# MERLIN: A French-German Space Lidar Mission Dedicated to Atmospheric Methane
## 3 Methodology  
As a novel feature, MERLIN will make use of the IPDA Lidar technique to derive XCH\({}_{4}\). The envisaged methodology and basic measurement concept has been developed in the framework of two dedicated ESA studies [84; 85] to support the Advanced Space Carbon and Climate Observation of Planet Earth (A-SCOPE) study for CO\({}_{2}\)[86], and subsequent studies focusing on CH\({}_{4}\)[55; 87]. The Lidar instrument measures the reflected or scattered radiation from the Earth's surface and from cloud tops along the satellite footprint as depicted schematically in Figure 1. For each measurement, the ground spot will be illuminated by spectrally narrow laser pulses having slightly different frequencies in the 1.64 \(\upmu\)m spectral domain, commonly denoted as online and offline frequencies, respectively. To be sensitive to the CH\({}_{4}\) concentration changes close to the Earth's surface, the online frequency will be accurately positioned on the wing of a pressure-broadened CH\({}_{4}\) absorption line. In contrast, selection of a frequency position on the CH\({}_{4}\) absorption line center would give highest sensitivity in the stratosphere. In general, the absorption feature of spectrally narrow laser radiation is determined by the Weighting Function (WF), which in principle describes the relative contribution of an atmospheric layer at pressure \(p\) to XCH\({}_{4}\) (see Figures 1 and 2 in [53] and Equation (3)). The spectral precision is possible since the spectral width of the laser pulses is set by the constructor at about 60 MHz (FWHM). Hence, it can be regarded as being quasi-monochromatic compared to the pressure-broadened CH\({}_{4}\) absorption line of about 3 GHz (FWHM). As in usual laser differential-absorption methodology, each online measurement is accompanied by corresponding offline measurement that serves as a reference exhibiting significantly less CH\({}_{4}\) absorption. Both online and offline frequencies are sequentially emitted with a very short time delay (\(\Delta t\sim 250\)\(\upmu\)s) in order to observe near-identical light paths and surface scattering properties. The signals received by the payload can be described using the hard target Lidar equation [53]:  
\[P_{on,off}(r_{T})=D_{on,off}\frac{A}{r_{T}^{2}}O_{on,off}\rho_{on,off}\tau_{ on,off}^{2}(r_{T})\frac{E_{on,off}}{\Delta t_{eff}} \tag{1}\]  
For both frequencies, \(P\) is the instantaneous light power entering the detector area from reflecting target at range \(r_{T}\), \(D\) is the total optical efficiency, \(A\) is the size of the telescope area, \(O\) the overlap function between laser ground spot and the field of view (FOV) of the receiving telescope at the target, \(\rho\) [sr\({}^{-1}\)] is the target reflectance parameter defined as the reflected power towards the receiver divided by the incident power, \(\tau_{on,off}\) is the one-way atmospheric transmission, \(E_{on,off}\) are the emitted pulse energies at both frequencies which slightly differ in real lasers systems, and \(\Delta t_{off}\) is the effective pulse length, given by the time spread of the structured target, the temporal length of the emitted pulses, and the detector impulse response time. By applying the Beer-Lambert law, the Differential Atmospheric Optical Depth (DAOD) with respect to CH\({}_{4}\) is given by the ratio \(P_{off}\)/\(P_{on}\) of the measured Lidar signals:  
\[ \begin{split} DAOD(r_{T})\equiv\int_{TOA}^{r_{T}}m_{CH_{4}}(r^{ \prime})[1-q_{H_{2}O}(r^{\prime})]n_{air}(r^{\prime})[(\sigma_{on}(r^{\prime}) -\sigma_{off}(r^{\prime})]dr^{\prime}\\ =\frac{1}{2}\ln\big{[}\frac{P_{off}(r_{T})E_{on}}{P_{on}(r_{T})E_{ off}}\big{]}-DAOD_{other\;gess}\end{split}  \tag{2}\]In this equation, \(m_{CH4}\) is the dry-air mixing ratio of CH\({}_{4}\) at a given distance \(r\)', \(q_{H2O}\) is the water vapor mixing ratio, \(n_{air}\) is the number density of air, and \(\sigma_{on,off}\) denotes the respective molecular absorption cross sections for the selected online and offline frequencies.