Higher-Order Ionospheric Corrections derived from realistic electron density fields

We developed a rapid and precise algorithm to compute Higher-Order Ionospheric Corrections (HOIC) utilizing realistic electron density fields. The electron density field is derived from the International Reference Ionosphere (IRI) and the required magnetic field is the International Geomagnetic Reference Field (IGRF). Direct application of such HOICs is regarded impractical due to the large data volume to be handled. Therefore, we developed a parameterized version; for any location near the Earth's surface (grid with a resolution of 2.5° times 5°) a set of HOICs are computed (various elevation and azimuth angles) and the coefficients of a polynomial expansion (Zernike polynomials) are stored in a look-up-table. These look-up-tables cover the time period 1990-2019 and are available via FTP (ftp://ftp.gfz-potsdam.de/pub/home/GNSS/products/gfz-hoic/). We call this parameterized version GFZ-HOIC. A scalable version utilizing GNSS Total Electron Content (TEC) maps is under construction. A version available for real time applications is foreseen. With such accurate and easy-to-use HOICs available we performed extensive impact studies. For example, we examine how HOIC leak into estimated station coordinates, clocks, zenith delays and tropospheric gradients in Precise Point Positioning (PPP). The study includes a few hundred globally distributed stations and covers the time period 1990-2019. The PPP simulation shows the known significant systematic impact of HOICs on the estimated station y-coordinates and the estimated north-gradient components. In addition, the PPP simulation reveals the significant systematic impact of HOICs on the estimated zenith delays. This impact is not caused by higher-order terms in the formula for the refractive index of the ionosphere. This impact is caused by the ray-path bending effects. These ray-path bending effects are automatically taken into account thanks to the ray-tracing algorithm that is used in the derivation of the HOICs. In conclusion, GFZ-HOICs are both highly accurate and easy-to-use so that we can recommend them for practical applications.