# Presentation: 769555

## Methods and other considerations to correct for higher-order ionospheric delay terms in GNSS

**Methods and other considerations to correct for higher-order ionospheric delay terms in GNSS**

- M. Hernández-Pajares(1), M.Fritsche(2), M.M. Hoque(3), N. Jakowski (3),
- J.M. Juan(1), S. Kedar(4), A. Krankowski(5), E.Petrie(6), J. Sanz(1)
- (1) gAGE/UPC, Barcelona, Spain
- (2) Technical University of Dresden, Germany
- (3) German Aerospace Center DLR, Neustrelitz, Germany
- (4) Jet Propulsion Laboratory, Pasadena, USA
- (5) University of Warmia and Mazury, Olsztyn, Poland
- (6) Newcastle University, United Kingdom

- (1) Contact e-mail and http: _[manuel@ma4.upc.edu,  ](mailto:manuel@ma4.upc.edu,mhpajares@gmail.com)__[mhpajares@gmail.com](mailto:mhpajares@gmail.com)_, _[http://](http://www.gage.es/)__[www.gage.es](http://www.gage.es/)_

## Outline

- Introduction
- Is it necessary to routinely correct the I2+ terms in precise GNSS modeling?
- How should the I2+ correction be applied?
- How should the I2+ terms be computed?
- Conclusions

## Introduction

- The first order ionospheric term (I1) is the main contribution of the ionospheric delay to GNSS observations (99.9%, [2,1,7]).
- I1 can be removed when considering the carrier phase or the code ionospheric free combinations of dual frequency measurements (L3/Lc and P3/Pc).
- However, because of the increasing accuracy demand in precise GPS positioning, the study of the impact of the higher ionospheric terms –up to few cm in range- has become relevant.
- We are going to focus our attention in the **higher order ionospheric terms (I2+),** in particular in the second-order ionospheric term (I2), which is the most important one (typically more than 90%, and which uncertainty can reach up to more than 40% depending on the computation strategy), basically depending on the STEC and the magnetic field projection over the propagation direction at the ionospheric pierce point.
- We will briefly discuss the motivations of correcting higher order ionospheric terms, different approaches to do it, and recommendations to IGS Analysis Centers.

## Basic equations

- Both I2 and I3 terms (I2+=I2+I3) are defined here as the corrections to be applied (added) to Lc(L3) measurements, to remove the higher order iono effects.
- In the I3 approximation ([4]):
- The magnetic field term can be neglected at sub-mm error level.
- The shape term η is around 0.66 and Nmax can be estimated from VTEC, through the slab thickness (H=VTEC/Nmax).
- It can be easily adapted to include the ionospheric bending correction (typically up to few mm at low elevation, [6’’]).
- Pi,Li, Pc,Lc are the pseudoranges and carrier phases for frequencies i and I1-free combination, B0 is the magnetic field at the ionospheric pierce point, θ is the angle formed between B0 and the propagation direction, N is the electron density,fi the corresponding frequencies, STEC is the Slant Total Electron Content (N integrated along the ray path), etc...

- Yes, I2+ should be systematically corrected, in order to avoid biases of up to several centimeters in range, which produced errors in the estimations up to centimeter level in satellite dependent parameters (orbits, clocks, associated geocenter) and errors up to millimeter level in station coordinates.
- Such I2+ induced errors in precise GNSS modelling appear at different scales, associated with the corresponding TEC variation: subdaily, quasi-monthly (Solar rotation), seasonal, Solar Cycle (in particular the subdaily and seasonal variations can be important, not only on Solar Maximum conditions). In particular an apparent intranet deformation at millimeter level is produced linked to the spatial variability of I2+ effect.
- In general, when processing a global network of stations using double difference GPS positioning, the majority of the computation time is taken up by performing the least squares analysis rather than modelling the observations: it makes sense to spend a little more CPU time on the modelling to ensure the best results.

**1) Is it necessary to routinely correct the I2+ terms in precise GNSS modeling?**

**Notes:**
[EP] I would agree with you both in saying yes - it appears to have effects at the 'precise' level, particularly relating to the reference frame. The effects should also vary systematically due to the solar cycle on an interannual scale which could potentially introduce spurious trends to results.

[MF] From my point of view it is not a question which should be attributed to routinely GNSS processing only. As you all know, the I2 term induces a systematic bias to the range measurements and thus has an impact on all GNSS derived parameters (in case of neglecting it, of course).

