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PE_RS Grids and Datums October 2


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C O L U M N                                                     Grids and Datums

The contents of this column reflect     two shorter parallel chains: the                         before WWII, the False Easting and
the views of the author, who is re-     Guerara tie chain (1909-1910) and                        False Northing were changed from
sponsible for the facts and accuracy    the Southern El Oued tie chain                           zero to 100 km for each. Interest-
of the data presented herein. The       (1909-1910). The meridional chains                       ingly, this old Bonne Grid still in-
contents do not necessarily reflect     are the Biskra chain (1872-73, 1899-                     fluences current mapping in that
the official views or policies of the   1902), the Laghouat chain (1886,                         grid limits of the Lambert Conic
American Society for Photogramme-       1899-1902), and the Saïdia chain                         Grids are still defined by Bonne
try and Remote Sensing and/or the       (1896-97). Fill nets of first-order                      Grid values. The sheet boundaries
Louisiana State University              complementary, second-order, and                         of the new Lambert Grids are com-
Center for GeoInformatics (C 4 G).      third-order triangulations were sur-                     monly computed by a reversion of
                                        veyed from 1864, following the pat-                      the late Prof. Karl Rinner’s Bonne
The area of Northern Africa cur-
                                        tern of planned mapping. The sur-                        power series formulae published in
rently known as Algeria was
                                        vey work was executed and                                Zeitschrift für Vermessungswesen
brought under Roman rule during
                                        adjusted in 94 cartonnés (books of                       during the 1930s. That reversion al-
the Second Punic War (218 – 201
                                        sections), which progressed south-                       lows cartographers to compute the
B.C.). It was known to the Romans
                                        ward from the coastal areas accord-                      intersection of a constant Bonne
as Numidia. It was conquered by
                                        ing to military requirements. These                      Grid value with a chosen arc of the
the Arabs in the 8 th century and was
                                        cartonnés were numbered in chro-                         parallel or of the meridian. Those
mainly under the rule of the Otto-
                                        nological sequence of completion.                        intersections then were used to de-
man Empire until 1705, then it was
                                        Note that, in the English-language                       fine the limits with the graticule of
occupied by the French in 1830. Al-
                                        literature of North African Geodesy,                     the Lambert Conic Grids computed
geria gained independence from
                                        one will likely find “carton,” the                       by John W. Hager of the Defense
France following a referendum of 01
                                        derivative of cartonné.                                  Mapping Agency (ex Army Map Ser-
July, 1962. Algeria is the second
                                            This original work comprised the                     vice) in 1974.
largest country in Africa after the
                                        Colonne Voirol Datum of 1875, com-                           Based on original triangulations of
Sudan, with its coastline on the
                                        monly termed Voirol 75. The funda-                       the French Army, a local (temporary)
Mediterranean Sea extending for
                                        mental point is at the geodetic pil-                     Astro station was established in the
998 km. Algeria is bounded by Tu-
