TOTAL TROPOSPHERIC WATER VAPOUR AND PRECISION OF THE ABSOLUTE POSITIONING BY GPS IN VIỆT NAM

¹LÊ HUY MINH, ¹PHẠM XUÂN THÀNH, ¹NGUYỄN CHIẾN THẮNG,
¹TRẦN THỊ LAN, ²R. FLEURY, ²P. LASSUDRIE DUCHESNE, ³A. BOURDILLON,
⁴C. AMORY-MAZAUDIER, ⁵TRẦN NGỌC NAM, ⁶HOÀNG THÁI LAN

¹Institute of Geophysics, VAST, Hà Nội; ²École Nationale de Télécommunication de Bretagne, France ; ³Université de Rennes 1, France ; ⁴Centre d’Étude des Environnements Terrestres et Planétaires, France; ⁵Huế University of Natural Sciences, Huế;
⁶Institute of Physics of Hồ Chí Minh City, Hồ Chí Minh City

Abstract: In this paper we present the results of determination of the time variation of the residual of the daily mean navigation coordinates (de, dn, du) of the three GSV4004 GPS continuous stations in Hà Nội, Huế and Hồ Chí Minh cities and their correlations with respect to the daily mean IWV of the atmosphere in the same position. It found that the residuals du vary day-to-day in the range of about 1-2 m and around the annual period general tendency which is maximum in summer (June or July) and minimum in winter (December or January), and whose amplitude is of about ±0.8 m. The annual variation of the IWV is also maximal in summer and minimal in winter. It is found out that different coordinates have different correlations with respect to the total tropospheric water vapour. The residual du has highest correlation with respect to the IWV, their correlation coefficient are about 0.74 for the Hà Nội station; 0.66 for Huế and 0.255 for Hồ Chí Minh Cities. The residual de has the negative correlation with respect to the IWV, their correlation coefficient are about -0.4 for three stations. The residual dn has smallest correlation with respect to the IWV, about -0.2 or smaller for all three stations. The correlation coefficients of the monthly mean residuals du and the monthly mean IWV are of 0.95 in Hà Nội, 0.89 in Huế and 0.58 in Hồ Chí Minh City. These results in this paper show that it is necessary to carry out the repeated GPS measurement for tectonic studies in Việt Nam in winter (dry season) in order to limit the effect of the atmosphere.

I. INTRODUCTION

The propagation of signals from GPS (Global Positioning System) satellites to receivers on the Earth’s surface is considerably affected by the ionosphere and troposphere. The ionospheric dispersive medium produces a group delay of the GPS signal, which depends on the total electron density (TEC) of the ionosphere. Thanks to the double frequency GPS receivers, the TEC could be calculated using this group delay, which results in the fact that the effect caused by the ionosphere is eliminated nearly completely in GPS positioning. The troposphere is non-dispersive, so its influence on the GPS positioning is more complicated. To determine this influence at this moment, one must use some softwares, such as GAMIT/GLOBE [1, 2, 4], Bernese or Gipsy-Oasis. In the frame of scientific cooperation between the Institute of Geophysics and the University of Rennes 1, National High School of Telecommunication of Brest (French), three GPS receivers have been installed in Hà Nội, Huế and Hồ Chí Minh City since the April 2005 and January 2006. Using the data of these GPS receivers to study the TEC in Việt Nam and adjacent region has been presented in [8, 9]. This paper presents the estimation of atmospheric effects on the precision of positioning by three above GPS receivers in Việt Nam, basing on the comparison between the residuals of the coordinates determined by GPS and the integrated water vapour (IWV) from the NCEP-DOE AMIP-II reanalysis model.

II. DATA AND ANALYSIS METHOD

The data used in this paper is the continuous data from three GSV4004 Novatel’s GPS receivers in Việt Nam [8, 9, 10]. The observables of these receivers are C1, L1, D1, S1, P2, L2, D2 and S2, where C1 and P2 are C/A code and Y code pseudo-ranges, L1 and L2 are carrier phases, D1 and D2 are Doppler frequencies, S1 and S2 are raw signal strengths. Using the convert4 program of the OEM4PC software [10] we could obtain the coordinates and the altitude of the stations in each observation. From the data series of the ellipse coordinate components (latitude j and longitude l in degree; altitude in m) for each observation interval (1 minute or 30 seconds) in three stations, we calculate their daily mean values for the 2005-2006 period (2006 for Huế station). Then the residuals (dj, dl,dh) are computed by the formula:

Where, are the mean values of the daily mean data series. The ellipse coordinate residuals (dj, dl, dh) are converted into the local navigation coordinate residuals (de, dn, du), where de is east, dn north and du up component residuals in m, respectively by the formula [3, 5]:

Time variation of these (de, dn, du) data are used to compare with the one of the IWV data at each station.

