EGU General Assembly 2020
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

Altitude dependent empirical modeling of the topside ionosphere and plasmasphere using GPS- TEC from Swarm, GRACE-FO and the Sentinel satellites.

Lucas Schreiter1,2, Claudia Stolle2, Daniel Arnold1, and Adrian Jäggi1
Lucas Schreiter et al.
  • 1University of Bern, Astronomical Institute, Bern, Switzerland
  • 2GFZ Potsdam, Geomagnetism, Potsdam, Germany

Slant Total Electron Content (sTEC) measurements can be obtained by dual-frequency GPS
onboard Low Earth Orbiting (LEO) satellites. Within the last few years, a fleet of LEO Satellites at
altitudes ranging from 450 km (Swarm A/C) to 815 km (Sentinel 3) became operational. With
Swarm B, the recently launched GRACE-FO, and the Sentinel 1 and 2 satellites orbiting at
intermediate altitudes, we gain insight into the altitude dependent profile of the topside ionosphere
and plasmasphere.
We make use of this constellation to estimate a global three dimensional model of the electron
density distribution and will also carefully asses the impact of different profile functions, geometry-
free phase center variation maps and the P1-P2 receiver biases. Since the absolute value of the P1-
P2 biases are generally unknown, we focus on a consistent estimation for the whole LEO
We will present first results for selected months in 2019 and investigate the day to day variability of
the topside ionosphere and plasmasphere. We also intend to make use of COSMIC-2 data to
improve local time coverage in equatorial regions.

How to cite: Schreiter, L., Stolle, C., Arnold, D., and Jäggi, A.: Altitude dependent empirical modeling of the topside ionosphere and plasmasphere using GPS- TEC from Swarm, GRACE-FO and the Sentinel satellites., EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-4809,, 2020


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  • CC1: Comment on EGU2020-4809, David R. Themens, 03 May 2020

    Slide 5: Why did you choose to expand the model in apex altitude? These exponential/Epstein parameterizations are not often very representative in curved coordinates.

    Slide 6: While 350km for hm is somewhat consistent with GIMs, it is not consistent with reality. hm varies greatly with season, local time, and geographic/geomangetic location. As a result, you may get decent fits to TEC, but your resulting parameters Nm, Htop, and Hbot may not demonstrate physical behaviour. hm is actually very important for LEO application, much more so than for ground-based methods, because of the lost vertical symmetry to fix some issues in the layer assumption.

    Slide 6: What is your measurement window? i.e. how long of a time period is being used in your fit?

    Slide 10: Did you reserve a testing dataset that was not used in the fit, or was all of this data used in the fitting of your model?

    Slide 12: Is this just an example of one of the combinations your resolve? For getting TEC, I assume you're using the C/A-P2 or C/A-C2 combinations, not P1-P2. Often though, one will seperate the C/A-P2 bias into C/A-P1 and P1-P2 combinations. Is that what you have done here? If so, what does your combined receiver bias look like (e.g. C/A-P2)? Or have you mistakenly labeled your L1 pseudorange to L2 pseudorange bias at P1-P2. If that is what happened, please avoid naming it as such, it can be a bit confusing for geodetic audience members.

    Slide 13: If I'm not mis-interpreting your plot wrong, your colour scale is far from anything remotely close to reality. Did you by any chance use base e (ln) instead of base 10 (log) here?

    Slide 13: You do not appear to reproduce the Appleton Anomaly in NmF2. Do you have sufficient observational density to resolve it? What is your measurement density? The ability to infer vertical shape from these integrated measurements requires that there be intersecting ray paths in the topside so that information can be shared between satellites. Do you have sufficient ray intersections globally (within the effective resolution of your horizontal basis function, 24 degrees in lon x 12 degrees in lat) to provide enough degrees of freedom for signal to constrain a four-parameter vertical model like this? If you don't, the results in Slide 10 may be somewhat artificial due to overfitting.

    Slide 15 (11-23LT plot): The behaviour of your plasmasphere appears somewhat inconsistent with expected behaviour. The plasmasphere should be assimetrically stretched into the nightside (unless under storm conditions), such that the scale thickness of the nightside is much larger than the dayside in the plasmasphere. Your figure seems to suggest the opposite...

    It is very interesting work.

    • AC1: Reply to CC1, Lucas Schreiter, 04 May 2020

      Dear David Themens,

      tank you for your comments. I think there may be a lot do discuss. The model is still in a developing state, some open issues will have to be assessed. It is intended to make it an analogy to GIM maps providing short (currently 3h) snapshots but including variations with altitude.

      1-Apex coordinates

      The apex coordinates were used to trace along the magnetic field lines. This intended especially for the higher altitude regimes (~1000 km upwards), to some extent also following a bit the approach from N. Jankowski and M. Hoque(A new electron density model of the plasmasphere for operational applications and services, 2018, ) making use that the field lines may serve to a first-order approximation as isolines. For lower altitudes, this was also applied. The Layer function still is altitude dependent, I don't use the distance along the field line. However, these are strong and probably limiting assumptions.

      2-hm=350 km
      This was set according to GIM. Of course, the value is not constant in reality. For the specific date (1. July 2019, F10.7=68 SFU) I would also assume the maximum of hmF2 much lower. Unfortunately, the only measurements in these altitudes are ground-based. All the used satellites have upward looking antennas and no occultation antenna apart from GRACE-FO, where the occultation antenna is not operational. COSMIC-2 may provide a solution here. So, for now, I decided to stick to GIM.

