Precise alpine geoid determination without digital terrain models

The short wavelength geoid undulations, caused by topography, amount to several decimeters in mountainous areas. Up to now these effects are computed by means of digital terrain models in a grid of 100-500m. However, for many countries these data are not yet available or their collection is too expensive. This problem can be overcome by considering the special behaviour of the gravity potential along mountain slopes. It is shown that 90 per cent of the topographic effects are represented by a simple summation formula, based on the average height differences and distances between valleys and ridges along the geoid profiles, δN=[30.H.D.+16.(H-H').D] in mm/km, (error<10%), whereH, H', D are estimated in a map to the nearest 0.2km. The formula is valid for asymmetric sides of valleys (H, H') and can easily be corrected for special shapes. It can be used for topographic refinement of low resolution geoids and for astrogeodetic projects. The "slope method" was tested in two alpine areas (heights up to 3800m, astrogeodetic deflection points every 170km²) and resulted in a geoid accuracy of ±3cm. In first order triangulation networks (astro points every 1000km²) or for gravimetric deflections the accuracy is about 10cm per 30km. Since a map scale of 1∶500.000 is sufficient, the method is suitable for developing countries, too.