# MERLIN: A French-German Space Lidar Mission Dedicated to Atmospheric Methane
## 5 Performance
### XCH\({}_{4}\) Error Budget
Other potential error sources such as speckle noise and the noise from internal calibration chain have been minimized by design of these subsystems, as outlined in Section 4. The main part of the random error depends on the geophysical situation: It is mainly related to the surface reflectivity and to the aerosol load, which directly relates to the signal strength, and secondly to the surface pressure and other elements with minor impact (e.g., slope of terrain, CH\({}_{4}\) concentration, solar elevation angle, etc.). The performances are given in Table 4 for a typical reference scene with reflectivity 0.1 sr\({}^{-1}\) (typical of a vegetation surface), a median aerosol load, and a SSE (related to surface pressure) of 300 m, which corresponds to median altitude over land. A worst-case situation corresponds to sea and snow areas, where the 50 km random error might reach 50 to 100 ppb. In that case, the random error can be reduced by further averaging. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Parameter**} & \multicolumn{3}{c}{**User Requirements**} & \multicolumn{2}{c}{**MERLIN System**} \\ \cline{2-5}  & **Threshold** & **Breakthrough** & **Target** & **Specification Requirement** \\ \hline XCH\({}_{4}\) random error & 36 ppb & 18 ppb & 8 ppb & 22 ppb (27 ppb *) \\ XCH\({}_{4}\) systematic error & 3 ppb & 2 ppb & 1 ppb & 3 ppb (3.7 ppb *) \\ Spatial coverage & Global & Global & Global & Global \\ Resolution & Horizontal: 50 km averaging: vertical: total column & & \\ \hline \end{tabular}
\end{table} 
Table 3: User requirements for MERLIN (1-sigma error). * The values in brackets correspond to the actual targets after applying a correction factor of 1.23 to account for the actual MERLIN weighting function with enhanced sensitivity in the boundary layer (see text). For the systematic error, the situation is rather different than for the random error. Indeed, as shown in Table 5, there are many contributors, which have roughly the same magnitude: (i) the DAOD measured by the payload; (ii) the error on the surface pressure; and (iii) the error on the weighting function. The first one is caused by the yet limited variations of the on/off ratio between the atmospheric and the internal calibration path, and by the as-yet-unknown residual of non-linearity after the correction of the detector. The second one comes from both the uncertainty of NWP products and the error of SSE estimation (including platform altitude, attitude and Lidar ranging contributors). Regarding the third contributor, the cross-section knowledge depends on external parameters (temperature profile from NWP, spectroscopic parameters), but also of the Lidar itself, through the knowledge of the emitted frequency. As explained in Section 3, the \"online\" frequency has been chosen to be in a local minimum of the CH\({}_{4}\) manifold in order to reduce the sensitivity to laser stability. Moreover, the Doppler effect is minimized by the choice of an across-track pointing angle of \(-1^{\circ}\), for which the Doppler effects caused by the Earth rotation and the satellite movements almost compensate (a negative sign means the line-of-sight points east at the Ascending Node). Thus, the residual frequency error resulting from our limited knowledge of FRU measured frequency and the Doppler effect is almost negligible. For the error arising from the use of humidity profiles obtained from NWP, an optimal position of the offline wavelength guarantees a minor impact, due to compensating effects between the error impact on the water vapor DAOD corrective term and on the weighting function, as explained in chapter 3. Finally, the processing itself may contribute to the systematic error through the introduction of scene-dependent biases, for example in the horizontal averaging step [91]. The errors for individual contributors of Table 5 are obtained either from the basic equations of processing, or with more detailed simulations, for example for the errors related to frequency which