GLOBAL IONOSPHERE MAPS OBTAINED FROM GLOBAL NAVIGATION SATELLITE SYSTEM (GNSS) DATA AND THEIR PERFORMANCE AFTER INTEGRATION OF SATELLITE ALTIMETRY MEASUREMENTS

therein). Both observables of the system - carrier phase and code measurements - are affected by the ionosphere. According to Eq. (1) and Eq. (2), this effect depends on the signal frequency f and on the STEC between the satellite and the receiver. Thus, forming the so-called geometry-free linear combination by subtracting simultaneous observations at the two different frequencies L1 and L2, and in this way removing all frequency-independent effects (such as clock errors, troposphere delay etc.), leads to an observable, which contains only the ionospheric refraction I and the inter-frequency hardware biases Δb k and Δb i (usually in ns), associated with the satellite k and the receiver i. In the case of carrier phase observations the ionospheric observable reads as: )(42,1,4, i kk i k i k i k i bbcI   , (3) where k i 1, and k i 2, are the carrier phase observations at the two frequencies, corrected by the carrier phase ambiguities, k iI is the ionospheric refraction between the satellite and the receiver related to L1 (in meters), 2 2 2

1 ff is a factor for relating the ionospheric refraction on L4 to L1 and α is a constant used to convert meters into TECU. As it emerges from Eq. (3), the geometry-free linear combination is very appropriate for extracting information about the ionosphere. It has to be noted, that the derived ionospheric parameters are affected by the inter-frequency hardware biases (e.g. Manucci et al., 1998), also called Differential Code Biases (DCB), so when modelling the ionosphere it is necessary to estimate them as additional unknowns. In 1998 a special Ionosphere Working Group of the International GNSS Service (IGS) was initiated for developing global ionospheric TEC gird (Feltens and Schaer, 1998, Hernandez-Pajares, 2004). Up to now, four Analysis Centres (AC) - Centre for Orbit Determination in Europe (CODE) (Hugentobler et al., 2006), European Space Agency (ESA) (Feltens, 1998), Jet Propulsion Laboratory (JPL) (Manucci et al., 1998), and Universidad Politecnica de Cataluna (UPC) (Hernandez-Pajares et al., 1999), deliver daily global maps of vertical TEC and DCB values in the IONospheric EXchange (IONEX) format (Schaer et al.,

by using different estimation methods. Since the end of 2005 a combined IGS solution is also available.

3. Ionosphere parameters from satellite altimetry data Satellite altimetry missions with double-frequency radar altimeter on-board, such as TOPEX/Poseidon (T/P) and Jason-1, also provide information about the ionosphere. The T/P mission was launched in August 1992 for observing the ocean circulation and was operational till October 2005. Jason-1, launched in December 2001, is the follow-on to T/P and has inherited its main features –orbit, instruments, measurement accuracy, etc. The orbit altitude of the two missions is 1336 km. The primary sensor of both T/P and Jason-1 is the NASA Radar Altimeter operating at

6 GHz (Ku-band) and 5.3 GHz (C-band), simultaneously. The two widely separated frequencies allow TEC to be detected directly from the nadir altimetry sampling data along the satellite track (Imel, 1994).

4 TEC estimation from GNSS and satellite altimetry In order to asses the precision of the TEC estimates from GNSS and from satellite altimetry measurements, the results of the two methods have often been compared (Brunini et al., 2005, and references therein). Although there is a good general agreement between GNSS and altimetry derived TEC, some questions still remain open. One of them is related to the better understanding of the frequency-dependent systematic errors in the altimetry measurements, which would bias both the sea-level height and the TEC estimates (Chelton et al., 2001). Moreover, several studies have shown that T/P and Jason-1 overestimate the vertical TEC by about 3-4 TECU compared to the values delivered by GNSS (i.e. Brunini et al., 2005). This is a contradiction because opposite to GNSS, the altimetry derived TEC is not sensitive to the plasmaspheric contribution (TEC above ~1300 km height above the Earth surface) due to the lower orbit altitude of the altimetry satellites. On the other hand, most of the ionosphere models from GNSS data are based on the Single Layer Model (described in

1.), which does not account well for the ionospheric contribution above the altitude of the altimetry missions (Brunini et al., 2005). It has to be pointed out, that when using a single layer model, the STEC values derived from GNSS measurements have to be converted into vertical TEC (VTEC), while the altimetry missions deliver directly the vertical values. The mapping function used for this convertion is also a potential error source for the GNSS TEC estimates. Finally, for comparing with altimetry TEC, the values derived from GNSS have to be interpolated for regions far from the observing stations, i.e. such comparisons are performed in the worst scenario for GNSS.

