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The absolute dynamic topography, from which the ocean’s currents can be derived by geostrophy, is obtained, either by subtracting the geoid height from the altimetric Mean Sea Surface height above the reference ellipsoid, or by estimating the ocean Mean Dynamic Topography and adding it to the altimetric sea level anomalies, which are known with centimeric accuracy. Huge improvements have been made since the launch of the first satellite altimeters, for the estimation of both the geoid and the Mean Dynamic Topography. At the present time, satellite-only geoid models based on GRACE data are useful for oceanographic studies at scales greater than 300 km. In the meanwhile, a number of methods have been developed to estimate the shortest scales of the ocean’s Mean Dynamic Topography. Most recent MDT solutions have a global \({\raise0.7ex\hbox{1} \mathord{\left/ {\vphantom {1 4}}\right.\kern-\nulldelimiterspace}\lower0.7ex\hbox{4}}^ \circ \) resolution. Consequently, an increasing number of scientific studies have been recently published, based on the use of the absolute dynamic topography signal, covering a number of topics, from the assimilation of altimetric data into operational ocean forecasting systems, the study of eddy-mean interactions, the computation of volume transport, the monitoring of ocean currents. Finally, further improvements are expected from the future exploitation of GOCE data, from which the geoid will be mapped at 100 km resolution and 1–2 cm accuracy. However, in the upcoming context of high resolution wide-swath altimetry, and increasing need for high resolution coastal products, the merging of GOCE data with higher resolution sources of data will be mandatory.

The marine geoid defines the hydrostatic equilibrium shape that sea level would take in the absence of tides, currents and winds. The geoid is not directly observable, but its height above a reference ellipsoid may be calculated from a model of the Earth’s gravity field. Satellite altimeters measure the instantaneous sea surface height, which is the sum of the geoid plus the dynamic topography associated with the ocean’s responses to tidal and atmospheric forcings. In the early days of altimetric oceanography, knowledge of the geoid was poor and so altimeters are usually placed in exact repeat orbits to facilitate observation of the temporal variations in sea surface height. Recent gravity field models have geoid height errors around 5 cm and geoid slope errors around 1.5 μrad. Errors in the models are primarily at full wavelengths shorter than 20 km, so that some dynamic topography signals may now be directly observed. While satellite gravimetry from missions such as GRACE has improved the long wavelength geoid, there is considerable geoid power at wavelengths too short to be measured by gravimetry at orbital altitude. Determination of the geoid at mesoscale and shorter wavelengths has come from altimetry. Careful filtering has allowed to separate the geoidal height and ocean dynamics signals in the altimeter data, and thereby to refine the marine geoid. Verification of this comes from comparison of marine gravity field models against ship gravimetry. Further improvements in the accuracy of the marine geoid will require a satellite altimeter mission with improved signal-to-noise ratio and a spatially dense (less than 5 km) network of groud tracks. One may hope that CryoSat-2 will offer some improvement.

It is demonstrated that no global model of the wet tropospheric zenith delay is able to reproduce the value obtained directly on the basis of aerological sounding with comparable accuracy. The spectacular artifacts resulting from the global model application are apparent seasonal variations of the GPS station altitude with respect to the reference ellipsoid. The method for the construction of a local wet tropospheric zenith delay model, based on a sufficiently representative sample of local aerological data, is proposed. Its systematic error does not exceed that of instantaneous local wet tropospheric zenith delay determination from the aerological data (0.5 cm) and reduces the apparent seasonal variations of altitude. The model is very convenient in every day use: it is sufficient to multiply the value of the actual refractivity at the ground level by a certain factor determined for a given month.

Many problems of geodynamics depend on spatial relationship of points and their temporal variations. To solve these problems it is convenient, but not necessary, to use a reference frame. To use a reference frame, a scheme is needed by which the coordinates of any point expressed in this frame could be obtained. Coordinates are hardly ever measured directly. Instead, they are computed from measurements of other quantities within the framework of a theory that relates the measured quantities with the coordinates. Such a scheme will be called a reference system. Reference systems have been realized using simple theories and reducing the measurements with the best available, but not always complete, theories. This geometric (static) method has been used to a great extend to define astronomic reference systems (star catalogues) and geodetic reference systems (geodetic datums). With space techniques, a method can be used based on dynamic principles. A space object moving according to a certain theory (assumed to be known) defines in a time dependent way the representative points. A reference system of this type is the WGS 72.

In conventional geodetic systems, locations of points on the surface of the earth may be defined either by means of natural (astronomic) or geometric (geodetic) coordinates. The natural coordinates, the astronomic latitude (Φ), longitude (Λ), and the orthometric (mean sea level height (H), being gravity dependent, are conventionally referenced to the geoid and are determined from “natural” observations (astronomic, gravimetric and spirit leveling). The geometric coordinates, the geodetic latitude (ϕ), longitude (λ) and height (h), are referenced to a (generally) rotational ellipsoid of arbitrary size, shape and orientation, and are determined from geometric (length and/or direction) observations.

The center of mass of the Earth is commonly taken as origin for the coordinate systems used in satellite geodesy. In this paper the notion of the “geocenter” is discussed from the point of view of mechanics and geophysics. It is shown that processes in and above the crust have practically no impact on the position of the geocenter. It is possible however that motions of the inner core may cause variations of the geocenter of the order of 1 m. Nevertheless the geocenter is the best point for the origin of a coordinate system. Mather’s method of monitoring geocenter motion is discussed, and some other possibilities are mentioned. Concerning the scale problem, the role of the constant GM and time measurements in satellite net determinations are briefly discussed.

Single measurements of gravity cannot give sufficient information about the position of measuring points with respect to some terrestrial reference system. Only a set of gravimetric stations all over the Earth combined with a determination of their coordinates allows one to determine (from the solution of Molodensky’s problem) the heights of these stations with respect to a level ellipsoid with center at the geocenter. Given in addition their heights above some reference ellipsoid, whose position in the Earth’s body is fixed through a set of reference points on its surface, the position of the geocenter in the same reference system may be obtainedo