Common adjustment of geoid and mean sea level with least squares collocation

Various vertical reference levels are used in the coastal zone, for various purposes. Being able to transform accurately and efficiently between them is of increasing interest since the need for seamless data over sea and land is growing due to sea-level rise, coastal engineering, and more frequent storm surges. We present a method for simultaneous calculation of models linking the ellipsoid, the geoid, and mean sea level using least-squares collocation. The method includes calculations of interpolated model surfaces together with associated standard error surfaces that provide estimates of the models’ uncertainty. We have applied the method on data from Norway, including sea level data and GNSS/levelling points, and calculated a mean sea surface and a dynamic ocean topography model. The estimated formal errors of the models range 0.4–1.8 cm and 0.5–3.5 cm, respectively. To assess the dynamic ocean topography model, we compared it with satellite altimetry-based datasets. Depending on which dataset used for comparison, we obtained mean differences between −3.2 and \(1.2~\textrm{cm}\) and standard deviations between 4.2 and 5.0 cm at the outer limit of the domain of the estimated models where the distances to the observations are at their longest.