[MHP] Yes, I think so as well (the ?routinely? term was motivated by the IGS analysis centers which should be the main target of the incoming IGS meeting). We showed that the I2 correction should be applied, in line with the conclusions of your previous works of JPL and TUM/TUD groups, in order to maximize the accuracy of geodetic products. 
But I have to say that in our study we show a different impact, compared with some of your previous works: an important part of the correction would benefit to satellite clocks and orbits, for instance, more than to the site coordinates. This is related with the point you raise in the second point, the consistency in the I2 correction application. I feel this is well understood, but do not hesitate in giving any additional input about.

[MF]  Regarding any "mean" bias(es) that is (are) induced one major concern  has to be put on homogeneity. As you may agree, the modeling of the I2 term only makes sense if both the product generation AND the use of  that products handle the I2 correction in a consistent way.

- Regarding any "residual" effects (artifical site displacements) in  addition to e.g. a common shift of the station network origin I would always prefer to model this effect.

[MHP] I fully agree as well. We also discussed and showed that the I2 correction should be applied consistently, i.e. avoiding its use with products computed without correcting it (for instance the application of a PPP strategy to I2-corrected GPS observations, by using satellite products computed WITHOUT correcting I2, should be avoided).

[MF] In addition, the magnitude of the TEC varies within time (not only  within a day but also on an annual scale). In summary, we are facing an effect being time-dependent in magnitude that impacts our "lovely“  observations. I would very much appreciate to AVOID this :-)

[MHP]  I fully agree as well! As you indicate, this is true at several scales: subdaily, quasi-monthly (Solar rotation), seasonal, Solar Cycle (in particular the subdaily and seasonal variations can be important, not only on Solar Maximum conditions).

[NJ-MH] This question remains unanswered from our side, the answer depends on the user requirements. Precise GPS reference networks estimate the cm level, so I2+ estimations could eventually help in ambiguity fixing.

## I2 effects on subdaily differential estimation

**Satellite clock effect****: ****significant (up to +2cm)**** and dependent on I2 at reference station**

**Carrier phase bias effect****: ****significant (up to +4cm)**** and dependent on I2**

**Coordinates**** (north shift of AOML): ****Small efect (up to ~1mm)**** and ****NO**** significant dependence on I2 at reference stat. The small observed effect ****depend on the relative I2 value****, regarding to the reference station (I2-I2ref).**

## Mean I2 effect on receiver positions (21 months, 2002 -03)

**Mean I2 effect on receiver positions ****(21 months, 2002 -03)**

**Receiver position effect****: Confirming previous results with differential scenario, ****the dependence on the difference of I2 values wrt neighbour receivers****, producing long term effects at mm level ****and few tenths of mm for daily repeatibility effect, in terms of**** intranet apparent deformation.**

**Some of the ****hints**** of these computations: **
**I2 processing complete**** for all the geodetic parameters, ****realistic magnetic field model**** (see below) and more ****homogeneous distribution of receivers****.**

## Subdaily residual I2 effect on satellite orbits and clocks (averaged on year 2003)

**Subdaily residual I2 effect on satellite orbits and clocks (averaged on year 2003)**

**Confirming importance of I2 effect on satellite clocks ****and orbits (up to 1 cm and several mm, ****latitudinal signatures****)**

**NORTH**** **

**EAST**** **

**RADIAL**** **

**CLOCKS**** **

**BIAS**** **

**STD.DEV.**** **

**Latitude / degrees **

**Local Time / hours **

**I2 effect on Satellite Orbit estimation**

- The overall I2 effect (orbit displacement + dynamical integration) produces a general averaged Z-displacement of the orbits of several millimeters.
- It is correlated with the **Global Electron Content** (GEC, VTEC integrated along the overall Ionosphere, computations from 2002.3 to 2004).

