# Impact of Satellite Attitude on Altimetry Calibration with Microwave Transponders
## 3 Satellite Attitude and Transponder Calibration
### Calibration Accounting for Satellite Attitude  
For altimeter calibration with a transponder, it is common practice that the corrected measured range \(r(t)\) is used for the evaluation of range and datation biases based on Equations (8) and (11), respectively. As already described in Section 3.1, this measured range is transferred from APC to CoG by the processing Agencies using the CoG correction \(\delta r\). The description provided in the product handbook of each altimetry mission states that  
Figure 3: Topographic and bathymetric profile along the Jason-3 D018 (descending) pass, starting from the north with the CDN1 transponder in Crete, passing over the sea region between Crete and Gavdos, and reaching the GVD1 transponder south in Gavdos. The generated averaged waveforms of the transponder signals are also shown (bottom). the CoG correction is defined as the distance along the z-axis between APC and CoG in the satellite body reference frame. Since this parameter is derived using the geometry of the spacecraft, its value is constant for the entire duration of a mission and for its observations. A review of previous investigations showed that the measured range used for calibration is indeed referred to CoG. For example, Hausleitner et al. [27] mentions that the Jason-2 altimeter range is referred to the CoG, by applying a CoG correction, given in the GDR products. Inspection of Jason-2 GDR products reveals that this parameter is in fact constant. The work of Cristea and Moore [26] also mentions that a constant CoG offset is also applied to reduce the observed range for the satellite geometry prior to the calculation of EnviSat range bias using a transponder. It is important to examine the implications of applying a constant CoG correction to the measured range instead of a varying correction originated from alterations in satellite attitude. We firstly discuss the case of altimetric measurements over oceans. Figure 4a shows an example of an ideal attitude for an orbiting satellite, where its altimeter antenna points perpendicularly to the ellipsoid. The ocean surface point, OCN1, can be considered a nadir-located target. The line segments \(|\)OCN1, APC\(|\), \(|\)APC, CoG\({}^{\prime}|\) and \(|\)OCN1, CoG\({}^{\prime}|\) represent the observed range referred to APC, the constant CoG correction and the observed range referred to the CoG', respectively. The CoG' point represents the apparent CoG of the satellite at which the measured range \(r(t)\) is referred to after applying the CoG correction \(\delta r\) using Equation (9). Finally, the line segment \(|\)OCN2, CoG\(|\) denotes the distance between the true CoG and the sea surface. From the geometry of Figure 4a, it is evident that, for an ideal attitude, the distances \(|\)OCN1, CoG\({}^{\prime}|\) and \(|\)OCN2, CoG\(|\) are equal. It is therefore reasonable to consider that the measured range is correctly referred to the true CoG when the constant distance between APC-CoG along the z-axis is used. Figure 4b shows the case of non-ideal attitude, where only a pitch rotation (exaggerated) is displayed for simplicity. Assuming that all rotations are performed with respect to the CoG, the non-ideal attitude results in a change in the position of APC and thus CoG\({}^{\prime}\). As a consequence, \(|\)OCN1,CoG\({}^{\prime}|\) distance is no longer equal to \(|\)OCN2,CoG\({}^{\prime}|\) distance, and therefore the measured range is not realistically referred to the true CoG. We continue by examining the impact of satellite attitude on altimetric measurements acquired over point targets (e.g., during an altimeter calibration with a transponder). A fundamental difference here is that, unlike ocean surface, transponders are practically never located directly at the nadir of the altimeter antenna.