco. All                      warrant the extra effort. For instance,
original triangulation, the “Recon-                                  computations were performed in Paris.                       the Lambert Conformal Conic projec-
naissance Triangulation,” was started                                The Réguliere Datum of 1922 is based                        tion was used only to the cubic term
about 1910 and covered a major por-                                  on the origin at the astronomic station                     in the formulae for the tables of the
tion of the country. It was accom-                                   Merchich 1921 (south of Casablanca),                                                            CONTINUED ON PAGE 658

                                                                                                                                                         C L I F F O R D         J .       M U G N I E R

PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING                                                                                                                                     J u n e 19 9 9            657
      ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○   ○

                              Grids & Datums                                                                                                              C O L U M N

 CONTINUED FROM PAGE 657                                                                                  muthal Equidistant Grid is defined at the origin point (Camp
                                                                                                          monument at Maison Guizol) where: (fo) = 29° 02’ 06” North,
 developed meridional distances. This resulted in French                                                  the Central Meridian (lo) = 10° 30’ 06” West of Greenwich,
 Army projection tables that have become part of the arcane                                               and the Scale Factor at Origin (mo) = 1.0. The False Origin is
 lore of computational cartography. This “secret” has been ex-                                            50 kilometers each for Eastings and Northings. The orienta-
 plicitly detailed in the French literature for a century, but ap-                                        tion of the Grid is defined to “Fourmi” as: a g = 40° 19’ 47”.
 parently ignored by readers of English-only papers. Standard                                             The Mogador 1957 Lambert Grid origin is: (fo) = 31° 30’ North,
 Lambert formulae will not work for Morocco, and the use of                                               the Central Meridian (lo) = 10° 00’ West of Greenwich, and
 fully conformal formulae will yield computational errors that                                            the Scale Factor at Origin (mo) = 0.999932968. The False Ori-
 exceed 15 meters! Note that mathematical elegance is not                                                 gin is 200 kilometers each for Eastings and Northings. In
 what matters in a country’s coordinate transformations; what                                             1921, the position of Mogador Mat on the Reconnaissance Tri-
 matters is computational conformity to local legal standards.                                            angulation was: f = 31° 30’ 36.7” North, l = 9° 46’ 31.2” West
 In Morocco, one had better use the French Army Truncated                                                 of Greenwich. The same point on the Réguliere Datum of
 Cubic Lambert Conic projection. Watch out for that “shrink-                                              1922 is: f = 31° 30’ 13.178” North, l = 9° 46’ 23.643” West of
 wrap” software in perfect conformity with United States                                                  Greenwich. The Mosque d’Agadir has also been recomputed
 Standards.                                                                                               on the Réguliere Datum of 1922 as: f = 30° 25’ 54.785” North,
     The Maroc Nord and Maroc Sud zones have an eastern                                                   l= 9° 37’ 36.811” West of Greenwich.
 limit to their Grids that are defined by the 448,000 meter                                                  The Kingdom of Morocco added two more zones to their na-
 Easting (X) coordinate of the North African ellipsoidal Bonne                                            tional Grid system to cover the annexed former Spanish Sahara.
 projection. The intersection of this Grid limit with the grati-                                          Maintaining a single national Central Meridian (lo) = 6G West of
 cule was a graphical simplicity but a computational night-                                               Greenwich; for Zone III the Latitude of Origin (fo) = 29G North,
 mare until the paper of Karl Rinner was used at AMS. In the                                              the Scale Factor at Origin (mo) = 0.999616304, and the False Ori-
 1930’s, Professor Rinner published a paper (in German) de-                                               gin is 1,200 kilometers Easting, 400 kilometers Northing. For
 tailing his development of the formulae for the ellipsoidal                                              Zone IV the Latitude of Origin (fo) = 25G North, the Scale Factor
 Bonne projection in series form. AMS developed a reversion                                               at Origin (mo) = 0.999616437, and the False Origin is 1,500 kilo-
 of his series, and computational algorithms were developed                                               meters Easting, 400 kilometers Northing. The National Imagery
 for the North African Bonne in Morocco among other places.                                               and Mapping Agency (NIMA) lists the shift from “MERCHICH
     In the past 50 years or so, a couple of other places on the                                          Datum” (sic) to WGS 84 Datum as: DX = +31 meters ±5 m, DY =
 Atlantic coast have been rumored to be datums in Morocco.                                                +146 meters ±3 m, DZ = +47 meters ±3 m. This relation is based
 Those places are Modagor and Sidi Ifni. Neither of these are                                             on nine stations somewhere in Morocco.
 datums; rather, they are local Grids based on the Réguliere
 Datum of 1922. In particular, the Sud d’Ifni 1955 Hatt Azi-                                                                          ............

                   GPA AD                                                                                          Waypnt. AD
                  1/4-V, b&w                                                                                       1/4-V, b&w

658   J u n e 19 9 9                                                                                                PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING

Shared By: