COMBINATION OF GPS AND SATELLITE ALTIMETRY DATA FOR GLOBAL IONOSPHERE MAPS

frame must rotate synchronously with the Sun, so the temporal variation of the electron content is slow and can be averaged for a short period, e.g. 1-2 hours. The coordinates in the sun -fixed system are defined as (Brunini, 1997): G  and    UTs G (4.4)  , s - latitude and longitude in the sun-fixed reference frame, G , G - geographical latitude and longitude. The results improve further if geomagnetic latitude is used, especially for global ionosphere models (Meza, 1999). Finally, for combining the GNSS and altimetry data we apply a least -squares adjustment (Gauss -Markov model) on each set of different observations and combine the normal equations by adding the relevant N-matrices. 6th International Multidisciplinary Scientific GeoConference SGEM2006 www.sgem.org Int er nat ional Confer ence SGEM 200 6 270

RESULTS The current results of our study are presented and discussed in this chapter, considering as example the outcomes for day 025 in 2005. For clarity, the models developed within this work are referred to as IGG (Institute of Geodesy and Geophysics) models.

1 Global Ionosphere Maps –GNSS -only and combined models A Matlab based software was developed for computing two -hourly GIM and the corresponding RMS (Root Mean Square) maps. The software allows to choose whether a GNSS -only or a combined solution with altimetry data added on the normal equation level will be developed. Input data are the daily RINEX files from the used IGS GNSS stations (Figure 5.1a), the daily navigation message and, for the combined models, the altimetry ionospheri c corrections for the regarded day (Figure 5.1b). The approximate duration of the whole computation process on a standard LINUX PC with data from 180 stations and degree and order of the spherical extension 15 mn is about 12h. As can be seen on Figure 5.1, despite of the relative lower number of altimetry observations, their distribution partly balances the gaps over the oceans between the GNSS stations, which is the main motivation behind adding altimetry data to the GNSS ionosphere model . Fig. 5.1a: Used GNSS stations SGEM 200 6 - Section III 271 Fig. 5.1b: Altimetry data (Topex/Poseidon) Figure 5.2 shows the two-hourly GIM and the corresponding RMS maps from the IGG GNSS -only solution. As anticipated, the highest RMS values appear in areas with poor GPS coverage, which is mainly above the sea surface. Due to the lower number of altimetry data compared to the number of GNSS observations, a lower  a priori has to be applied on the altimetry data in the combined model. Tests with different values of ALT 0 were made. The aim of this weighting is to improve the ionosphere model in areas with altimetry observations without worsening its general quality. On Figure 5.3 the RMS maps of the IGG combined model with 20 , 00 ALT TECU are shown. It can be seen, that compared to the GNSS -only model the RMS values here have decreased exactly in the areas with altimetry observations. In Figures 5.2 and 5.3 the 2-hourly maps for day 025 2005 start at 1UT (upper left hand side plot) and accordingly the 12-th map is for 23UT (lower right hand side plot). IGG combined models with three different ALT 0 were compared to the IGG GNSS - only solution. A summary of the results is shown in Table 1.; the a posteriori error of the reference IGG GNSS -only solution is 94 , 5 apost TECU . Negative or zero apost and RMS values (in bold) denote improvement or no change in the IGG combined versus the IGG GNSS -only mode l. The combined model with 20 , 00 ALT TECU shows the best results concerning the RMS – a maximum decrease with nearly no change in the maximal values and just a slight increase of the a posteriori error . As for the VTEC , there is a general trend for increase of the values when adding altimetry data, which agrees with the results from several recent studies (e.g. Brunini et al., 2005) showing that the altimetry is overestimating the ionosphere compared to GNSS. Still, a variance estimation has to be carried out in order to assess the optimal relative weighting of the two data sets. 6th International Multidisciplinary Scientific GeoConference SGEM2006 www.sgem.org Int er nat ional Confer ence SGEM 200 6 272 ALT 0 = 1 ALT 0 = 0,20 ALT 0 = 0,05 apost 0,00 0,03 0,31 maxmax / RMSVTEC  0,91 / 0,00 6,09 / 0,02 9,20 / 0,22 minmin / RMSVTEC  -0,54 / -0,12 -6,26 / -1,01 -13,26 / -1,81 meanmean RMSVTEC  / 0,02 / 0,00 0,26 / -0,01 0,69 / 0,04 Table 1. : IGG GNSS- only minus IGG combined (in TECU) Fig. 5.2a: 2-hourly GIM, IGG GNSS -only model Fig. 5.2b: RMS maps, IGG GNSS -only model SGEM 200 6 - Section III 273 Fig. 5.3: RMS maps, IGG combined model with 20 , 00 ALT TECU All IGG models were compared with GIM produced by the IGS analysis center CODE (Center for Orbit Determ ination in Europe). The agreement is very good with mean difference CODE minus IGG GNSS -only for the regarded day