- The I2+ correction should be applied in a consistent manner, by using GNSS products (such as satellite orbits and clocks) computed after applying these corrections on GNSS measurements.
-  There are two possible strategies (among others with specific coefficients at different regions as e.g. Europe, see [6] and [6’]), applicable at global scale:
- (1) **Forming a *****new linear combination of observables Lc*(L3*),Pc*(P3*), with coefficients dependent on magnetic field*** (and on STEC for I3) to cancel out I1+I2+ effects.
- This is a compact approach but with a new carrier phase bias which is variable, depending on the magnetic field, ray geometry and STEC (or ionospheric phase combination ambiguity).
- The method of Brunner and Gu does not require calculation of the TEC and is time dependent.  It is done by introducing a new 'dynamic' LC combination, which includes the second order term, though it introduces an error into the bias term.  This is the default method implemented in GIPSY, though the TEC option is available as well.
- (2) **Correcting each measurement separately (again using magnetic field and electron content), before to perform the I1-ionospheric free combinations Lc(L3).**
- As the magnitude and sign of the correction term depend on the signal's direction (intersection angle with the magnetic field) and the actual TEC, it would be preferable to use a model that allows to correct each individual measurement in order to maintain the carrier phase ambiguities as constant values, but you can need an external source for STEC (see next section).

**2) How should the I2+ correction be applied?**

**Notes:**
[EP] At the observation level is the approach we have taken too. In general, when processing a network of e.g. 60 stations using double difference GPS positioning, the majority of the computation time seems to be taken up by performing the least squares analysis rather than modelling the observations. With this in mind, it makes sense to spend a little more time on the modelling to ensure the investment of CPU time in the least squares adjustment provides the best result (though Iappreciate other approaches may be different.Is it necessary to routinely correct the I2+ terms in precise GNSS modeling?
[MF] As the magnitude AND sign of the correction term depends on the signal's direction (intersection angle with the magnetic field) and the actual TEC I would prefer to use a model that allows to correct each individual measurement. I do not think that it is a problem to anybody nowadays to calculate and apply an additional correction term for each individual observation. This is of course not a dogma, just an oppinion of mine (but we have done it for all the reprocessing at TUM/TUD).
[MHP] I agree as well. The intention of the question was also thinking on the ?consistency? of the correction application, point mentioned by you in previous point.
[NJ-MH] For estimating I2+ there are different approaches possible. As suggested in our papers we recommend the application of semiempirical formulas to correct higher order effects at L1 and L2 separately or using the L3 combination. The coefficients for the magnetoionic term are specific for ground based measurements at different regions as e.g. Europe. Ray path bending correction is globally valid. The approach is not applicable for precise satellite orbit corrections. 

- Once the iono single-layer simplification is taken, there are two sources to deal with: the electron content source to compute the STEC, and the magnetic field source to compute the magnetic field projection along the observation line-of-sight, at the iono pierce point.
- The correction for both Lc/L3 and Pc/P3 observations can be computed in different ways:
- The STEC can be computed from VTEC maps (IGS GIMs or regional maps provided by other services) to provide STEC vs.  using carrier phase smoothed Pi(P4) observations corrected from DCBs, for computing STEC.
- The magnetic field can be computed by using a dipolar geomagnetic model vs. a more realistic model as the IGRM.
- In particular the usage of DCB-corrected Pi(P4) observations is good enough to provide an STEC estimate (even better at low latitudes and elevations, compared with the usage of actual IONEX VTEC maps, and it can be easily applied in real-time), combined with the use of a more realistic geomagnetic model such as IGRM (I2 improvement greater than 50% in certain regions such as South Atlantic).

**3) How should the I2+ terms be computed?**

**Notes:**
[EP] The strategy we have followed to date is (using an adapted version of the GAMIT software): Compute the I2 and I3 corrections as set out in Kedar et al. (2003), Fritsche et al. (2005), after Bassiri & Hajj (1993). TEC from CODE IONEX files IGRF magnetic field. I can't comment as yet on the difference found using the IGRF as opposed to the dipole model for the magnetic field, though (as you mention) looking at Hernandez-Pajares et. al. (2007), it would seem there may well be a significant effect.

[MF] Is there any other "efficient" way to calculate I2 compared to the formulation of Bassiri and Hajj (used by Kedar et al., Fritsche et al., ...). I'm asking this question just to emphasize to think about an adequate relation between the "calculation effort (i.e. CPU consumption) for any kind of I2-modeling and the resulting/necessary accuracy. Thus, do we need to know the I2-correction just with a certain accuracy (what would that be?) or would we like to know it as accurate as possible (magnetic dipole model vs. a more realistic model?)?