1. Global models of the ionosphere in 3D The global maps created in this study represent the ionosphere in longitude, latitude and time and are based on the Single Layer Model (SLM). SLM assumes that all free electrons are concentrated in an infinitesimally thin layer above the Earth’s surface. The height H of this thin shell is usually set between 300 and 450 km. A signal transmitted from the satellite to the receiver crosses the ionospheric shell in the so-called ionospheric pierce point. The zenith angle at that point is z’ and the signal arrives at the ground station with zenith distance z. The relation between the measured slant TEC along the ray path and the vertical value at the pierce point is given by a mapping function (Eq. (5)). In this study the Modified Single Layer Model (MSLM) was adopted (as in www.aiub.unibe.ch/ionosphere/) and the mapping function for the transformation between STEC and VTEC reads as: 2 )sin(1 1 cos

(         zHR RzVTEC STECzF e e  , (4) with α = 0.9782 and H = 506.7 km. The GNSS-derived STEC values are extracted from the geometry-free linear combination applied on dual-frequency carrier-phase smoothed code observations. Data from around 180 stations of the International GNSS Service (IGS) is used with sampling rate of 30 seconds. In the case of satellite altimetry, the original ionospheric correction from T/P and Jason-1 is adopted and converted into VTEC by a factor depending on the operational frequency of the altimeter. In this work for the global representation of VTEC a spherical harmonic extension up to degree and order 15 was chosen (Schaer, 1999):      max

0 ))sin()cos()((sin~),( n n n m nmnmnmV msbmsaPsE  , (5) where: VE - Vertical Total Electron Content, β - geomagnetic latitude of the ionospheric pierce point, G - geographical longitude,   UTs G - sun-fixed longitude of the ionospheric pierce point, nmnmnm PNP ~ - normalized Legendre function from degree n and order m, nma and nmb - the unknown coefficients of the spherical extension. A Matlab-based software was developed for computation of 12 two-hourly GIM per day and of the corresponding RMS (Root Mean Square) maps, and daily values of the DCB for all the GNSS satellites and receivers. As mentioned in 1.4, several studies show that despite of the lower orbit altitude of the altimetry satellites, the vertical TEC delivered by these missions is higher than the values obtained from GNSS. Due to this contradiction it can be assumed, that the altimetry measurements are biased by an instrumental offset, similar to the GNSS DCB. The combination of ionosphere data from GNSS and altimetry, realised by stacking of the normal equations (see Eq. (6)), allows the independent estimation of technique-specific constant time delays additionally to the combined ionospheric parameters. Thus, we developed combined ionosphere models with additional estimation of one constant daily Jason-1 bias. Since the Jason-1 bias is computed as a single unknown, it includes the effect of the plasmaspheric component (TEC above ~1300 km height above the Earth’s surface), additionally to the actual Jason-1 instrumental offset.

2. Combination For the combination of GNSS and altimetry data a least-squares adjustment (Gauss- Markov model) is applied on each set of observations and then the normal equations are combined. This is done by adding the relevant normal matrices obtained from the two types of observations: ALTALT T ALTGNSSGNSS T GNSSALTGNSSCOMB ApAApANNN  22 (6) where N and A are the corresponding normal and design matrices and p denotes a matrix with the weights on its main diagonal. At this stage of our work we adopt equal weights ( 1GNSSp ) for all GNSS observations in both the GNSS-only and the combined solution, and a lower a priori variance of TECUalt 25.00  ( 4ALTp ) for the altimetry measurements. Concerning the relative weighting of the altimetry data, different strategies are possible. On the one hand, due to the much higher number of GNSS measurements compared to satellite altimetry, the Jason-1 data should be overweighted, in order to increase its impact on the combined GIM. In the case of overweighting, however, it becomes crucial to assess the bias between GNSS and altimetry TEC, discussed in section 1.4. On the other hand, if we take into account the higher noise of the altimetry measurements compared to the carrier-phase smoothed code observations from GNSS, a lower weight should be applied on the Jason-1 derived observations. It has to be pointed out, that the relative weighting acts like a scaling factor for the contribution of the altimetry data in the combined GIM. It is a very complex issue, depending on the different spatial and temporal distribution of the observations and on their specific systematic errors. Therefore, the relative weighting of the two types of measurements needs to be optimised and is a matter of further investigation. Nevertheless, it can be anticipated that the combination of GNSS and altimetry data will improve the general robustness and reliability of the GIM and their quality particularly over the oceans. As it can be seen in Fig.1, the spatial distribution of the altimetry observations helps to balance the gaps between the GNSS stations. Moreover, the combination procedure allows the independent estimation of technique-specific constant time delays and can thus be used to indicate and model the technique-specific systematics. Fig.1 a) IGS GNSS stations used for the IGG GIM; b) footprints of T/P and Jason-1 in two-hourly intervals, day 022 2005

Results Both the GNSS-only and the combined solutions developed within this work are referred to as IGG (Institute of Geodesy and Geophysics) GNSS-only and combined models. Some of the current results of our study are presented below, considering as example the outcomes for day 022 in 2005.

