4.4 Comparison of the abridging Molodensky and Burša-Wolf parametrization

The most important differences between the abridging Molodensky (AM) and the Burša-Wolf (BW) methods are shown in Table 4:

AM parametrization

BW parametrization

Easier

More complex

Usually less accurate

Usually more accurate

The parameters can be easily computed

The parameter estimation is difficult

The parameters are unambiguous

There are two conventions at the rotation parameters

Known by all GIS software packages

Known by most (but not all) GIS software packages

Table 4. Comparison of the abridged Molodensky (AM) and the Burša-Wolf (BW) datum parametrization methods.

Here we have to note that the mapping authorities of the United States follow the AM-parametrization, while the NATO adapted the BW-method.

Applying any of these methods, due to the errors of the previous geodetic network adjustments, the transformation accuracy fits to the geodetic needs (a few centimeters) only in a small area. The high-accuracy transformation exercises should be accomplished by other methods, e.g. using higher order polynomials. However the GIS software packages usually don’t let the users to define polynomial transformations – however the usage of correction grid (GSB – Grid Shift Binary) files sometimes offers a good solution. However, out aim for the accuracy of a few meters (according to the map reading) is usually fulfilled by both methods. The usual errors of transformation from historical and modern Hungarian networks to the WGS84 are shown in Table 5:

System

Average (max.) error of AM

Average (max.) error of BW

Second survey (1821-59)

30 (200) m

Transformation not defined

Third survey (1863-1935)

5 (12) m

1,5 (4) m

DHG (1943)

2 (5) m

2 (5) m

EOV (1972)

1 m

0,2 (0,5) m

S-42 (1983)

1 m

0,2 (0,4) m

Table 5. The most frequent application errors of the two methods in Hungary. DHG (Deutsche Heeres Gitter) is the WWII German geodetic network, applied to Central and Eastern Europe.

The main source of the application errors is that usually there is no easy way to computation of the AM-parameters from the BW-type seven-parameter set. If we know the seven parameters of a BW-transformation, the three parameters of the AM-type transformation of the same datum cannot be obtained by just omitting the scale factor and the rotation parameters, keeping the shift ones only!

Sometimes it is tried to improve a less accurate BW-parameter set by substituting just the shift parameters from another transformation. As we see in the next chapter, it is incorrect; in most cases, the parameters of the BW transformation cannot be obtained separately.

If a parameter set (both AM or BW-type) provides incorrect results, especially if the transformation error is the double of the error without any datum transformation, try to inverse the signs of all of the parameters. If this does not correct the results, in case of the BW-method, try to change the signs of just the rotation parameters. Check whether the units we use are following the needs of the software used (arc seconds or radians). In most softwares, the scale factor should be given in ppm (part per million), while in other cases, the true value (a number close to the unity) is expected (the ’no scale difference’ is expressed by zero in the first and by one in the second case). And finally; most software uses the newly set parameters only after restart.