[MHP] As you know the range correction for both Lc/L3 and Pc/P3 observations can be computed in different ways. Once the iono single-layer simplification is taken, there are two sources to deal with: the electron content source to compute the STEC, and the magnetic field source to compute the magnetic field projection along the observation line-of-sight, at the iono pierce point. Different possibilities appear: to use VTEC maps (GIMs) to provide STEC vs. using Pi/P4 DCB-corrected observations, for computing STEC; and by using a dipolar geomagnetic model versus a more realistic one (such as the IGRM) to compute the magnetic term. I understand that this can be a more open point. In our approach we show that using DCB-corrected Pi observations is good enough, combined with the use of a more realistic geomagnetic model (I2 improvement greater than 50% in certain regions).
As you say, probably different approaches can be valid. For me is clear the goodness of using a more realistic geomagnetic model (very important improvement in some regions such as the South Atlantic), which are available in FORTRAN open source for instance. And on the other hand the usage of DCB-corrected pseudorange can presently offer some practical advantages, among other considerations, to the analysis centers (for real-time or rapid products, they don't need the availability of Global VTEC maps in advance). 
I would like to get more consensus in this point. Or at least to identify/list several approaches in the higher iono term computation, indication its pros and cons.

[SK] Just pointing out that there is also the method of Brunner and Gu, which does not require calculation of the TEC and IS time dependent.  It is done by introducing a new 'dynamic' LC combination, which includes the second order term, though it introduces an error into the bias term.  This is the default method implemented in GIPSY, though the TEC option is available as well.  We have a paper in the workings, which compares the Bassiri and Hajj method to the Brunner & Gu method.  Will be happy to talk about it in Miami if necessary.

[NJ-MH] Corrections can easily be made by the user itself when knowing the formulas, corresponding coefficients and TEC. TEC might be provided by IGS or other TEC services available in the user region.

## A simple and accurate approach  to compute and apply the I2 correction: STEC term

**The Slant Total Electron Content, STEC,**** can be computed in a simple and accurate way, ****from carrier-smoothed geometry-free combination of pseudoranges (PI≡P4), after removing interfrequency bias values for transmitter and receiver ** (D, D’, quite stable on time, available on advance).
- This approach is not affected by the single-layer accuracy limitations in VTEC IONEX format, and can be understood as a new I1+I2 free carrier phase combination with constant bias: Lc’=α·L1+β·L2+γ(B)·P1+δ(B)·P2+ε(B)·(D+D’)

**DCB-corrected smoothed pseudorange  (PROPOSED)**

**Aligned ionospheric carrier phase (TRUTH)**

**STEC derived from IONEXmap**

## I2 at geomagnetic conjugate points (receiver positions)

## A simple and accurate approach  to compute and apply the I2 correction: Magnetic field term

**The Magnetic Field, B,**** is the second dependence of I2, which can be computed by using the more accurate International Geomagnetic Reference model (IGRM), reducing the error up to 60% regarding the previously used dipolar model (this is specially evident at the Atlantic South Anomaly -****see relative error of dipolar model at left hand plot, and comparison of I2 corrections in Ascension Island, ASC1, at right hand plot-****).**

**Summarizing approaches to compute I2+**

|  | STEC
source | Don’t require an external source (suitable for real-time) | Can be assumed a constant iono-free carrier phase ambiguity? | Scope | I2+ correction error
(assuming a nominal I2+ value of 2cm and a realistic geomagnetic field model –such as IGRM-) |
| --- | --- | --- | --- | --- | --- |
| Correcting measurements from I2+, including STEC | Klobuchar
model | OK | OK
 | Global | 30-50% (~6 to 10 mm) |
| (Kedar et al. 2003 [7], Fritsche et al. 2005 [4]) | IGS VTEC in IONEX format | NO | OK
 | Global | 10-20% (~2 to 4 mm) |
| (Hernandez-Pajares et al. 2007 [5]) | DCB corrected PI(P4) |  OK
 | OK
 | Global | ~0.1 to 1 mm (depending whether smoothed Pi is used or not) |
| New “dynamic” Lc combination
(Brunner & Gu 1991 [2]) | - | OK | NO
 | Global | 0.1% of Bi(B4) (from 1 to 10 mm for first LI measurement aligned to BI up to unbounded values otherwise) |
| (Hoque & Jakowski 2007 [6,6‘]) |    - | OK | OK
 | Regional | ~1 to 3 mm (depending on user positions) |

## Recommendations on higher ionospheric order terms for IGS ACs

- The higher order ionospheric correction (I2+) should be incorporated as an standard model term.
- The I2+ correction should be applied consistently.
- With GNSS products, such as satellite orbits and clocks, computed after applying these corrections on GNSS measurements.
- The I2+ correction should be computed in a simple and accurate way:
- The magnetic field should be computed from a more realistic model (such as the IGRM)  than the dipolar one.
- The slant ionospheric delay (STEC) can be computed from VTEC maps (such as those computed by IGS in IONEX format).
- It can be preferable, in particular for low elevation, low latitude usage or when no external GIM or TEC source is available (such in real-time), to compute STEC from  the carrier smoothed geometry free combination of pseudoranges Pi(P4), corrected by the corresponding interfrequency biases.