1. GNSS-only model In Fig.2 the IGG GNSS-only VTEC and RMS maps for 17:00 UT are shown. As expected, the precision of the maps is lower in areas where no GNSS sites are located, which is mainly above the sea surface and in the southern polar region. The a posteriori sigma of the GNSS-only solution is TECUgnss ap 74.4 . The mean bias between the estimated VTEC maps and the GIM provided by the IGS Analysis Center CODE (Center for Orbit Determination in Europe) is 0.4 TECU with a standard deviation of ±0.5 TECU. Fig.2 a) VTEC and b) RMS map, IGG GNSS-only model, day 022 2005, 17:00 UT

2. Combined solution The impact of altimetry data integration on the estimated GIM is evident over the areas coinciding with the footprints of Jason-1, shown in Fig.1b. In order to demonstrate the differences between the GNSS-only and the combined IGG GIM, the VTEC and RMS values along the Jason-1 track were interpolated from the two global maps for day 022 2005 and plotted as a function of time (Fig.3). As it can be seen in the lower plot in Fig.3, in the case of overweighting the altimetry data the combination with Jason-1 measurements causes a decrease of the RMS along the altimeter track, reaching up to 2 TECU. As for the VTEC (Fig3., upper plot), there is a general trend for increase of the VTEC values along the Jason-1 track in the domain of low ionosphere activity, which is mainly in mid and high latitudes. This effect can be interpreted as the positive contribution of the altimetry data in areas, where nearly no GNSS observations are available. However, in the combined model also a decrease of VTEC can be observed, coinciding with the ionospheric maximum as it travels with the Sun along the electromagnetic equator. This decrease is most probably related to the insufficient performance of the altimetry measurements in low latitudes, caused by the contribution of the topside ionosphere. As already mentioned, the altimetry measurements do not account for the topside ionosphere and therefore, despite of the discussed TEC overestimation, the integration of altimetry data in the GNSS GIM leads to a decrease of the obtained TEC over the area where the plasmaspheric contribution reaches its maximum. Fig.3 VTEC and RMS interpolated along the Jason-1 track from the IGG GIM for day 022 2005.

3. Comparison with raw Jason-1 data In order to investigate the obtained results and examine the self-consistency of our approach, we used the same procedure, which is applied for routine validation of the rapid and final global ionosphere maps produced by the IGS Analysis Centres (AC) (Hernandez-Pajares,

In this validation procedure raw VTEC delivered by Jason-1 along its track is compared with the corresponding values interpolated from the global maps from GNSS data. In our case the comparison is performed for the IGG GNSS-only and the IGG COMB GIM with estimated Jason-1 bias for day 022 2005. Fig.4 shows the mean bias for the regarded days of the two different IGG GIM compared to Jason-1. The comparison is performed in time (upper plot) and in latitude (lower plot). Fig.4 Jason-1 minus the IGG GNSS-only and IGG combined solutions, mean bias in time and latitude, day 022 2005 The difference between the raw Jason-1 VTEC and the IGG GNSS-only GIM has a mean of 1.51 TECU in time (upper plot) and 1.57 TECU in latitude (lower plot). The magnitude of these differences generally corresponds to the estimated Jason-1 bias for that day (1.46 TECU). As expected, with mean differences of 0.05 TECU in time and 0.26 TECU in latitude, the IGG COMB GIM with estimated JB coincides better with the Jason-1 raw data (after removing the computed offset), than the IGG GNSS-only solution. For both the IGG GNSS-only and COMB GIM the differences with the Jason-1 raw data increase at higher latitudes, and, on the contrary, in the equatorial area they become even negative (Fig.4 lower plot). This behaviour of the differences can be regarded as a visualisation of the insufficient performance of the altimetry TEC measurements in low latitudes, caused by the contribution of the topside ionosphere.