      3-Time window for fit
      I have used a three hour time window (reference time +/- 90 min.) This is approximately two full revolutions for each satellite.

      4-Test data-set
      The fit was performed on the full data-set. For earlier tests, I did remove one full constellation (for example Sentinel 1A and 1B). Currently, I don’t have these tests available, but I surely can redo.

      5-P1-P2 bias
      This actually is the estimated receivers' P1-P2 bias for each arc. I really use P1-P2. The RUAG receivers (Swarm and Sentinel), as well as the Blackjack (GRACE FO), provide P1 and P2. C2 is not used. It would be possible also to make use of C/A, go from C/A to P1, and from there to P2 or C2. Usually, the C/A noise is significantly larger, therefore P1 was used. The C/A-P1 receiver could be directly estimated from the RINEX file removing the GPS-satellite biases using differential Code biases (provided CODE).

      6-ln or log_10
      it is the ln. If more convenient I can reproduce the plot using log_10

      7-Appleton Anomaly
      This may come from an observational issue. The Swarm (A/C) local times are near 12/24 LT and show no pronounced anomaly (neither in sTEC nor in the Langmuir probe measurements). GRACE-FO is around 7/19 LT but also here no pronounced anomaly is visible. Maybe due to the altitude. Also, the GIM shows no pronounced anomaly (This may be due to the limited resolution of spherical harmonics d/o 15). I will reproduce the Nm plot with log_10 and projected to 350 km. Maybe this will provide a hint. Also, I can provide you with plots showing the input data. Also, I can go back and find a date with a little less solar min.

      8-Slice at nightside
      I agree that the day-side should be compressed and the night-side extended. I will have a look into to figure out the causes.

      Best regards,
      Lucas Schreiter

      • CC2: Reply to AC1, David R. Themens, 04 May 2020

        Regarding 2) While your satellites are above hm in all but the most rare of circumstances, because you have parameterized the topside in this manner, there is still a single hm (for each localtion and time) that is optimal for your chosen basis set. Imagine that you had perfect electron density profile measurements from the plasmasphere to the satellite altitude. Because of your parameterization, there exists a specific hm and Nm pair that optimally fits that data, even though you don't have measurements near the peak (e.g. extrapolated). The only reason to use fixed values for parameters is if the fit is under constrained (i.e. fewer degrees of freedom than there are parameters in your basis set), which is very likely to be the case. Even from the ground with a dense network of measurements, GNSS receivers have trouble providing more than a couple degrees of freedom in the vertical, even when logging ten satellites at once. This becomes a particular problem when you have to spend one of those DoFs on a receiver/satellite bias solution. I plot of the ray geometry during your reconstruction would be helpful for inferring the stability of your fit.


        Regarding 4) A simple test would be to use your reconstructed 3D ionosphere to compare to in situ measurements, such as those from DMSP at 830km (sun synchonrus morning and evening sector), as is done by Fabricio Dos Santos Prol in his presentation (). Further comparisons to RBSP in situ measurements from their upper hybrid frequency-inferred electron density would provide you with an idea of how you are doing in representing the plasmasphere (). There is also Irina Zhelavskaya's excellent plasmaspheric model (). I'm sure she would be happy to collaborate on some comparisons to your reconstructions. Your parameterization lacks a plasmaspause, so there may be some challenges in that respect, but comparisons may provide you with some ideas on how to modify/improve your parameterization.


        Regarding 5) It is very uncommon for people to use the L1P-L2P combination for the determination of total electron content, as far as I'm aware. The P-codes are reconstructed by the receiver using L1C. They will be smoother than the C codes, but largely because the process of L1-aided tracking effectively superimposes a time smoothing filter to the C/A code observations (). Regardless, it isn't a problem if you don't care about small time scales, which this method doesn't.


        Regarding 7) The Appleton anomaly is well defined by two seperate crests near the F2-peak, but in the topside those crests converge into a single maximum. Your TEC estimates are dominated by contributions decently far above the peak, so some satellites may not see it at all while others, closer to the peak, may have a muted crest effect. Regardless, I would expect an Appleton anomaly in Nm even if it may not be well pronounced in TEC. It is likely present in the in situ electron density measurements (say, from Swarm).


        I look forward to your further validation results. 

        • CC3: Reply to CC2, David R. Themens, 04 May 2020

          hmm... it seems to be removing any links I place in the text. They were supposed to point to, hopefully, helpful resources. 

          In 4) the Prol presentation is D1768 EGU2020-7526

          In 4) the RBSP electron density reference was: Kurth, W. S., De Pascuale, S., Faden, J. B., Kletzing, C. A., Hospodarsky, G. B., Thaller, S. and Wygant, J. R. ( 2015), Electron densities inferred from plasma wave spectra obtained by the Waves instrument on Van Allen Probes. J. Geophys. Res. Space Physics, 120: 904– 914. doi: 10.1002/2014JA020857.

          In 4) Irina Zhelavskaya's presentation is D3011 EGU2020-16970

          In 5) the reference was: McCaffrey, A.M., Jayachandran, P.T., Langley, R.B. et al. On the accuracy of the GPS L2 observable for ionospheric monitoring. GPS Solut 22, 23 (2018).

          Hope these help.