**THANK YOU!**

**Is I2+ related with N/S deformation in IGS combined SINEX frame?**

- Could be I2+ a possible explanation for the larger variation in the weekly network-averaged N/S component of the IGS combined SINEX frame  (after removing Helmert differences)?  There is a large common-mode annual signal in the N/S but not in E/W and much smaller in the U/D.  The dispersion among ACs also seems to be largest in the N/S component.
- At “short term” (left-hand plot, since GPSweek 1350): Apparent correlation with -GEC, qualitatively compatible with I2 origin in a similar way that has been found between geocenter/satelllite and GEC ([4], [8], [5]).
- The apparent correlation seems quite good for some receivers.
- Moreover in the residuals for receivers around the geomagnetic equator the signature is much more clear, than considering all of them. This is again qualitatively compatible with the potential I2 origin ([5]).
- Within this period a  geomagnetic-latitudinal effect compatible with [5] is observed, being significant in the periods with higher GEC (such as GPSweek 1440) and practically flat for low GEC periods (GPSweeks 1432 and 1450).
- At “long term” (right-hand plot, since GPSweek 1000), such apparent correlation is not evident with too large effects.

- [1] Bassiri, S., and G. Hajj (1993), High-order ionospheric effects on the global positioning system observables and means of modeling them, Manuscr. Geod., 18, 280– 289.
- [2] Brunner, F., and M. Gu (1991), An improved model for the dual frequency ionospheric correction of GPS observations, Manuscr. Geod., 16, 205– 214.
- [3] Datta-Barua, S. T. Walter, J. Blanch, P. Enge, Bounding Higher Order Ionosphere Errors for the Dual Frequency GPS User, ION GNSS 2006, Long Beach, USA, Sept. 2006.
- [4] Fritsche, M., R. Dietrich, C. Knöfel, A. Rülke, S. Vey, M. Rothacher, and P. Steigenberger (2005), Impact of higher-order ionospheric terms on GPS estimates, Geophys. Res. Lett., 32, L23311, doi:10.1029/2005GL024342.
- [5] Hernández-Pajares, M., J.M.Juan, J.Sanz and R.Orús, Second-order ionospheric term in GPS: Implementation and impact on geodetic estimates, Journal Geophys. Res., Vol. 112, B08417, doi:10.1029/2006JB004707, 2007.
- [6] Hoque M. M., N. Jakowski, Higher order ionospheric effects in precise GNSS positioning, J Geod ,81:259–268 DOI 10.1007/s00190-006-0106-0, 2006
- [6’] Hoque M. M. and N. Jakowski, Mitigation of higher order ionospheric effects on GNSS users in Europe, GPS Solutions, 12 (2), DOI 10.1007/s10291-007-0069-5, 2007.
- [6’’] Jakowski N., F. Porsch, and G. Mayer, Ionosphere - Induced -Ray-Path Bending Effects in Precision Satellite Positioning Systems, SPN 1/94, 6-13, 1994
- [7] Kedar, S., G. A. Hajj, B. D. Wilson, and M. B. Heflin (2003), The effect of the second order GPS ionospheric correction on receiver positions, Geophys. Res. Lett., 30(16), 1829, doi:10.1029/2003GL017639.
- [8] Petrie, E., M. King and P. Moore, Sea Level Change using Vertical Land Motion from GNSS: Higher-Order Ionospheric Effects, Geophysical Research Abstracts, Vol. 10, EGU2008-A-01900, 2008.

**References**

**Notes:**
[EP] The strategy we have followed to date is (using an adapted version of the GAMIT software): Compute the I2 and I3 corrections as set out in Kedar et al. (2003), Fritsche et al. (2005), after Bassiri & Hajj (1993). TEC from CODE IONEX files IGRF magnetic field. I can't comment as yet on the difference found using the IGRF as opposed to the dipole model for the magnetic field, though (as you mention) looking at Hernandez-Pajares et. al. (2007), it would seem there may well be a significant effect.