Conclusions and outlook It was shown that the combined GIM from GNSS and altimetry data have the potential to contribute to the accuracy of the global ionosphere modelling as well as to the better understanding of the ionosphere as a whole. Still, the combined GIM must be further optimised, with main focus on the relative weighting of the results from the different techniques. An important topic is to consider and properly model the technique-specific error sources. Therefore, as next step in our study the behaviour of the differences between the GNSS-only solution and the altimetry TEC (discussed in 3.2 and 3.3) can be implemented for the development of a function, which accounts for both the instrumental bias and the plasmaspheric contribution, and can be adopted in the combination procedure instead of a constant bias for the altimetry satellites. Finally, in order to achieve a global coverage and higher accuracy and reliability of the ionosphere models, the combination method can be adopted also for ionospheric data from other space geodetic techniques, such as VLBI and DORIS. Acknowledgements Project P16136-N06 is funded by the Austrian Science Fund (FWF). Thanks to the International GNSS Service (IGS) and to ADSCentral, GeoForschungsZentrum Potsdam (GFZ), for the free supply with GNSS and altimetry data. We are also grateful for the free availability of the Generic Mapping Tools (GMT) and the GPS Toolkit (GPStk) software. Many thanks to Dr. Manuel Hernandez-Pajares for his assistance! References

Brunini, C., Global ionospheric models from GPS measurements. PhD thesis, Universidad Nacional de La Plata, La Plata, Argentina, 1997

Brunini, C., Meza, A., Bosch, W., Temporal and spatial variability of the bias between TOPEX- and GPS-derived total electron content. J. Geod. 79, 4-5, pp. 175-188, 2005

Chelton, D.B., Ries, J.C., Haines, B.J., Fu, L.L., Callahan, P.S., Satellite altimetry. In: Satellite altimetry and Earth sciences. Academic, London, pp. 57-64, 2001 Center for Orbit Determination in Europe, Global Ionosphere Maps Produced by CODE, http://www.aiub.unibe.ch/ionosphere/

Feltens, J., Chapman profile approach for 3-D global TEC representation. In: Proceeding of the IGS AC Workshop, pp. 285-297, Dow, J.M., Kouba, J., and Springer, T. (Eds.),

Darmstadt, Germany, February 9-11, 1998

Feltens, J., Schaer, S., IGS Products for the Ionosphere. In: Proceeding of the IGS AC Workshop, pp. 225-232, Dow, J.M., Kouba, J., and Springer, T. (Eds.), Darmstadt,

Germany, February 9-11, 1998

Hargreaves, J.K., The solar-terrestrial environment. In: Cambridge atmospheric and space science series, Cambridge University Press, 1992

Hartmann, G.K., Leitinger, R., Range errors due to ionospheric and tropospheric effects for signals above 100 MHz. Bulletin Geodesique 58, pp. 109-136, 1984

Hernandez-Pajares, M., Juan J.M., Sanz, J., New approaches in global ionospheric determination using ground GPS data. J. Atmos. Solar Terrestrial Phys. 61, pp. 1237-1247, 1999 Hernandez-Pajares M., IGS Ionosphere WG Status Report: Performance of IGS Ionosphere TEC Maps (Position paper), IGS Workshop, Bern, March 2004

Hugentobler, U., M. Meindl, G. Beutler, H. Bock, R. Dach, A. Jaggi, C. Urschl, L. Mervart, M. Rothacher, S. Schaer, E. Brockmann, D. Ineichen, A. Wiget, U. Wild, G. Weber, H. Habrich, and C. Boucher, CODE IGS Analysis Center Technical Report 2003/2004, in IGS 2004 Technical Reports, edited by Ken Gowey et al., IGS Central Bureau, Jet Propulsion Laboratory, Pasadena, California, USA, in press, 2006

Imel, D.A., Evaluation of the TOPEX/POSEIDON dual-frequency ionosphere correction. J. Geophys. Res. 99, C12, pp. 24895-24906, 1994

Mannucci, A. J., Wilson, B., Yuan, D., Linqwister, U., and Runge, T., A global mapping technique for GPS-derived ionospheric total electron content measurements. Radio Sci. 33, pp. 565–582, 1998

Meza, A., Three dimensional ionospheric models from earth and space based GPS observations. PhD thesis, Universidad Nacional de La Plata, La Plata, Argentina, 1999 Orús, R., Hernández-Pajares, M., Juan, J.M., Sanz J., and García-Fernández, M., Validation of the GPS TEC maps with TOPEX data. Adv. Space Res. 31, Issue 3, pp. 621-627, 2003

Schaer, S., Gurtner, W., Feltens, J., IONEX: The IONosphere map eXchange format version 1. In: Proceeding of the IGS AC Workshop, pp. 233-247, Dow, J.M., Kouba, J., and

Springer, T. (Eds.), Darmstadt, Germany, February 9-11, 1998

Schaer, S., Mapping and predicting the Earth’s ionosphere using the Global Positioning System. PhD thesis, Bern University, Switzerland, 1999