6.2 The projection analysis and the deliberate selection of projection

In many cases, we don’t know the exact projection of a map or scanned cartographic database. However, when rectifying them, we shall define a coordinate system. For this we shall look up, or, if this is not feasible, we shall estimate the projection type, the projection parameters, and, if needed, the geodetic datum.

Before declaring the coordinate system of a map unknown, we shall try to look up its metadata in the literature. We can seek for references in the text of the map frame (Fig. 36). In some cases, the projection type is given, while the parameters are not. In many cases, we find a reference to a national grid, without its details; we can seek for detailed reference in textbooks or by internet search. Topographic maps are hardly made in ‘unresolved’ coordinates systems (however, the 1980’s Hungarian hiking maps provide interesting exercise for the analyzer). The national grid and its datum of the area provide always a good starting point, even it is not referenced. If there were more standard grids of the country in the questioned time frame, all of them are worth to try. Sometimes the sheet labeling system helps to select the correct projection.

Frame of an American topographic map

Fig. 36. In many US topographic maps not only the projection type (here: Lambert Conformal Conic) but also the projection parameters (here: the standard parallels) are given. Lucky case!

For example, the possible coordinate systems of a map or cartographic database in Hungary are: EOV, Gauss-Krüger grid, Budapest-centered Stereographic grid. The EOV has been introduced in 1975; therefore prior to this date there were no maps in this system. The Gauss-Krüger grid was used even for civilian purposes from the 1960s. However, the coordinate system was secret: in these maps there are either no coordinate reference (the geographic coordinates of the corners can be computed), or a Stereographic grid is provided. If the sheet label starts with ‘L/M-33/34’ (the dividers mean alternatives), the map is in Gauss-Krüger system. The sheet label of the 1:75000 scale Stereographic maps is of four digits. The label of the 1:25000 sheets of this system is completed by a hyphen and a number 1-4, the geographic longitudes are often given from the Ferro prime meridian. The above mentioned Hungarian hiking maps are in Gauss-Krüger system but they are rotated to magnetic north and their kilometer grids follow no standard system.

If the area of the map with unknown projection is small, it is practically not important, which projection is selected for the rectification. Within 10-20 kilometer distances, the deflections are not exceeding our aimed accuracy of about 5 meters. In this case, the selection of the geodetic datum is important; one base point is enough for its parametrization (see Point 4.5). The size and shape of the ellipsoid is not really important, its dislocation should be set to optimum horizontal fit.

If the scale of our map is low, and it shows a relatively large area, the situation is lucky from a point of view, that the accuracy of the map reading, the half map millimeter represents several hundred meters on the terrain. Therefore, and projection can be selected that approximates the real map projection with this, very large, error margin. Besides several hundred meters of accuracy level, the selection of the geodetic datum is either less important. For the selection of the projection, we shall analyze the latitude-longitude grid.

In mid-latitudes (e.g. in Europe), the latitude lines in the overview maps are often more or less concentric circles, while the meridians are more or less straight lines, pointing to the pole, while the angles between them are equal to each other. In this case, we can use a Lambert conformal conic projection, even if it is not the native projection of the map.

A common error is, when the rectification is made by geographic coordinates of the cross-sections of the parallels and meridians. This is an incorrect procedure, resulting large errors. The correct procedure is to analyze the latitude-longitude grid, estimate a projection type and estimate its best parameter set. Upon completing this, the coordinates of the cross-sections should be transformed to this newly defined projection for ground control point definition. When we use the real projection of the map, the rectified result is a rectangular image, without distortion at the corners (Figs. 37 & 38). In case of small-scale maps, the geodetic datum selection is not important.

Lazarus map of 1528 in Google Earth

Fig. 37. The map of Hungary by Lazarus (1528), rectified in its own projection: the result is an undistorted rectangle.

Lipszky map of 1810 in Google Earth

Fig. 38. The map of Lipszky (1810): the geo-referred map is an exact rectangle, the yellow zone around it is the envelopping arc trapezoid.