The "SITRA" : methodological approach (part 4)

Conversion of the coordinates

For convention the datum is defined as the whole parameters that individualize the system of geodetic reference, characterized by the ellipsoid of rotation and by its position. The ellipsoid is mathematically a representable surface, directed in such motion by approximate to the best the geoid (equalpotential surface of the gravitational field passing for the middle level of the seas) in a point, motto point of emanation, select, generally, in the central part of the zone to be represented.

The procedure that brings to the orientation of the ellipsoid in the point of emanation can be synthesized through the following phases : determination of the geographical coordinates of the point of emanation (you determine through astronomic procedures) and determination of the direction of the celestial or astronomic meridian.

In the practice the definition of datum is tied up to a series of points materialized on the terrestrial surface, to which determined values of the coordinates are attributed (such operation constitutes the so-called realization of the datum). To every geodetic datum, therefore, a geodetic net is associated, tightly consequential from a datum group of measures and from the relative calculation of compensation that, through the coordinates of its vertexes, it defines and it materializes the datum up to notable distances from the point of emanation.

Generally every Country is endowed with at least a proper geodetic datum, whose definition stays valid for a lot of time. In Italy at least three different systems of reference coexist because the historical evolution of the geodetic nets and the cartography (without considering the cadastral system that represents one of them further). The first system, following a chronological order, it goes up again to 1940 and has been defined as it systematizes geodetic national "Roma40." It is currently the system of Italian official reference, whose ellipsoid, says International or Hayford, is directed to Mt. Mario (in Rome). For the determination of the geographical coordinates, the values of longitude are calculated beginning from the passing meridian for Mt. Mario, while those of longitude beginning from the equator.

Fig. 1 : Compensation ED50

There isn’t a materialized geodetic net in partnership to this system of reference, because a new compensation was not effected, but simply a "transport" of the vertexes of the fundamental geodetic net of 1° order ; such points maintained, in the new system, all of their inaccuracies and not homogeneity Then were performed, with modern calculation methods, partial compensations of some blocks. The second datum has been elaborated in 1950, using as surface of reference the International ellipsoid of Hayford, having however middle orientation on a series of European observatories. This datum, of European value, it is known with the acronym of ED50 (European Datum 1950) and the coordinates of longitude are calculated beginning from the meridian in Greenwich, while the values of latitude are always measured from the equator. The net in partnership drift from a selection of chains of triangles drawn by the nets of the single states, compensates in block to European level (Fig.1).

Finally, in the last decades, with the advent of the satellite positioning, a datum of world value has been defined, the WGS84 (World Geodetic System) used by GPS (Global Positioning System). Unlike the first two systems this uses a very different ellipsoid from the precedents, also it defined WGS84, with orientation ellipsoid central, that is the center of the coincident ellipsoid with the center of terrestrial mass and the axis of coincident rotation with the axis of terrestrial rotation calculated in 1984.

Fig.2 : Net IGM95

Also in the case of the global data, the concrete definition of the system of reference passes through points materialized on the ground, of which the coordinates are established. Also in this case, therefore, to the datum it is in partnership a geodetic net : it deals with international nets, increased then to national level. In Italy, the geodetic net that realizes the datum WGS84 is the net IGM95 (Fig.2), determined by the Military Geographical institute with measures GPS performed around halves the years’ 90. Such net constitutes an increasing of the European net EUREF (what in turn part of the world net is IGS) based on the European datum ETRS89, in agreement with the European continental base and practically coincident with the WGS84.

They exist then, to local level, realized nets or in progress of realization from various Corporate body (Regions, Inventory, Provinces, etc.) what increases subsequently the IGM95 net. In Molise such net has been realized by the Region in 2004. In the last years they have begun working besides in Italy numerous permanent stations GPS/GNSS, for a lot of which the coordinates are been calculated WGS84 through connections to the net IGM95. With these progressive increases, the system WGS84 is materialized on the territory and it practically becomes accessible to all the technical consumers.

