## Appendix A Sources of Noise  
For an instrumental link budget the contribution of each noise source has to be considered. There are five different and independent kinds of noise: the background-radiation noise, the shot noise (\(\sigma\)s), the dark-current noise (\(\sigma_{D}\)), the Johnson-Nyquist noise (\(\sigma_{JN}\)), and the quantification noise (\(\sigma_{O}\)). Their standard deviations are expressed by the symbol \(\sigma\).  
The background-radiation noise is negligible in our airborne measurements, because a strong optical density (OD \(\sim\)3) was used to compensate the large field-of-view (\(\sim\)4 mrad). It is also negligible in our simulated spaceborne measurements with a much smaller field-of-view(\(<\)57 \(\upmu\)rad). We take an example of a NIR (1064 nm) lidar system onboard the ISS with instrument parameters shown in Table 1, and an interference filter of 0.45 nm bandwidth [60]. Via the 6S radiative transfer modeling [77] for the worst case (_i.e._, solar and satellite zenith angles are both 0\({}^{\circ}\)), the background sky radiance was found to be 0.2 \(\mathrm{W\cdot m^{-2}\cdot sr^{-1}\cdot nm^{-1}}\). The background light is then evaluated [44] as 1.8 \(\times\) 10\({}^{-7}\) A, which is negligible compared to the lidar signal.  
In analog detection mode, lidar signal \(S\) is expressed in volt with \(R_{c}\) the load resistance. Since the noise was expressed as a current, the signal-to-noise ratio (SNR) can be expressed as follows [44]:  
\[SNR=\frac{S/R_{c}}{\sqrt{{\sigma_{S}}^{2}+{\sigma_{D}}^{2}+{\sigma_{JN}}^{2}+ {\sigma_{Q}}^{2}}} \tag{1}\]  
The standard deviations of each noise can be expressed by [44]:\[\left\{\begin{aligned} \sigma_{S}(\lambda,h)=\sqrt{\frac{G\cdot\frac{ \hbar c}{\lambda}\cdot\zeta\cdot c}{2\cdot\Delta z\cdot QE\cdot R_{c}}\cdot S( \lambda,h)}\\ \sigma_{D}=G\cdot NEP\cdot\sqrt{\frac{c}{4\cdot\Delta z}}\\ \sigma_{IN}=\sqrt{\frac{k_{B}\cdot T_{K}\cdot c}{R_{c}\cdot\Delta z} }\\ \sigma_{Q}=\frac{1}{2\sqrt{3}}\cdot\frac{S_{max}/R_{c}}{2^{n_{b}}} \end{aligned}\right. \tag{10}\]  
where \(G\) is the system gain of the pre-amplification and the detector, \(\lambda\) is the wavelength, \(\zeta\) (\(\sim\)1 or \(\sim\)1.5 for photon-counting or analog detections, respectively) is a correction factor by taking into count the statistic gain fluctuation of the photo-detector, \(\Delta z\) is the vertical sampling resolution along the lidar line-of-sight, \(QE\) is the quantum efficiency of the photo-detector, \(NEP\) is Noise-equivalent power of the detector (\(\sim\)10\({}^{-15}\) W\(\cdot\)Hz\({}^{-1/2}\) for a photomultiplier, \(\sim\)10\({}^{-13}\) W\(\cdot\)Hz\({}^{-1/2}\) for an avalanche photodiode), \(T_{K}\) is the detector's temperature (\(\sim\)25 \({}^{\circ}\)C), \(n_{b}\) is the bit number for the quantification and \(S_{max}\) is the maximal amplitude of the quantification. The Planck constant, the light velocity, and the Boltzmann constant are h (\(\sim\)6.62 \(\times\) 10\({}^{-34}\) J\(\cdot\)s), \(c\) (3 \(\times\) 10\({}^{8}\) m\(\cdot\)s\({}^{-1}\)), and \(k_{B}\) (1.38 \(\times\) 10\({}^{-23}\) J\(\cdot\)K\({}^{-1}\)), respectively.  
In photon-counting detection mode, \(\sigma_{IN}\) is not involved and \(\sigma_{D}\) is negligible compared to photon numbers (\(\sigma_{D}\) is about 3.5 \(\times\) 10\({}^{4}\) times smaller than \(\sigma_{S}\) for our airborne lidar system). The quantification noise based on 12 bits is negligible (and \(\sigma_{Q}\)\(\sim\)2.8 \(\times\) 10\({}^{-7}\) A). The shot noise, whose standard deviation \(\sigma_{S}\) is proportional to the square root of the lidar signal, is the main source of noise, and was taken into account in our simulations. The expression of SNR for both photon-counting and analog detections can be derived from Equations (1), (10) and (10).