Influence of the Second-Order Ionospheric Delay on GNSS Geodetic Solutions

The level of accuracy reached today by reference GNSS technology is in great part a consequence of progress in modelling various contributions to the observables. At the same time, advances in modelling of a single effect will not necessarily lead to improvements in the final result if there exist greater mismodelled contributions from other sources. One of the effects, the importance of which has been recently understood, is the ionospheric effect of second order. The commonly accepted ionosphere-free linear phase combination eliminates the plasma-induced phase delay in GNSS measurements in the approximation of zero magnetic field. However, due to interaction of the GNSS carrier wave, propagating in an ionospheric plasma, with the geomagnetic field a small additional delay is introduced in the phase observable. The magnitude of such a delay is of the order of~1~cm, and it depends on the geographic coordinates of the observer, local time, season, and solar activity. We use International Reference Ionosphere (IRI2007) and International Geomagnetic Reference Field (IGRF2005) models to create worldwide maps of the second-order ionospheric delay and resulting geodetic displacements for different time, seasons, and phases of solar activity cycle. We show that, due to diurnal and seasonal variability of the second-order ionospheric delay, there are apparent oscillations of geocentre position. We demonstrate that the pattern of such oscillations changes with the phase of solar activity cycle. In applications to kinematic and sub-daily static positioning, we demonstrate that due to high horizontal gradients of electron total content during morning and evening hours, taking into account the second-order ionospheric effect becomes meaningful not only for the global, but also for regional networks. In the case of daily static solutions accounting for the second-order ionospheric delay can help improving the solution precision. Based on the results presented we recommend introducing the modelling of the second-order ionospheric delay in routine GNSS processing for global geodetic networks, especially in view of the forthcoming solar activity maximum.