                                        lar of the Colonne Voirol                                port city of Oran by Capitaine Faure
nisia and Libya on the east, by
                                        Observatory, and the astronomical                        during 1905-1906. Station Tafaraoui
Niger and Mali on the south, and on
                                        coordinates are Φ o = 36° 45' 07.9" N                    coordinates are Φ o = 39 G 3778.26" N
the west by Mauritania, the former
                                        (40 G8357.8") and Λ o = 3° 02' 49.45"                    and Λ o = 3 G 1532.06" East of Paris.
Western Sahara, and Morocco. The
                                        East of Greenwich (0 G7887.3" East                       The reference azimuth to Tessala is
highest point is Tahat at 3,003 m,
                                        of Paris). The reference azimuth                         α o = 62° 09' 57.73" and the ellipsoid
and the lowest point is Chott
                                        from south to Melab el Kora is α o                       of reference is the Clarke 1880
Melrhir at –40 m. Algeria is mostly
                                        = 322° 16' 52.7" and the ellipsoid of                    (IGN). The observations were later
high plateau and desert; the Atlas
                                        reference is the Clarke 1880 (IGN)                       adjusted and used in the 1930 hy-
and Saharan Atlas mountains are in
                                        where a = 6,378,249.2 m, and 1/f                         drographic survey of that portion of
the north along with narrow discon-
                                        = 293.4660208. The baselines mea-                        the coast of Algeria and the port of
tinuous coastal plains.
                                        sured for the Algerian triangulation,                    Oran. The Lambert Conic Grid was
   The triangulation of Algeria was
                                        with dates of execution, are Blida                       used by the French Navy for the hy-
carried out by the Dépôt Général de
                                        (1854, 1912), Bône (Annaba) (1866,                       drographic survey.
la Guerre from 1854 to 1887. After
                                        1885), Oran (1885, 1910), Laghouat                           The reader will notice that I have
1887, the Société Géographique de
                                        (1914), Ouargla (1920), Mercheria                        left off the word “conformal” when
l’Armée, headquartered in Paris,
                                        (1932), Biskra (1932), and Navarin                       describing the Lambert Conic Grids
continued the work. The first-order
                                        (1949). The original mapping was                         of Algeria. That is because the origi-
net of triangulation consists essen-
                                        cast on the ellipsoidal Bonne pro-                       nal systems that succeeded the ellip-
tially of two parallel chains and
                                        jection – the ubiquitous projection                      soidal Bonne Grid in 1906 were not
three meridional chains. The paral-
                                        du jour for the Europeans of the                         fully conformal. There are two origi-
lel chains are the coastal chain from
                                        time. The North African (ellipsoi-                       nal zones: for Nord Algerie, the Lati-
the Moroccan to the Tunisian bor-
                                        dal) Bonne Grid Latitude of Origin                       tude of Origin (φo) = 36° North (40G),
ders (1860-1868) and the chain Aïn
                                        (ϕ o) = 35° 06' N (39 G00 N), the Cen-                   the Central Meridian (λo) = 2° 42' (3 G)
Sefra-Laghouat-Biskra-Gabes (in Tu-
                                        tral Meridian (λ o) = 2° 20' 13.95"                      East of Greenwich, and the Scale
nisia) (1889-1895). There are also
                                        East of Greenwich, and, some time                                                            CONTINUED ON PAGE 1115

