# MERLIN: A French-German Space Lidar Mission Dedicated to Atmospheric Methane
## 5 Performance
### XCH\({}_{4}\) Error Budget  
The random error is usually defined as the part of the error which tends towards zero when enough independent data are accumulated. For practical issues, in order to get a definition that can be easily handled when estimating the instrument error budget, we define the random XCH\({}_{4}\) error as the part of the error with spatial and/or temporal evolution at high frequency (i.e., >1 Hz), with zero mean over the mission lifetime, and the systematic error as either varying at low frequency (i.e., <1 Hz), or being dependent on the scene observed. This ensures that the random error is strictly non-correlated between two measurements (defined after a 50 km averaging, thus separated by about 7 s). Consequently, the horizontal averaging of data described in Section 4 leads to a reduction of error by square root of \(N\), with \(N\) being the number of shot-pairs considered in the averaging process. Table 3 shows the user requirement related to these two types of errors. The \"threshold\" requirement is the minimum requirement to ensure that the MERLIN products are useful for CH\({}_{4}\) emission retrievals by inverse modeling. The \"breakthrough\" requirement is an intermediate requirement level that provides a significant improvement to the current satellite observation system and, given the current status of the instrument development, is regarded as the optimum from a cost-benefit point of view. The \"target\" requirements represent a tremendous improvement relative to what is achieved today and may be achieved by a follow-on MERLIN-type instrument. We note that the requirements in Table 3 apply to a total column with vertically constant weighting function. As illustrated in Figure 5b, MERLIN's online frequency has been chosen to obtain a weighting function with enhanced sensitivity in the boundary layer (about at least 1.23 higher than in the upper part of the atmosphere), yielding more variability in the XCH\({}_{4}\) retrieval. This offers the possibility to relax the requirements applying to MERLIN in Table 3 by a factor 1.23, making the actual targeted random error to be better than 27 ppb and the actual targeted systematic error better than 3.7 ppb (A-SCOPE-Report for CO\({}_{2}\), Figure 4.1, p. 43 in [86]). The actual target for random errors is between threshold and breakthrough values of the user requirements (Table 3). The (already ambitious) actual target for systematic errors is at the threshold level. The MERLIN system specification requirements (column 5 of Table 3) result from parameter analysis of the various error contributors as described in the following. As the processing of MERLIN data up to level 2 can be written in a fully analytical form, the error budget is estimated mostly through an analytical approach based on derivative computations from Equations (1)-(4). The random error on XCH\({}_{4}\) mostly depends on the random error of the measured DAOD, coming from the signal-to-noise ratio of the instrument. The error contributors to XCH\({}_{4}\) from the weighting function, such as the random part of the error from Numerical Weather Prediction (NWP) external data (temperature, surface pressure and humidity) or from spectroscopy, or from the target Scattering Surface Elevation (SSE) estimation, are negligible. Indeed, an upper estimate of the random error part arising from surface pressure (from NWP models and SSE) and spectroscopy errors is about 5 ppb compared to about 20 ppb for instrument-related errors. As the errors must be summed up quadratically, this contribution can thus be neglected. The error from the DAOD itself comes from several contributors, the first being the instrument noise. Half of it comes from detector noise, and the other part from amplifier noise and signal shot noise. Thanks to the orbit selection (dawn-dusk), the solar contamination is rather low and the background signal shot noise is almost always negligible.