The effect of anomalous global lateral topographic density on the geoid-to-quasigeoid separation

Abstract

The geoid can be computed from the quasigeoid by applying the geoid-to-quasigeoid separation. The geoid-to-quasigeoid separation is also needed for a vertical datum unification. Information about the actual topographic density distribution is required to determine accurately the geoid and orthometric heights. In this study, we estimate the effect of (lateral) anomalous topographic density on the geoid-to-quasigeoid separation. This became possible after releasing the first global lateral topographic density model UNB_TopoDens. This model provides also information about topographic density uncertainties. According to our estimates by using the UNB_TopoDens model, the effect of anomalous topographic density on the geoid-to-quasigeoid separation globally varies mostly within ±0.02 m. In mountainous regions (particularly in the Himalayas and Tibet), this effect could reach (or even exceed) ±0.1 m. The analysis also reveals that the errors in computed values of the geoid-to-quasigeoid separation attributed to the UNB_TopoDens density uncertainties (provided in terms of standard deviations for representative lithologies) are globally mostly within a few centimeters. In parts of mountainous regions with large topographic density uncertainties, however, these errors might exceed ±0.1 m. There is another crucial aspect we address here. According to the UNB_TopoDens model, the average topographic density for the whole landmass (except for polar glaciers) is 2247 kg m−3. This average density is considerably smaller than the value of 2670 kg m−3 that is typically used in geodetic and geophysical applications. This new estimate, if confirmed independently, might have implications on Helmert orthometric heights (adopted in many countries for a vertical datum realization). Changes in Helmert orthometric heights due to adopting this new estimate of the average topographic density are systematic and reach several decimeters. We, therefore, propose to use a gravimetric geoid model for a practical realization of vertical datums that incorporates the topographic density information in countries where Helmert orthometric heights are adopted. This recommendation is fully compatible with modern concepts for a vertical datum realization based on using a gravimetric geoid model and geodetic (ellipsoidal) heights. We also address inconsistencies in computations of Helmert orthometric heights and gravimetric geoid models, and propose to use only accurately computed orthometric heights (including variable topographic density term) to combine (or fit) a gravimetric geoid model with geometric geoid heights at GPS-leveling benchmarks.