TY - JOUR

T1 - On the geoid-quasigeoid separation in mountain areas

AU - Flury, Jakob

AU - Rummel, Reiner

PY - 2009/9

Y1 - 2009/9

N2 - The separation between the reference surfaces for orthometric heights and normal heights - the geoid and the quasigeoid - is typically in the order of a few decimeters but can reach nearly 3 m in extreme cases. The knowledge of the geoid - quasigeoid separation with centimeter accuracy or better, is essential for the realization of national and international height reference frames, and for precision height determination in geodetic engineering. The largest contribution to the geoid - quasigeoid separation is due to the distribution of topographic masses. We develop a compact formulation for the rigorous treatment of topographic masses and apply it to determine the geoid - quasigeoid separation for two test areas in the Alps with very rough topography, using a very fine grid resolution of 100 m. The magnitude of the geoid - quasigeoid separation and its accuracy, its slopes, roughness, and correlation with height are analyzed. Results show that rigorous treatment of topographic masses leads to a rather small geoid - quasigeoid separation - only 30 cm at the highest summit - while results based on approximations are often larger by several decimeters. The accuracy of the topographic contribution to the geoid - quasigeoid separation is estimated to be 2-3 cm for areas with extreme topography. Analysis of roughness of the geoid - quasigeoid separation shows that a resolution of the modeling grid of 200 m or less is required to achieve these accuracies. Gravity and the vertical gravity gradient inside of topographic masses and the mean gravity along the plumbline are modeled which are important intermediate quantities for the determination of the geoid - quasigeoid separation. We conclude that a consistent determination of the geoid and quasigeoid height reference surfaces within an accuracy of few centimeters is feasible even for areas with extreme topography, and that the concepts of orthometric height and normal height can be consistently realized and used within this level of accuracy.

AB - The separation between the reference surfaces for orthometric heights and normal heights - the geoid and the quasigeoid - is typically in the order of a few decimeters but can reach nearly 3 m in extreme cases. The knowledge of the geoid - quasigeoid separation with centimeter accuracy or better, is essential for the realization of national and international height reference frames, and for precision height determination in geodetic engineering. The largest contribution to the geoid - quasigeoid separation is due to the distribution of topographic masses. We develop a compact formulation for the rigorous treatment of topographic masses and apply it to determine the geoid - quasigeoid separation for two test areas in the Alps with very rough topography, using a very fine grid resolution of 100 m. The magnitude of the geoid - quasigeoid separation and its accuracy, its slopes, roughness, and correlation with height are analyzed. Results show that rigorous treatment of topographic masses leads to a rather small geoid - quasigeoid separation - only 30 cm at the highest summit - while results based on approximations are often larger by several decimeters. The accuracy of the topographic contribution to the geoid - quasigeoid separation is estimated to be 2-3 cm for areas with extreme topography. Analysis of roughness of the geoid - quasigeoid separation shows that a resolution of the modeling grid of 200 m or less is required to achieve these accuracies. Gravity and the vertical gravity gradient inside of topographic masses and the mean gravity along the plumbline are modeled which are important intermediate quantities for the determination of the geoid - quasigeoid separation. We conclude that a consistent determination of the geoid and quasigeoid height reference surfaces within an accuracy of few centimeters is feasible even for areas with extreme topography, and that the concepts of orthometric height and normal height can be consistently realized and used within this level of accuracy.

KW - Geoid

KW - Mean gravity along plumbline

KW - Normal height

KW - Orthometric height

KW - Quasigeoid

KW - Topographic masses

UR - http://www.scopus.com/inward/record.url?scp=69249221653&partnerID=8YFLogxK

U2 - 10.1007/s00190-009-0302-9

DO - 10.1007/s00190-009-0302-9

M3 - Article

AN - SCOPUS:69249221653

VL - 83

SP - 829

EP - 847

JO - Journal of geodesy

JF - Journal of geodesy

SN - 0949-7714

IS - 9

ER -