                                                                                                                                 CLIFFORD J. MUGNIER, C.P., C.M.S.

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C O L U M N                                                       Grids and Datums

CONTINUED FROM PAGE 1113                   consider a test point where φ = 33° N                    was reserved for military topo-
Factor at Origin (mo) = 0.999625544.       and λ = 3° E. For Nord Algerie on the                    graphic mapping, and local native
For Zone Algerie Sud, the Latitude         French Army Truncated Cubic Lam-                         systems continued in use. That tra-
of Origin (φo ) = 33° 18' North (37 G ),   bert Conic Grid, X = 528,064.182 m                       dition has resulted in some convo-
the Central Meridian (λo) = 2° 42' (3G)    and Y = –32,764.881 m; for the                           luted transformations being per-
East of Greenwich also, and the Scale      same test point on the Nord Algerie                      petuated in Algeria.
Factor at Origin (mo) = 0.999625769.       Lambert fully Conformal Conic                               The North Sahara Datum of 1959
The False Origin is 500 kilometers         Grid, X = 528,074.691 m and                              was obtained (in 1957-1958) by re-
for Eastings and 300 kilometers for        Y = –32,776.731 m. The computa-                          computing the results of the first-
Northings for both zones, and the          tional difference of the two formu-                      order nets and the first-order com-
same convention as used in the ad-         lae at the same test point is                            plimentary nets adjusted to the
jacent Kingdom of Morocco                  ∆X = –10.509 m and ∆Y = +11.850                          ED50, but referenced to the Clarke
(PE&RS, June 1999). The complete           m, for a total error of 15.839 meters!                   1880 (modified) ellipsoid where a
replacement of the Bonne Grid for          Mathematical elegance is not what                        = 6,378,249.145 m and 1/f
original topographic mapping in Al-        matters in a country’s coordinate                        = 293.465. The adjustment on the
geria did not happen until 1942.           transformations; what matters is                         Clarke 1880 (modified) ellipsoid
   During the 19 th century, projec-       computational conformity to local                        was performed such that it opti-
tion table computations were per-          legal standards. The certain condi-                      mized the fit of the shape of the
formed by hand, and all formulae           tion when a fully conformal Lam-                         geoid in North Africa, i.e., by re-
were commonly truncated past the           bert Conic will work in Algeria is                       ducing to a minimum the sum of
cubic term to ignore infinite series       based on when a particular Algerian                      the squares of the relative deflec-
terms considered at the time, too          map was compiled. That is, when                          tions of the vertical in the areas in-
small to warrant the extra effort.         the Algerian triangulation was re-                       volved. This principle was in-
For instance, the Lambert Confor-          computed for the European Datum                          tended to minimize the mean
mal Conic projection was used only         of 1950, the French dropped usage                        discrepancies between the geodetic
to the cubic term in the formulae          of the Truncated Cubic version on                        net used in the northern part of Al-
for the tables of the developed me-        the old Voirol 75. In summary, for                       geria and the astronomic net used
ridional distances. This resulted in       surveys and maps before 1948, one                        primarily in the southern part of
French Army projection tables that         must use the French Army Trun-                           Algeria. Some maps were stereo-
have become part of the arcane lore        cated Cubic Lambert Conic. After                         compiled on the North Sahara Da-
of computational cartography.              1948, one must use the Lambert                           tum of 1959 with the UTM Grid at
   Furthermore, another idiosyn-           fully Conformal Conic. The param-                        1:200,000 scale. However, many
crasy of the French Army formulae          eters of the two Lambert zones did                       maps were not cast on the UTM Grid.
is that the Lambert (fully) Confor-        not change for the Colonne Voirol                           The Lambert North Sahara Auxil-
mal Conic projection normally uti-         Datum of 1875; only the formulae                         iary Grid was directly applied to
lizes one of the principal radii of        changed. Things soon got more                            the geodetic coordinates in accor-
the ellipsoid called the Radius of         complex.                                                 dance with the definition of the
Curvature in the Plane of the Me-             In 1953-1954 the first-order                          Nord Algerie Zone with the fully
ridian (ρ o ). The French Army in-         coastal parallel chain was re-ob-                        conformal formulae. However, it
stead substituted the Length of the        served by the French. In 1959, the                       was never used in any publication
Ellipsoid Normal Terminated by the         Institut Géographique National                           or in mapping because of the large
Semi-Minor Axis (υ o) at the Lati-         (IGN), Paris, re-adjusted the entire                     discrepancies found between the
tude of Origin (λ o). Although not         first-order and first-order comple-                      rectangular coordinates of any
strictly conformal, this is the sys-       mentary triangulation to the Euro-                       given point on the Colonne Voirol
tem that was commonly used by the          pean Datum 1950 (ED50), incorpo-                         Datum of 1875 (Voirol 75) or the
French in all colonies (before             rating the results of all previous                       North Sahara Datum of 1959. This
WWII) that utilized the Lambert            surveys and adjustments. The rule                        computational experiment is the
Conic projection (including Syria;         of thumb for this Datum Shift is to                      reason for the development and
PE&RS, September 2001).                    increase both Latitude and Longi-                        subsequent adoption of the Lambert
   Standard Lambert formulae will          tude from the Colonne Voirol Datum                       Voirol 60 Grid System. This curious
not work for Algeria under certain         of 1875 to the European Datum                            system adds 135 meters exactly to
conditions, and the improper use of        1950. The UTM Grid was used for                          the X coordinates and adds 90
the fully conformal projection will        this purpose, as were all Datums                         meters exactly to the Y coordinates
yield computational errors that can        that were transformed to ED50. Like                      of the original Nord Algerie Zone
exceed 15 meters! As an example,           most countries, the ED50 UTM Grid                                                            CONTINUED ON PAGE 1116

PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING                                                                                                     O c t o b e r 2 0 01 1115
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                            Grids and Datums                                                                                                            C O L U M N