The daily IWV data at each station are computed from the NCEP-DOE AMIP-II reanalysis atmospheric model R-2 [5]. The IWV is the water vapour in different phases (vapour, liquid, ice...) in the atmospheric column of 1 m² session at each observation point assuming a homogeneous atmosphere.

In order to find the relation between the local navigation coordinate residuals and the IWV, their cross correlations are computed by the formula (between du and iwv) for example:

Where, du_i is up component residual, iwv_i the IWV on the i^th day, and are their means, respectively.

III. RESULTS AND DISCUSSION

Time variation of the (de, dn, du) in Hà Nội, Huế and Hồ Chí Minh cities are presented on the Fig. 1, 2 and 3, respectively. It shows that the navigation coordinate residuals vary from day to day, at each station du varies within a 1-2 m range, meanwhile dn and de in a 0.5-1 m range. Among three stations, the daily variation range is smallest in Huế, biggest in Hồ Chí Minh City. It exists clearly an annual variation in du time series, with a maximum in summer (July), a minimum in winter (January and December). During the 2005-2006 considered period, the variation amplitude of du is about ±1 m, and that of de and dn is about ±0.5 m. Hence, the precision of the absolute positioning by GSV4004 GPS receiver is of about 1-2 m, this has the precision quite similar to other receivers [10].

Figure 1. Daily mean de, dn, du in the Hà Nội station.

The day-to-day IWV data series from the NCEP-DOE AMIP-II reanalysis atmospheric model in three positions Hà Nội, Huế and Hồ Chí Minh City are presented on the Fig. 4. It shows that it varies from day to day with a clearly annual variation, maximum in summer (June-July) and minimum in winter (December-January). Hence, annual variations of the IWV and of the du are nearly similar. Their cross correlations are computed and presented in the Table 1.

We can see that the correlation coefficients between the IWV and the east and north components residuals (R_de-iwv and R_dn-iwv) are negative at each station and for each year 2005 and 2006. R_de-iwv are of about -0.4 for the 2006; R_de-iwv at Hà Nội and Hồ Chí Minh stations are small (-0.03 and -0.04) for the 2005. R_dn-iwv at three stations are small (). The residual du and the IWV at three stations have positive correlation coefficient; the average R_du-iwv is of 0.74 at Hà Nội, 0.68 at Huế and 0.255 at Hồ Chí Minh cities. The Fig. 5 shows the dependence of the R_du-iwv with respect to the latitude from Hồ Chí Minh City to Hà Nội, so the correlation coefficient R_du-iwv decreases significally near the equator.

Figure 2. Daily mean de, dn, du in the Huế station.

As mentioned above, it exists clearly an annual variation in the time series of the coordinate residuals and of the IWV. In order to eliminate the short period variations, the monthly means of the coordinates residuals and of the IWV were computed and presented on the Fig. 6 for the 2005 and Fig. 7 for the 2006. On these figures, each graph represents the time variation of one of the monthly mean coordinate residuals and of the monthly mean IWV. We can see that the amplitue of the annual variation of the du is of about ±0.8 m, of the de and dn is ±0.3 m. The correlation coefficients of the monthly means are presented in the table 2. R_du-iwv are of about 0.9, except for the 2006 in Hồ Chí Minh City R_du-iwv = 0.29. This is caused by the fact that the daily mean values of the du are very big (Fig. 3) from the 15^th to the 25^th June 2006, so the monthly mean du for the June is very far from the normal tendency. The is of 0.8, if the GPS data in June 2006 at the Hồ Chí Minh City station is not included. The are negative and significant (about -0.6 to -0.9) for the 2006; the R_dn-ivw are negative also but smaller (about -0.2 to -0.5). So for the monthly means values the correlation coefficients are larger than for the daily means. This could be understood by the fact that the coordinate residuals determined by GPS affected by the local atmospheric conditions, meanwhite the IWV data from the global model can not include these conditions, so when the data series are averaged for a longer time interval, then their correlations become better.