[MF] Is there any other "efficient" way to calculate I2 compared to the formulation of Bassiri and Hajj (used by Kedar et al., Fritsche et al., ...). I'm asking this question just to emphasize to think about an adequate relation between the "calculation effort (i.e. CPU consumption) for any kind of I2-modeling and the resulting/necessary accuracy. Thus, do we need to know the I2-correction just with a certain accuracy (what would that be?) or would we like to know it as accurate as possible (magnetic dipole model vs. a more realistic model?)?

[MHP] As you know the range correction for both Lc/L3 and Pc/P3 observations can be computed in different ways. Once the iono single-layer simplification is taken, there are two sources to deal with: the electron content source to compute the STEC, and the magnetic field source to compute the magnetic field projection along the observation line-of-sight, at the iono pierce point. Different possibilities appear: to use VTEC maps (GIMs) to provide STEC vs. using Pi/P4 DCB-corrected observations, for computing STEC; and by using a dipolar geomagnetic model versus a more realistic one (such as the IGRM) to compute the magnetic term. I understand that this can be a more open point. In our approach we show that using DCB-corrected Pi observations is good enough, combined with the use of a more realistic geomagnetic model (I2 improvement greater than 50% in certain regions).
As you say, probably different approaches can be valid. For me is clear the goodness of using a more realistic geomagnetic model (very important improvement in some regions such as the South Atlantic), which are available in FORTRAN open source for instance. And on the other hand the usage of DCB-corrected pseudorange can presently offer some practical advantages, among other considerations, to the analysis centers (for real-time or rapid products, they don't need the availability of Global VTEC maps in advance). 
I would like to get more consensus in this point. Or at least to identify/list several approaches in the higher iono term computation, indication its pros and cons.

[SK] Just pointing out that there is also the method of Brunner and Gu, which does not require calculation of the TEC and IS time dependent.  It is done by introducing a new 'dynamic' LC combination, which includes the second order term, though it introduces an error into the bias term.  This is the default method implemented in GIPSY, though the TEC option is available as well.  We have a paper in the workings, which compares the Bassiri and Hajj method to the Brunner & Gu method.  Will be happy to talk about it in Miami if necessary.

## Backup slides

## Conclusions

- It is necessary to incorporate the higher order ionospheric correction (I2+) as an standard term in precise GNSS models because: (1) the contribution of the I2+ effect is not negligible (several centimeters in range), (2) the algorithms are easy to implement. And (3) the I2+ effect, is significant to eliminate associated spurious trends, improving the GNSS accuracy, in particular on satellite clocks and orbits.
- The I2+ correction should be applied consistently, with GNSS products (such as satellite orbits and clocks) computed after applying these corrections on GNSS measurements. It would be preferable to use a model that allows to correct each individual measurement.
- The I2+ correction should be computed in a simple and accurate way, at least from IGS AC & ACCs perspectives. As it depends on STEC and magnetic field:
- Regarding to the magnetic field, it should be computed from a more realistic model (such as the IGRM)  than the dipolar one.
- Regarding to the STEC, among other sources, it can be computed from IGS VTEC maps in IONEX formats, or by correcting the geometry free combination of pseudoranges Pi(P4) by the corresponding interfrequency biases. The use of Pi(P4) is suitable for real-time application and is in general accurate enough for computing I2+ (and it can be still better at low latitudes and elevations).
- Potential relationship of I2+ effect with weekly network-averaged N/S component of the IGS combined SINEX frame has pointed out  (after removing Helmert differences): only at short term, last 2 years or so, but not for long term. More studies are needed: the reprocessing by correction the I2+ term in long time AC series can clarify this potential origin.

**THANK YOU!**

- 1) Is it necessary to routinely correct the I2+ terms in precise GNSS modeling?
- 2) How should the I2+ correction be applied?
- 3) How should the I2+ terms be computed?

**Questions**

## I2 estimation using STEC and a regional 

- The regional correction needs only slant TEC (derivable from direct link related TEC estimations at user level or from external VTEC maps via mapping function) as input.

**I****2**** estimation using STEC and a regional **
**(European) correction model **

- I2 values at Matera (Italy) during Halloween storm** **
- (28th to 31st Oct 2003)

## Backup slide 1: potential I2+ origin...

## Backup slide 2: potential I2+ origin...

## Backup slide 3: potential I2+ origin...