Once defined the geodetic datum in which he operates, the procedure that allows the passage from the curved surface of the earth that plain happens through a methodology note as geographical projections. The coordinates drawn on the plan are said Cartesian coordinates and they result of extremely easy to use. However a twice correspondence exists among the points of the ellipsoid and the plan of the paper that it allows to go up again to the position of a point on the ellipsoid, it notices its cartographic position, therefore the cartographic plain coordinates are entirely in practice equivalent to the geographical coordinates ((, (). In Italy three types of plain coordinates or kilometric are used on primarily the three geodetic data previously described :
 Gauss-Boaga Roma40
 UTM - ED50
 UTM - WGS84.

In Italy, and accordingly in Molise, the cartographic coordinates more used for defining the plane positions in the surveys, in the aerial photo elaboration, in the earth relief with traditional topographical techniques or GPS they are the coordinates Gauss-Boaga (N, W). In the system of reference Gauss-Boaga Italy is divided, from the passing meridian for Mountain Mario (Rome), in two fused (East and West) with ampleness of 6°. The fused two central meridians are respectively set to 9 and 15° by the fundamental meridian in Greenwich. To the purpose to avoid the use of negative numbers for the abscissas of the points set to West of the respective fundamental meridians, resorts to the fictitious move of the origin of the abscissas founding one "false origin." Particularly, for convention to the origin the value of 1500000 is assigned in the fused West and 2520000 in the fused East.

Also in the realization of the project SITRA one of the most onerous problems, both from the economic point of view and working, it is connected with the transformation of the coordinates (and therefore of the thematic cartographies) from a system of reference to another.

Particularly the problem that is set there it concerns the necessity to keep on maintaining the full compatibility and the maximum possible precision with some GISs you activate to level of territorial Corporate body (Region, Province, Common) starting, contemporarily, a trial allows to progressively migrate toward more recent systems of reference and "European", or toward the WGS84.

The existing GISs in Molise all have been realized using as datum the system of national geodetic reference (Roma40), and as system of plain coordinates that of Gauss-Boaga. From this the choice to maintain such datum as reference for the cartographies of base and job to be inserted in the SITRA. In the same time, however, they were thought to create some certified procedures of conversion to define new cartographies in the system of European reference for excellence or the WGS84.

In commerce numerous softwares that allow the transformation of the coordinates Gauss-Boaga coordinates WGS84 exist and vice versa, but with evident approximations above all when you effect on jobs performed to regional or local scale.

To today an only structure able exists to certify the conversions through a series of "grigliati" that they bring, stings for point, the differences of latitude and longitude among reported points to the datum Roma40 and reported points to the datum WGS84. Such structure, denominated IGMI (Institute Geographical Military Italian), it is also owner of the net IGM95 and, therefore, of the materialization of the points reported to the ellipsoid 1984 ellypsoidic central.

Such procedure, that realizes him through a realized software really from the IGMI, it allows the conversion of the coordinates of geographical elements excluding the introduction of coarse errors. The grid allow to transform the coordinates of any point on the national territory guaranteeing the declared and certified precisions (wanting) from the Military Geographical institute.

The grids are defined and referred in the system Roma40 with express geographical coordinates in degrees (you furnish to the 1/10000 of second, correspondent to around 3 mms) ; the points prepare him so that to draw an almost square sweater that covers the whole national territory with distance of 5’ in latitude and 7’30 ’’ in longitude. Knowing the positions of the points of the two grids is possible to calculate the parameters of transformation for every point of which is wanted to define the conversion.

The use of the IGMI’s grids implicates the purchase of the necessary software to effect the interpolation of the points ; only in such way it is possible to guarantee analytical correctness in the transformations (for which the introduced error is respectable) and uniformity. The software, denominated VERTO, allows to perform the conversion of express positions in geographical and cartographic coordinates among the Geodetic Systems of Reference used today more commonly in Italy (Roma40, ED50 and WGS84).

Once completed the SITRA, we will start the procedures of conversion of the coordinates that will allow to use the bases of data in both the systems of reference : Gauss-Boaga, to be able to keep on maintaining an homogeneous cartography for representation on the whole regional territory ; WGS84 to be able to open the Territorial Informative System for the Environmental Risks to European contexts as foreseen by the project NOE.