VIEWS: 16 PAGES: 3 POSTED ON: 8/12/2010
○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ C O L U M N Grids and Datums DEMOCRATIC AND POPULAR REPUBLIC OF ALGERIA 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. PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING O c t o b e r 2 0 01 1113 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 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 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ 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