On quality of NKG2015 geoid model over the Nordic countries

Abstract The NKG2015 geoid model covers the Nordic and Baltic countries and has been computed based on the least-squares modification of Stokes’ formula with additive corrections method. New and precise terrestrial, airborne and shipborne gravimetric measurements, the recent global gravity model of the gravity field and steady-state ocean circulation explorer (GOCE) and detailed digital terrain models over each territory have been used for computing this new geoid model. Some estimates for the error of this model have been roughly presented by comparing it with the global navigation satellite system (GNSS) data over each country. In this paper, our goal is to have a closer look at the relative error of this model by performing some statistical tests and finding the proper corrective surface for absorbing the systematic errors over each country. Our main assumption is realisticity of the errors of GNSS/levelling data and we will investigate its consequences in estimating the error of the geoid model. Our results show that the 4-parameter corrective surface is suitable for modelling the systematic trends of the differences between the gravimetric and GNSS geoid heights in Sweden, Denmark and Finland, but a filtered discrepancies by a confidence interval of 95% should be used for Sweden. A 7-aparameter model is suitable for the filtered discrepancies with the confidence interval of 95% in Norway. Based on the selected corrective surface and our newly developed regional iterative variance estimator, the confidence interval for the error of NKG2015 geoid model in Sweden, Denmark and Norway yielded 0-6.5 mm, 1.8-5.2 mm, 14.8-17.7 mm, respectively with a confidence level of 95%. We could not estimate the geoid error in Finland because the given error of the GNSS/levelling heights is significantly larger than the size of residuals. Based on the selected corrective surfaces and our presented local variance estimator, the average error of geoid becomes 3.6, 2.4, 8.8 and 5.8 mm with a confidence interval of 68%, respectively, over Sweden, Denmark, Norway and Finland.