# Comparing GRACE-FO KBR and LRI Ranging Data with Focus on Carrier Frequency Variations
## 5 Range Differences between LRI and KBR  
The LRI and KBR ranging data can be directly compared at the instantaneous range level, i.e., after the light-time corrections of KBR and LRI and KBR antenna offset correction have been applied. The light-time correction is different for KBR DOWR and LRI TWR [45]. The ionospheric effect is already removed by default in KBR1B datasets, but the correction is provided separately in case one wants to derive the variations in electron content of the ionosphere. Since KRB1B data are provided at a rate of 0.2 Hz and LRI1B data at a rate of 0.5 Hz, the data have to be resampled, ideally through low-pass filtering and decimation in order to avoid aliasing.  
The LRI data, as provided in the official v04 LRI1B dataset, have already been deglitched, which is a process that removes steps and glitches in the ranging data that are correlated with some thruster activations [19]. Moreover, the LRI ranging data are rescaled and time-shifted such that KBR-LRI residuals are reduced. This rescaling is necessary due to the LRI absolute laser frequency \(\
u_{\mathrm{R}}\), defining the conversion factor from phase to range, only being known with low accuracy in GRACE-FO. In contrast with the KBR frequencies \(\
u_{\mathrm{A/B}}^{\mathrm{K/Ka}}\), the laser frequency \(\
u_{\mathrm{R}}\) cannot be directly measured in-flight on GRACE-FO, although attempts to derive the frequency from laser telemetry are being made [41]. However, future missions will likely host a LRI scale factor unit that enables measurements of a time-resolved frequency [47].  
The deglitching and rescaling of LRI data was sub-optimal in v04 LRI1B data before 30 June 2020, but improved significantly thereafter due to changes in processing [48].  
We previously derived an alternative LRI1B product from level1a data, which we label as v50 in order to distinguish it from the official v04 product [49]. A comparison of both datasets is shown for January 2019 in Figure 3. Other time periods, they exhibit the same characteristics. The range signal in GRACE-FO has dominant 1/rev (and 2/rev) oscillations of several 100 m amplitude and a continuous spectrum containing the interesting gravity field information and non-gravitational accelerations up to approx. 35 mHz. At high frequencies, the LRI and KBR range data are dominated by the respective instrument noise.  
The traces showing the difference between KBR and LRI reveal that these residuals are dominated by KBR noise at frequencies above 35 mHz and the residual level increasestowards lower frequencies. The residuals show pronounced 2/rev oscillations in LRI1 Bv04 and LRI1 Bv50 with a few-micron amplitude. However, LRI1 Bv04 has an additional 1/rev oscillation. When we re-estimate a scale and time-shift of LRI1 Bv04, this 1/rev peak vanishes in the residuals and the results get closer to LRI1 Bv50. This is an indication of the scale and time-shift being slightly inaccurate in the official v04 data. Therefore, we will often show the original LRI1 Bv04 data as well as our rescaled and time-shifted version without the 1/rev oscillations in the following.  
The day 16 January 2019 is visible as an outlier in the residuals (upper left plot of Figure 3) because the deglitching did not properly remove a glitch in the LRI1 Bv04 data, which then disturbed the time-shift estimation.