, 0  IGGCODEVTEC TECU . Overall, the mean VTEC values in the CODE model are slightly lower than these from IGG. It also has to be pointed out, that in general the RMS of the IGG models are up to 4 TECU lower than CODE’s RMS . The mean difference in RMS for the regarded day is 24 , 2 IGGCODERMS TECU . A possible explanation for this difference is the high sampling rate (30 sec) we use and consequently the high number of observation s in the IGG ionosphere models which results in lower RMS in the entire IGG solution .

2 Satellite and receiver DCB As a by-product differential P1-P2 code biases (DCB) for all GNSS satellites and ground statio ns are estimated daily as constant values, with a zero-mean condition imposed on the satellite bias estimates. They agree well with the monthly values provided by CODE (Fig.5.4). 6th International Multidisciplinary Scientific GeoConference SGEM2006 www.sgem.org Int er nat ional Confer ence SGEM 200 6 274 Fig. 5.4: Estimated GPS and GLONASS satellite and receiver DCB vs. CODE’s DCB SGEM 200 6 - Section III 275 The differential code biases are assumed to remain constant up to one month. In order to prove the stability of the daily estimated DCB a time series over one week (days 022 to 028 in 2005 ) was computed. The results can be seen on Figure 5.5. Fig. 5.5a: GPS satellites DCB Fig. 5.5b: GLONASS satellites DCB 6th International Multidisciplinary Scientific GeoConference SGEM2006 www.sgem.org Int er nat ional Confer ence SGEM 200 6 276 Fig. 5.5c: GLONASS receiver DCB Fig. 5.6: Total number of observations The GPS satellite DCB show almost no variations in the regarded period as well as most of the GPS receiver DCB. The GLONASS satellite DCB and their RMS show a bigger variation (e.g. R02 and R17). Still, this is more likely to be a computational problem, due to the much lower number of observations to GLONASS satellites compared with the number of GPS observations for the time span (Fig. 5.6). Moreover, there are only 18 to 20 stations per day tracking GLONASS. Their DCB are quite stable and the variability seems to depend also on the number of observations - e.g. station gope has ca. 3000 observations per day more than station mat1.

OUTLOOK The combined ionosphere model must be further optimised with main focus on the relative weighting of the individual results from the different techniques. Other tasks are the consideration and modelling of the technique -specific error sources in the altimetry SGEM 200 6 - Section III 277 and as a next step - combination with other techniques such as VLBI and DORIS. Finally, for the purpose of validation, comparisons of the combined GIM with external data and statistics have to be made. REFERENCES:

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

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

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

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

Hobiger, T., Boehm J., Schuh H., VLBIONOS - Probing the ionosphere by means of very long baseline interferometry , Oesterreichische Zeitschrift fuer Vermessung & Geoinformation (VGI), 1/2003, pp. 29 - 39, 2003

Meza, A., Three dimensional ionospheric models from earth and space based GPS observations , PhD thesis, Universidad Nacional de La Plata, Argentina, 1999

Schaer, S., Mapping and predicting the Earth’s ionosphere using the Global Positioning System , PhD thesis, Universitaet Bern, Switzerland, 1999 6th International Multidisciplinary Scientific GeoConference SGEM2006 www.sgem.org