# Benefits and Lessons Learned from the Sentinel-3 Tandem Phase
## 4 Methodology for Inter-Comparisons
The uncertainty associated with the match-up can be reduced to a negligible value if care is taken to colocalize the measurements. For the SRAL altimeter, the match up uncertainty can be minimized by finding pairs of spatially nearest measurement points, rather than by using the simultaneous observations. For optical images, two approaches can be followed. One consists of finding tie-points using image correlation in sensor geometry. This procedure is accurate but time-consuming. The other approach consists of re-projecting images of both sensors in cartographic projection. This approach introduces an interpolation error in the comparison, but it is faster and more straightforward. The approaches have been compared, and the latter has been eventually retained for the study. It is useful to consider a relatively large grid cell for the projection of radiometric comparisons (typically 0.5\({}^{\circ}\)): this reduces the impact of measurement noise, cloud motion, and parallax effects. Applying cloud masking or filtering for the most homogenous cells further improves the comparisons. At this point, the difference \(\Delta L\) can be compared to a priori knowledge of the measurement uncertainty. In order to do so, one may need to separate the common uncertainty (with spatial and/or temporal correlation, e.g., due to calibration errors) from the independent uncertainty (due to measurement noise). Indeed, some of the common uncertainty components will be canceled out in taking the difference and so will not contribute to the final signal. Note here that we use the simplified phrases \"independent uncertainty\" and \"common uncertainty\" as shorthand for the more formal \"uncertainty associated with independent effects\" and \"uncertainty associated with common effects\". Uncertainties themselves, representing a distribution, cannot be independent, common, random, or systematic, it is the unknown errors that have these correlation structures. The difference between sensors, \(\Delta L\), will include known differences in instrument characteristics, such as the slightly different spectral responses for the two OLCI instruments. Such differences can be corrected for in the comparison, modifying the difference to \(\Delta L\)' = \(L_{\text{A}}-L_{\text{B}}+\delta\), and extending the uncertainty expression in Equation (1) to include an uncertainty associated with the correction itself (e.g., from the uncertainty associated with the spectral response functions and/or the spectral radiance of the scene). Following such corrections, the comparison may show up further, previously unknown, differences between the sensors, if the differences are (statistically) larger than the uncertainty associated with the differences for some or all of the observations. Ideally, the identified, previously unknown, differences will be corrected through an improved understanding of the instrument model (recalibration) rather than through a simplistic correction to the measurement (bias correction). Recalibration can be performed either while respecting known differences in, e.g., spectral response functions (harmonization) or by correcting for these as though both instruments were identical (homogenization). For recalibration, the differences must be understood at the instrument level. This can be supported through a detailed sensitivity analysis of the observed differences. The methodology used here consists of plotting the inter-sensor differences as a function of the variable using appropriate statistical binning. The techniques include generation of geographic maps or regional averages, across-track histograms, plotting the differences as a function of the signal itself to investigate non-linearities, examples of which are shown below. Tandem data also provide an opportunity to compare the statistics of \(\Delta L\) to the total uncertainty given in Equation (1) \(\sqrt{(u^{2}(L_{\text{A}})+u^{2}(L_{\text{B}}))}\) using ex-ante uncertainty models. This is particularly interesting as uncertainty models are otherwise very difficult to validate.