Table 1. Correlation between the de, dn, du local navigation coordinate residuals
and the IWV in Hà Nội, Huế and Hồ Chí Minh City for the 2005-2006 period

Station	Year	Rde-iwv	Rdn-iwv	Rdu-iwv
Hà Nội	2005	-0.04	-0.15	0.71
	2006	-0.40	-0.08	0.77
Huế	2006	-0.44	-0.16	0.68
Hồ Chí Minh City	2005	-0.03	-0.04	0.32
	2006	-0.37	-0.20	0.19

Figure 3. Daily mean de, dn, du in the Hồ Chí Minh City station.

To find the correlation between short period variations of the coordinate residuals and of the water vapour, the long period variations of the daily mean datum series have been approximated by the polynomials and then excluded. After some tests with the different degree polynomials, we selected the 15 degree polynomial to approximate the variations with the periods longer than about 1 month (Fig. 8).

The short period variations of the coordinates residuals (dde, ddn, ddu), and of the IWV (diwv) are obtained by eliminating the long period variations approximated by the 15^th degree polynomials as mentioned above. For example, the Fig. 9 represents the time variations of the ddu and of the diwv at Hà Nội station for the 2005-2006 period. We can see that the curves ddu and diwv represent short period variations with the wave lengths from some days to some decades and there is a certain correlation between them. The correlation coefficients between the diwv and the dde, ddn, ddu at three stations Hà Nội, Huế and Hồ Chí Minh City for the 2005-2006 period are presented in the Table 3. We can see that, the R_ddu-diwv are positive, significant and decrease also from Hà Nội to Hồ Chí Minh City as the R_du-iwv, but for three stations they are smaller than the values correspondent in the Table 2. The R_dde-diwv and R_dn-diwv are small for the 2005-2006 period. As mentioned above, the absolute positioning by GPS is affected by the local atmospheric conditions (not including non-atmospheric noises), meanwhile the IWV is computed from the global model, whose local characteristics are averaged, so the correlations between the diwv and the dde, ddn, ddu cannot be as large as those between the monthly mean iwv and de, du, dn.

Figure 4. IWV in Hà Nội (top), Huế (middle) and Hồ Chí Minh cities (bottom).

Figure 5. Correlation coefficient R_du-iwv as a function of the geographic latitude.

Figure 6. Time variation of monthly means de, dn, du (open diamonds)
and of the IWV (open squares) for the 2005.

Figure 7. Time variation of monthly means de, dn, du (open diamonds)
and of the IWV (open squares) for the 2006.

Table 2. Correlation between the monthly means of the coordinate residuals and of the IWV

Station	Year	Rde-iwv	Rdn-iwv	Rdu-iwv
Hà Nội	2005	-0.09	-0.28	0.95
	2006	-0.87	-0.35	0.95
Huế	2006	-0.92	-0.25	0.89
Hồ Chí Minh City	2005	0.05	-0.50	0.88
	2006	-0.64	-0.22	0.29

Figure 9. Short period variations of the IWV diwv (top)
and of the up component residual ddu (bottom) at Hà Nội station.

Table 3. Correlation between short period variations of the coordinates residuals
and of the IWV.

Station	Year	Rdde-diwv	Rdde-diwv	Rddu-diwv
Hà Nội	2005	0.01	-0.15	0.40
	2006	-0.03	0.04	0.58
Huế	2006	0.03	0.12	0.43
Hồ Chí Minh city	2005	0.07	0.15	0.28
	2006	-0.05	-0.01	0.19

IV. CONCLUSIONS

The results in this paper show that the precision of the absolute positioning by the Novatel’s dual-frequency GPS receivers is of about 1-2 m.

The precision of the absolute positioning by GPS is dependent clearly on the tropospheric IWV. But the precision of the determination of different coordinate components depend differentially on the IWV, the smallest precision in the determination of the up component (or altitude). In the Việt Nam region, in the dry season, the humidity is small, the atmospheric influences on the absolute positioning by GPS are also small. So to increase the precision of the geodesic measurements by GPS, they would be carried out in the dry season (on December and on January).

The results in this paper show also that the precision of the absolute positioning by GPS in the equatorial and low-latitude regions (from Huế to the South of Việt Nam) is smaller than in the middle latitudes, so the geodetic measurements by GPS in the South of Việt Nam are may be paid more attentions to the atmospheric conditions.

Acknowledgments: This paper is realized with the financial support of the Basic Research project No 7.119.06: “Treatment of data of the three continuous GPS stations at Hà Nội, Huế and Hồ Chí Minh cities with the main application in the study of the total electron content of the ionosphere in Việt Nam and of the crustal movement in the stations”.

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