  CONTINUED FROM PAGE 1115                                                              R x = +0.4405", R y = +0.4565", and
  parameters. In other words, the                                                       R z = –0.2244". The U.S. National Im-
  Lambert Voirol 60 Grid has a False                                                    agery and Mapping Agency (NIMA)
  Easting = 500,135 m and a False                                                       does not list a three-parameter trans-
  Northing = 300,090 m. According to                                                    formation in TR 8350.2 for transform-
  the French Army in June of 1970,                                                      ing from ED50 to WGS84 in Algeria.
  “Under these conditions, when we                                                      However, the non-satellite-derived
  compare the LAMBERT – VOIROL                                                          NIMA parameters from the Colonne
  75 with the LAMBERT VOIROL 60                                                         Voirol Datum of 1875 to WGS84 are
  coordinates, the shift between the                                                    ∆X = –73 m, ∆Y = –247 m, and ∆Z
  two is always less than 50 m in ab-                                                   = +227 m, with no stated accuracy.
  solute value. This value does not                                                     NIMA states that, from the Colonne
  represent a mathematical relation,                                                    Voirol Unified Datum of 1960 to
  but rather the result of comparing                                                    WGS84, the parameters are ∆X = –
  the two sets of coordinates. It shows                                                 123 m, ∆Y = –206 m, and ∆Z = +219
  up the inaccuracies in the initial                                                    m, and each parameter is stated ac-
  VOIROL 75 system. The maps made                                                       curate to ±25 m. NIMA further
  with the LAMBERT VOIROL 60                                                            states that, from the North Sahara
  rectangular coordinates are all ref-                                                  Datum of 1959 to WGS84, the param-
  erenced to the geographic coordi-                                                     eters are ∆X = –86 m, ∆Y = –93 m,
  nates of the NORTH SAHARA geo-                                                        and ∆Z = +310 m, and each parameter
  detic system.” The current parlance                                                   is stated accurate to ±25 m.
  for this in English is the “Voirol                                                        Using a 1° by 1° 30' mesh of
  Unified 1960 Grid” on the “North                                                      ED50 coordinates over northern Al-
  Sahara Datum of 1959.” Note that                                                      geria, a set of 54 North Sahara Da-
  there is no classical origin for this                                                 tum of 1959 and WGS84 coordi-
  Datum due to the fact that it is de-                                                  nates were derived by others using
  rived from the ED50.                                                                  the transformation developed by
     In 1966, the Army Map Service                                                      IGN. I solved for the three-param-
  (AMS) developed a series of conver-                                                   eter transformation from the North
  sions on a Carton-by-Carton basis                                                     Sahara Datum of 1959 to WGS84 us-
  for transforming from Voirol 75 to                                                    ing the WGS84 Geoid such that ∆X
  ED50 with UTM coordinates. As an                                                      = –131.798 m, ∆Y = –75.442 m, and
                                                                                        ∆Z = +329.895 m. The geodetic re-
  example of the transformation se-
                                                                                        sidual RMS expressed as meters for
  ries for Algeria, the following is for
                                                                                        ∆ϕ = ±1.74 m, for ∆λ = ±1.04 m, and
  coordinates in UTM Zone 31 whose
                                                                                        for ∆h = ±4.52 m. For comparison, I
  eastings are greater than 355,000 m:
                                                                                        then solved for the North Sahara
  Carton 59: N = 0.9998873966 n –
                                                                                        Datum of 1959 to WGS84 transfor-
  0.l0000869984 e + 691.561 m and E
                                                                                        mation using the EGM96 Geoid
  = 0.9999391272 e + 0.0000869984 n
                                                                                        such that ∆X = –59.156 m, ∆Y =
  – 416.633. The stated RMSE for this
                                                                                        –77.366 m, and ∆Z = +311.265 m.
  Carton is ±0.200 m. The adjacent
                                                                                        The geodetic residual RMS ex-
  Carton 60, when used with the ap-
                                                                                        pressed as meters for ∆ϕ = ±2.12 m,
  propriate coefficients, has a stated
                                                                                        for ∆λ = ±2.51 m, and for ∆h = ±4.35
  RMSE of ±2.759 m!
                                                                                        m. In conclusion, because the IGM
     In recent years, the IGN derived a
                                                                                        seven-parameter solution cannot be
  seven-parameter transformation from
                                                                                        fully evaluated, the preferred trans-
  ED50 to WGS84 for North Africa. The
                                                                                        formation from the North Sahara
  quoted accuracy is ±2 m in X, Y, and
                                                                                        Datum of 1959 to the WGS84 Datum
  Z, and, when applying this transfor-
                                                                                        in the format given in TR 8350.2 is,
  mation, the resulting heights are ap-
                                                                                        then, ∆X = –159 m, ∆Y = –77 m,
  proximately 30 m higher than ex-
                                                                                        ∆Z = +311 m, ∆a = –112.145, and
  pected for Algeria. The parameters
                                                                                        ∆f x 10 4 = –0.54750714.
  are ∆X = –130.95 m, ∆Y = –94.49 m,
  ∆Z = –139.08 m, ∆s = +6.957 ppm,                                                                          ............

1116 O c t o b e r 2 0 01                                                                                                  PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING

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