Measuring the quality of the classical height system through its self-consistency (congruency) is investigated in this dissertation. Measuring the congruency is done by comparing the geoidal heights determined from a gravimetric geoid model with test geoidal heights derived at GNSS/Leveling points. The components of this measurement are computed as accurately as possible, e.g., the Stokes-Helmert approach is used to determine the geoid model, gravimetric and topographic corrections are applied to the spirit leveling observations to derive rigorous orthometric heights at test points, and finally, the geodetic heights are taken from GNSS observations. Four articles are included in this dissertation, one is discussing a modification to the Stokes-Helmert approach for using the optimal contribution of the Earth gravitational models and the local data. The second paper applies the methodology presented in the first paper and presents the detail results for a test area. The third paper is a discussion on the accuracy of the classical height system against Molodensky’s system and presents a numerical study to show that the classical system can be computed as accurately as Molodensky’s. The last paper presents a methodology to find the most probable solution of the downward continuation of surface gravity to the geoid level using the least-squares technique. The uncertainties of the geoidal heights are estimated using least-square downward continuation and a priori variance matrix of the input gravity data. The total estimation of the uncertainties of the geoidal heights confirms that geoid can be determined with sub-centimetre accuracy in the flat areas when, mainly, the effect of topographic mass density is taken into account properly, the most probable solution of downward continuation is used, and the improved satellite-only global gravitational models are merged with local data optimally.
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