The international reference ionosphere (IRI2007) and International Geomagnetic Reference Field (IGRF2005) models are used to create a worldwide model of apparent Global Navigation Satellite Systems (GNSS) site displacements due to unmodeled higher-order ionospheric delays for different time, seasons, and phases of the solar activity cycle. It is shown that diurnal and seasonal variability of the higher-order ionospheric delays causes apparent oscillations of the geometric center of the Earth's figure as determined by GNSS. The amplitude of the oscillations in the z direction reaches 2.5 mm for the semiannual and 3.5 mm for 11 year components when satellite orbits are considered fixed and degree 1 parameterization is used. Failure to account for the higher-order ionospheric delay when performing precise orbit determination for space-borne receivers, flying above, while the ground-based fiducial network is located below the ionosphere, will result in biases between the ground and the space segment. Such biases, changing with time and location, can cause difficulties in interpretation of results from satellite altimetry and satellite gravity missions, as systematic biases in orbital parameters can be interpreted as manifestations of geophysical processes. On the basis of the results presented, it is recommended to introduce the modeling of the second-order ionospheric delay in routine GNSS processing for global geodetic networks, especially in view of the forthcoming solar activity maximum.