5.3 Substituting projections

Sometimes we face the problem that our GIS module does not know the projection equations of one of our used systems. More frequently, we shall geo-refer a map of unknown projection. This sub-chapter discusses the procedures used in these cases.

The less-used projections are not necessarily programmed in GIS software packages. The Hungarian EOV with its double projection or the Czecho-Slovak Křovák system is often not supported in these packages. A simple user cannot make this programming work, even using the software development kits. However, it is always an option, to choose another projection type from the supported ones and to give its parameters, keeping the difference of the original and this, so-called substituting projections as low as possible. In the following, some examples are shown to use substituting projections.

A) Substituting the Hungarian EOV grid by Hotine- or Laborde-projection

The standard of the EOV grid contains a double projection: first from the IUGG67 (GRS67) ellipsoid to the aposphere, then from that surface to the cylinder. The normal parallel of the first projection is different from the latitude of the origin of the second one. In the GIS packages, the Laborde- and Hotine-projections (sometimes called also RSO; Rectified Skew Orthomorphic, or simply Oblique Mercator projection) are practically such double projections, where the origins of the two successive projections are the same. The specific case of the EOV grid is not programmed, and it is not easy to implement by ourselves.

Therefore, to use the EOV grid, we shall use substituting projection. According to analyses, this double projection is much more sensitive to changing the origin of the aposphere → cylinder step than to the position of the aposphere. So, the origin of the first projection step can be modified, to make the two origins the same. This approximation results a new, substituting projection. However, the difference between the grid coordinates provided by this method and by the original standard equations, are less than 0,2 millimeters throughout Hungary (the valid area of the projection). This makes the method applicable not only for GIS applications but also for high-accuracy geodetic use, too.

It is easy to give parameters for the Laborde-projection to use this approximation: besides the coordinates of the, now united, projection origin and the scale factor, the azimuth of the central line should be given at the origin, which is 90 degreed. The case of the Hotine-projection is slightly different: from the False Easting of the origin, we shall subtract the distance of the origin and the equator along the central line.

B) Substituting the Hungarian EOV grid by Lambert Conformal Conic projection

The Laborde- and Hotine-projections are not widespread used and in some GIS applications, they are not implemented. However, the Lambert Conformal Conic (LCC) projection is very common and known in most packages. Therefore it is worth to seek a parameter set for the LCC to approximate the EOV grid coordinates. This concept, first published by Gy. Busics, was that the central line of the LCC projection follows a parallel, which almost follows the central line of the EOV’s oblique Mercator projection. The difference between these two lines is up to a few meters in Hungary. In the practice, the origin coordinates and the scale factor defined in the above point A) can be interpreted as parameters of a LCC projection. The accuracy of this approximation is a few meters in Hungary, which suits fine the aims of GIS applications.

C) Substituting the Hungarian EOV grid by Transverse Mercator projection in small area

Some GPS receivers (especially the older Garmin ones) allow the user to give the parameters of the Transverse Mercator (TM) projection, while defining a user grid. It was shown by B. Takács that – albeit the central lines of the two projections are perpendicular – it is possible to use position-specific parameters in any area with the radius not greater than 15-20 kilometers with the accuracy of GIS needs. The procedure is the following:

FE=EEOV-ETM

FN=NEOV-NTM

D) Substituting the Budapest-centered Stereographic grid by Roussilhe-projection

The problem of the Budapest-centered Stereographic projection is of the same type as it was mentioned in point A), the double projection, with different origins. In this case, the difference is much more than at the EOV grid. However, the procedure is the same: we omit the ellipsoid → aposphere projection and giving parameters to the oblique Stereographic (Roussilhe) projection, based on just the ellipsoidal coordinates of the origin at the second projection. Because of the larger latitude difference, the accuracy is lower here, however does dot exceed 2 centimeters throughout Hungary.

E) Substituting the Czecho-Slovak Křovák grid by Lambert Conformal Conic projection

The Křovák grid is based on an oblique conformal conic projection, used exclusively in the former Czechoslovakia and its successor states. Many GIS software packages do not support this projection (or support it just because it was programmed to handle this very grid). The central line of the projection is east-west directed in the southeastern edge of Subcarpathia (Ukrainian region, formerly a part of Czechoslovakia). Going westward, it more and more leans to north. This central line cannot be defined by any other projection, so the approximation can be done only with considerable error.

It is possible to define different Lambert conformal conic grids for Slovakia and the Czech Republic, with different parameter sets. As its central line is closer to the original one in Slovakia, here the accuracy is better (average error is 6 meters, the maximum is 12 meters in Slovakia). This is acceptable for geo-referencing e.g. the 15-meter resolution Landsat ETM satellite images or topographic maps with the scale of 1:25000 or less, but not for more accurate purposes. The average approximation error in the Czech Republic is 40 meters while its extreme maximum is 82 meters. This enables the geo-reference of 1:100000 scale maps, the 90-meter resolution SRTM elevation dataset or the 250-meter resolution MODIS satellite imagery.

Finally, if we have no meta-data or reference about the projection of the map to be geo-referred, we have to choose and parametrize a projection, whose latitude-longitude grid fits well to the one of the original map.