Background.

The ionosphere causes by far the largest unmodeled phase offsets in VLBI data at low frequencies and can be a significant contributor even at the highest frequencies of the VLBA. Typical ionospheric delays in the test experiments reported here are on the order of 10 ns at 2.3 GHz, equivalent to about 25 turns of phase. The ionospheric delay scales with the wavelength squared, while the phase scales with wavelength. Thus the above numbers imply roughly 175 turns at 90 cm, equivalent to a geometric error of something like 160 m. At 43 GHz (7mm), the same ionosphere would still contribute about 1.3 turns of phase or about a centimeter of path. Therefore, one cannot totally ignore the ionosphere at any frequency. The ionosphere is especially problematic because it is highly variable. Day/night variations are typically an order of magnitude and shorter term variations are also large.

The geodetic/astrometric VLBI community have long used dual frequency observations at 2.3 and 8.4 GHz (S and X bands) to remove the ionosphere. They use multiple baseband channels to span on the order of 100 MHz at 2.3 GHz and 400 MHz (sometimes much more) at 8.4 GHz. These wide spanned bandwidths allow accurate ``multiband'' delay determinations. Then the two delays (S and X) can be be used to calculate a non-dispersive component that is the same at both bands, and a dispersive delay that scales with wavelength squared and is the result of the ionosphere. The non-dispersive delay then has the ionosphere removed and can be used for solutions for source and station positions, Earth orientation, and troposphere. Note that this scheme does not provide an absolute measurement of the ionosphere. It gives a measurement of the difference in the ionospheres over the two stations in a baseline. Plus, there are arbitrary, but hopefully constant, delay offsets between the bands at both stations (different at each station) that give an arbitrary dc offset to the measured ionospheric values. This is not a problem for the geodetic/astrometric projects because it looks like a clock offset and is treated as such. But it complicates comparison of S/X ionosphere measurements with measurements based on other types of data.

Geodetic measurements using the GPS navigation system are subject to the same ionosphere that affects VLBI since both are based on measurements of delays of radio signals propagating through the ionosphere. Their solution is also similar -- the geodetic GPS observations use two frequencies within L band. The GPS community has a world wide network of receivers working all the time and so is able to gather large amounts of data about the ionosphere. Several analysis centers are now making global ionospheric models based on GPS data. Five such centers make these models available on the CDDIS (Crustal Dynamics Data Information System) data archive where they can be accessed on the internet if you have a password (which either of us can supply). The models available at CDDIS are in IONEX format and are for every 2 hours on a 5 degree grid in latitude and longitude.

In addition to the above models, NRAO has an arrangement with a private company, SATLOC, where they allow us to use ionospheric models that they provide in real time in return for us allowing them to place a receiver at our St. Croix site. Their models are calculated in real time every 10 minutes on a 2 degree grid (See VLBA Scientific Memo 22 for more details) and are intended to be used in real-time applications, mostly in agriculture. They are distributed from a satellite to special receivers at each point of use. NRAO has been provided with such a receiver which is installed at the AOC. The models are not archived unless we do it. These data are on shorter time scales and on a finer grid than the global models, but only cover the continental US. If we plan to use these models on a regular basis, we would need to establish an automated procedure to capture and archive the data, instead of doing this on a case-by-case basis as at present.

The AIPS task TECOR, written by Chris Flatters, is used to read the ionospheric models in IONEX format. It interpolates the TEC values in time and in space to the point at which the line-of-sight from each antenna to the source passes through the assumed nominal height of the ionosphere (450 km). The ionosphere is assumed to be infinitely thin. The interpolation is done in a coordinate system in which the sun direction remains fixed. Due to the large day-night differences, the ionosphere is much more constant in this frame than in one that rotates with the Earth. Note that TECOR requires an IONEX file that covers the full time range of the observations. Unfortunately the files from CDDIS start at 1:00 and go to 23:00 UT. Then another file is used for the next day. If the observations extend beyond 23:00, or start before 1:00, it is necessary to edit together the two IONEX files, which is laborious and a bit tricky. Hopefully it will be possible to get around this in the future.

In this memo, we report on comparisons of ionospheric results obtained from the GPS models and from S/X dual band observations. We treat the S/X measurements as "truth" since they directly measure the instantaneous ionosphere in the line-of-sight, subject to a constant offset that is different at each station, as mentioned above. We looked at two experiments. One was one of the regular geodetic projects from the geodetic community (RDV11). The other (TP015) was a specially designed test project in which 5 sources with reasonably high flux density and well determined astrometric positions were observed in a phase referencing style. The 5 sources were in a cluster with separations of roughly 3 to 10 degrees. The main object of the exercise was to determine if the GPS ionospheric models could provide useful improvements for phase referencing observations. Typically such observations are of target sources which are too weak to use the S/X scheme and/or are not at appropriate frequencies to measure the ionosphere directly.

In order to make the comparisons, it was necessary to derive the S/X ionospheric measurements. AIPS has some quirks that make this rather difficult. To make the corrections, we need separate multiband delays for each of S and X band. In a data set with both bands, the SN and CL tables are not structured to contain 2 multiband delays. If the bands are separated, putting the information back together is difficult. Geodetic observers deal with the ionospheric corrections outside of AIPS using SOLVE, which we could not access easily. Not wanting to struggle with the complexities of AIPS programming, we wrote a special purpose program outside of AIPS to do the derivation. That same program is able to make comparisons with GPS results and provide displays, a few examples of which will be shown below. The program is not intended for general use by the user community. In addition to the program that derives the S/X results, an additional program was written that plots the ionospheric delays, both raw, and referenced to some antenna and, ultimately to some source. This enables a direct comparison of the results from the various methods under circumstances comparable to how they would be used in phase referencing observations.

We also used the TP015 data to make phase referenced images of 4 of the target sources based on ionosphere corrected phases referenced to the fifth source. Those images were examined for quality and for astrometric accuracy. This process produced somewhat confusing results. Some are shown below, but it would seem that other effects, probably mainly the troposphere, were significantly affecting the data. For this reason, the conclusions of this memo are based mainly on the direct comparisons of measured ionospheric delays, rather than on the quality of phase referencing results.