Research Activities
The routine data processing and analyses are enlarged by several additional research activities. The current subjects of interest are shortly described in following subsections
Advanced Analyses of the post fit observation residuals
DORIS residuals are usually presented as rangerate residuals (in mm/s), but they can be expressed as phase count residuals (mm) as well. The basic relation between the rangerate and the count residuals is simple: the rangerate residual multiplied by the length of the observation time interval is equal to the count residual. The situation is more complicated due to the frequently switched chained/unchained observation mode. The observations with different time intervals are usually acquired (and processed) together. It is thus desirable to analyze the residuals of both types of observations separately, i.e., to distinguish the mixed “short” 7 s or 9 s observation intervals (unchained mode) and the “long” 10 s observation intervals (chained mode), or at least to pay attention to their ratio. Note that if observations with different time intervals are processed together, there is a difference between the minimization of the sum of squared rangerate residuals and the minimization of the sum of squared count residuals. In the GOP solution, the sum of squared count residuals is minimized. All results described in this chapter are derived from the daily GOP singlesatellite solutions with adjusted orbits, station coordinates, ZTD and beacon frequency offsets but with fixed ERP.
A profound and detailed comparison of the “short” and “long” measurement accuracy based on the analysis of postfit residuals is difficult, since both types of observations are processed together. The amount of the short observation intervals is usually too low to be processed separately. The presented approach can thus give only an approximate estimation of the relation between the measurement precision and the length of the observation interval.
The approximate computation of the post fit residual RMS of the chained and unchained observations σ_{c} , σ_{u} (eq. 4)
(4a) σ_{u} = √( (Σe^{2} / n_{u})*(n / n  u))
(4b) σ_{c} = √( (Σe^{2} / n_{c})*(n / n  u))
was used to compare the residuals of both types of the measurement, where 'e' are postfit residuals referring to unchained or chained observations, n is the total number of observations, n_{u} the number of unchained observations, n_{c} the number of chained observations, and u the total number of estimated parameters. The fact, that the short (unchained) observations have higher rangerate residuals but lower count residuals than the long ones (chained), makes it clear that the measurement noise partly depends on the length of the observation time interval. We may, as a simple approximation, explain the accuracy of the count measurements as the result of a combination of two uncorrelated processes, where the first one is independent and the second one dependent on the count interval. More specifically, we may write the variance of the count measurements in the form (eq. 5)
(5) σ^{2}
= σ_{1}^{2}
+ (Tσ_{2})^{2}
where σ_{1} is related to the phase measurement noise while σ_{2} relates to the frequency dependent noise and T is the count interval. We may thus write (eq. 6)
(6a) σ_{u}^{2}
= σ_{1}^{2}
+ T_{u}^{2} σ_{2}^{2}
(6b) σ_{c}^{2}
= σ_{1}^{2}
+ T_{c}^{2} σ_{2}^{2}
where T_{u} (T_{c}) is the time interval of the unchained (chained) observation. We may then use the postfit residual RMS computed using eq. 1 as the estimate of the observation standard deviation for the short and long observation intervals. The system of the two equations (eq.6) can be then solved for the two noise components σ_{1} and σ_{2}. The values obtained by this procedure for the time period 20022008 are similar for all satellites except for SPOT2. The unchained observations of SPOT2 are based on a 9 s time interval, while unchained observations of the other satellites have 7 s time interval. The standard deviation σ_{2} ranges between 0.225 and 0.257 mm/s for all satellites except for SPOT2, where σ_{2} is 0.307 mm/s. On the other hand, σ_{1} is lower in the case of SPOT2 (2.57 mm) than for the other satellites (2.773.16 mm). Fig. 9 shows the corresponding average values for each year of the analyzed time interval. The estimated relations between constant and timedependent term are very similar, except for SPOT2.
Spot5 and South Atlantic Anomaly
The SAA is based on the geometry of the Van Allen radiation belts. The Van Allen radiation belts are symmetric with the Earth's magnetic axis, which is tilted with respect to the Earth's rotational axis by an angle of ~11 degrees. Because of this tilt, the inner Van Allen belt is closest to the Earth's surface over the south Atlantic ocean, and farthest from the Earth's surface over the north Pacific ocean.


The analysis of singlesatellite solutions disclosed a SPOT5 specific abnormality, related with the well known South Atlantic magnetic Anomaly (SAA). The effect of the SSA on the Jason1 DORIS observation has been well known, but the significant effect on the SPOT5 observations is an original discovery of GOP analyses center. The estimated station height and other related parameters, derived from SPOT5 singlesatellite solution, are significantly biased. Fig. 2 shows the differences between the weekly estimated station coordinates, using the SPOT5 singlesatellite solution and the combined solution GOP31. The highest bias was found in the station height, where the differences between both solutions reached the highest values for South America stations Cachoeira Paulista (205 mm), Arequipa (74 mm) and Santiago (68 mm). In addition, the bias is getting higher during the time, as documented by Fig. 2. The horizontal positions show the largest absolute differences (from 30 to 45 mm) for the same stations and also for Kourou.
Corresponding differences were similarly detected also in comparison between estimated ZTD (Zenithal Troposphere delay) and GNSS ZTD and confirmed by analyses of the estimated frequency offset. Figure 3 shows the daily behavior of the estimated oscillator frequency offset, displayed for the master beacons (equipped with atomic clock). The behavior for SPOT5 (affected by SAA) and Envisat (not significantly affected) is completely different. In the case of SPOT5, frequency is strongly rising during flight through the SAA area. This part of the daily arc corresponds to the observation time span of the station Kourou (KRVB).