Two deterministic and three stochastic modifications of Stokes’s formula: a case study for the Baltic countries

In regional gravimetric geoid determination, it is customary to use the modified Stokes formula that combines local terrestrial data with a global geopotential model. This study compares two deterministic and three stochastic modification methods for computing a regional geoid over the Baltic countries. The final selection of the best modification method is made by means of two accuracy estimates: the expected global mean square error of the geoid estimator, and the statistics of the post-fit residuals between the computed geoid models and precise GPS-levelling data. Numerical results show that the modification methods tested do not provide substantially different results, although the stochastic approaches appear formally better in the selected study area. The 2.8–5.3 cm (RMS) post-fit residuals to the GPS-levelling points indicate the suitability of the new geoid model for many practical applications. Moreover, the numerical comparisons reveal a one-dimensional offset between the regional vertical datum and the geoid models based upon the new GRACE-only geopotential model GGM01s. This gives an impression of a greater reliability of the new model compared to the earlier, EGM96-based and somewhat tilted regional geoid models for the same study area.