## 4 Link Budget
### Link Budget under Ideal Atmospheric Conditions  
The link budget is firstly studied under ideal atmospheric conditions (Atmosphere model in Table 1). In our simulation, only shot noise is taken into account as the others noise sources can be considered negligible (see Appendix A). The SNR of lidar signals depends on the instrumental parameters, the  
Figure 12: Multiple scattering effect simulations at (**a**) 355 nm and (**b**) 1064 nm for oaks in summer by using a similar orbit of ISS at 350 km. atmospheric optical thickness, the surface characteristics and the platform altitude. For a given lidar system, the SNR decreases exponentially as the FOT increases. Firstly, we considered the actual instrumental parameters of the four referenced spaceborne lidar missions (CALIPSO, ICESat, MERLIN, and ADM-Aeolus) as shown in Table 3. Here we considered two types of forest with FOT of 1 or 2. The corresponding GE SNR of these spaceborne lidar systems are calculated, and given in Table 5. Lidar products of the ICESat mission have been used for forest studies (e.g., [48, 68, 69, 70]). Through the results of our EES, the _GLAS_ lidar can well mapping the open forest with a FOT \(\leq 1\), which occupies \(\sim\)30% of the forest area by considering the FOT distributions derived from our airborne lidar measurements. But it cannot well study denser forests with a lager FOT due to a low SNR. Secondly, our EES simulations were performed for lidar systems with same instrumental parameters (given in Table 1) onboard five spatial platforms: CALIPSO, ICESat, MERLIN, ADM-Aeolus, and ISS. The values of required energies (_E_) were found out at both the UV and NIR wavelengths (Table 6), by considering getting SNR \(\sim\)10 at the ground level. These simulations show that it will be difficult to detect dense forests (_FOT\(>2\)_) at a UV wavelength. Even for the ISS, the required energy of the lidar system is \(\sim\)220 mJ to detect a medium dense forest (_FOT\(=2\)_), which means good detections for temperate deciduous forests in winter and temperate conifer forests, but poor detections for temperate deciduous forests in summer or tropical forests. The values of \(E\) retrieved in the NIR domain are more realistic for a spaceborne mission because they remain lower than 80 mJ for medium dense forests (_FOT\(\leq 3\)_), which represent \(\sim\)90% surface of the forest area according to the referenced FOT distribution (Figure 5). Thus, only the NIR domain will be considered hereafter for the link budget for realistic atmospheric conditions. Obviously, the low orbit will be preferred for dense forests (_FOT\(>2\)_). Accounting for the above considerations, for a given lidar system and a chosen orbit, there is a maximum value of the total optical thickness (_TOT\({}_{max}\)_) for which the ground echo is still detectable. The lower the orbit is, the larger _TOT\({}_{max}\)_ will be, as expressed by Equation (1). If we take an example of a lidar system with instrumental parameters given in Table 1, emitting 100 mJ laser pulses at 1064 nm, the _TOT\({}_{max}\)_ for systems onboard five spaceborne platforms were calculated and given in Table 6. As in Equation (4), the TOT is the sum of half the FOT and the total atmospheric optical thickness \(\tau\), the latter one is equal to 0.1565 under ideal atmospheric conditions (Table 1). Then, we can get the corresponding _FOT\({}_{max}\)_ (maximal forest optical thickness) to study the forest density limit of each spaceborne lidar system. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Mission** & CALIPSO & ICESat & MERLIN & ADM-Aeolus \\ \hline
**Lidar** & CALIOP & GLAS & IPDA & ALADIN \\ \hline
**Orbit altitude z\({}_{\theta}\) (km)** & 705 & 600 & 506 & 400 \\  & _FOT_\(=1\) & 24.5 & 10.0 & 9.1 & 12.9 \\
**GE SNR** & _FOT_\(=2\) & 14.8 & 6.1 & 5.5 & 7.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: SNR at the ground level (GE SNR) of lidar signal by using actual parameters of four spaceborne lidar missions (Table 3), and the Atmosphere model and Surface characteristics in Table 1.