1. GPS Ionospheric Mapping at Natural Resources Canada
NRCan has developed a process for producing regional TEC maps over Canada in near-real-time. The technique is based on a spherical cap harmonic analysis method to interpolate vertical estimates on a standardized mapping grid. In addition to creating these maps we provide an estimate of the positioning errors encountered by GNSS users associated with the ionospheric TEC.
Reza is the one who works with the TEC data, so this is basically a summary of one of his papers. I’ll be reading from a script for some of this because my relative expertise is minimal, so if you have questions I’ll have to pass them on to Reza. My contribution to this project has been in developing and coding the spherical cap harmonic algorithm used in the mapping.
Reza Ghoddousi-Fard, Robyn Fiori
Ghoddousi-Far, R., P. Héroux, D. Danskin, and D. Boteler (2011), Developing a GPS TEC mapping service over Canada, Space Weather, 9, S06D11, doi: /2010SW

2. Introduction
As you know GNSS observations of TEC for ionospheric mapping are widely used in the space weather community to study the evolution of the ionosphere with applications to a wide array of GNSS users. Global TEC maps, like the one shown here are regularly produced and are being used to improve single frequency positioning in GPS wide-area augmentation systems for air navigation. However, as GNSS networks with continuous tracking stations are densified, the motivation for regional TEC mapping increases to improve accuracy resulting in TEC maps with better temporal and spatial resolution. Here we look at doing that over Canada using a spherical cap harmonic analysis algorithm.

3. Regional TEC mapping using SCHA - 1
The fitting is done by first identifying a spherical cap which covers Canada and transforming from a north-pole centered to a spherical cap centered coordinate system. Using that coordinate system we next represent the vTEC using a series expansion. This is very similar to the more familiar spherical harmonic expansion except the basis functions described by the Associated Legendre Functions are defined using a non-integer degree term nk(m) opposed to an integer degree term k. Here k is an indexing term for that non-integer degree nk(m). In spherical harmonic analysis the degree ‘k’ is forced to be an integer value to promote continuity at the poles. Because we’re only working with one pole and we don’t want to force a constraint at the outer region of the spherical cap, we don’t use that boundary condition.
In this equation P are the Associated Legendre Functions of non-integer degree and A and B are fitting coefficients that must be determined. These coefficients are solved by minimizing the difference between the vTEC represented in this way at measurement coordinates, and the measured values. We use singular value decomposition to do this.

4. Regional TEC mapping using SCHA - 2
Slant TEC estimates at pierce points are used to determine the vertical TEC. For regional TEC mapping the pierce point coordinates are converted to the spherical cap coordinate system centered over Canada. Using TEC at all pierce points in this coordinate system, mapping coefficients are determined. Using these coefficients TEC is then calculated along a grid of points within the spherical cap. This plot shows TEC calculated at the grid points. These points are next contoured to create a more complete picture.

5. Daily and Near-Real-Time TEC Mapping
We have two products: daily and near-real-time vTEC maps. For daily maps data from 75 stations is processed using the spherical cap harmonic algorithm to create maps for each two hour period. The station locations are shown here in green. The daily maps for a given day are all calculated at 6:30 am the next day so that the 24 hour observation file for that day can be used to estimate the average station and satellite differential code biases. The near-real-time TEC maps are generated every 15 minutes using data from 22 high-rate GPS stations using differential code biases estimated the previous day. These stations are indicated in red. Both types of maps have advantages and disadvantages. Although the daily files are only produced every two hours the following day, the output is of high resolution because there are so many stations involved. The near-real-time maps are of lower resolution, but they’re produced every 15 minutes.

6. Comparing Regional TEC to the GPS broadcast ionospheric model
The next thing I want to show you is how the Canadian regional TEC maps compare with the GPS broadcast ionospheric model. To illustrate this, consider a daily TEC map taken from the Halloween storm. These Figures show the GPS broadcast ionospheric model and the Canadian regional TEC map for the same interval. Both are drawn using the same colour scale, and you can see there are big differences of as much as ~40 TEC units. The regional model was able to pick up enhancements over the Canadian prairies (where I’m from) and the Canadian Arctic, which the GPS broadcast ionospheric model was not. This probably isn’t surprising to most of you.

7. Comparison of Regional SCHA and Global Ionospheric Maps
The IGS provides ionospheric maps at 2 hour intervals, similar to the daily regional TEC maps. Reza has compared the daily regional TEC maps to the IGS global maps by looking at the difference between the two at the location of the pierce points used to generate the regional maps. This Figure shows these results for a 36 day quiet period in Overall, the mean differences for the entire studied period is TEC units indicating no significant systematic bias between the two results. When activity levels are higher, we would expect the regional TEC map to have higher values and provide a better representation of local ionospheric variation since the global map contains less data from Canadian regions. How can we validate the TEC data during disturbed periods?

8. Validation through comparison to ePOP
One step taken in validating our product is to compare the measured and modelled vTEC at the location of pierce points. This really only tells us how well the mapping algorithm represents the input data points, and not how well the model represents the true vTEC. We can go a step further and create maps excluding certain points and then compare the measured and modelled vTEC at the location of the excluded points. As Mike pointed out in his , this again really only determines how well the model represents the inputted vTEC though, and not necessarily the true TEC, because the differential code biases have been estimated and corrected prior to data being mapped. Basically, any error in the input value is propagated into the model. So, although we can show how well the model represents the input values, we can’t necessarily extrapolate that to say how well the model represents the true TEC.
Something we’ll be looking at shortly is how well the TEC maps agree with GPS data from the GAP instrument onboard the enhanced Polar Outflow Probe or ePOP satellite. This Figure shows a TEC map with a portion of an ePOP satellite pass overplotted. Below you see the TEC projected onto that satellite pass. Unfortunately, complications with ePOP data streaming mean that it is not possible to obtain a continuous GAP data set and data are only available for short periods of time, so the data set won’t be as large as we might like for generating statistics of this kind.

9. Positioning Validation
Evaluation of ionospheric delays in the position domain is something that Mike touched on in his . This is something that Reza has started to look at as well. This Figure is from a poster Reza presented at the IGS meeting last year. Here two different ionospheric maps were compared in the position domain and the bar graph shows the mean and bias of the residual between the two values.

10. Thank You!