## 2 Methodology  
### Overview  
The modeling of the lidar signal can be achieved based on a semi-empirical approach using the airborne lidar measurements and the radiative transfer equation applied to the laser beam propagation into a scattering medium (leaves, branches, trunks). The lidar instrument ULICE (Ultraviolet LIdar for Canopy Experiment) was embedded on an Ultra-Light Aircraft (ULA) (Figure 1) as for previous atmospheric [41] and canopy [25] studies. It performed airborne measurements over different forest biomes between 2008 and 2014, from temperate to tropical forests, to obtain a representative database of lidar vertical profiles. This database is used to initialize analytical and statistical modeling of the lidar signal, so as to simulate spaceborne observations. The canopy lidar or topographic lidar typically use wavelengths in the near infrared (NIR, _i.e._, 1064 nm), which corresponds to the fundamental emission of a commercial solid-state Nd:YAG laser. However, we will show that there are significant multiple scattering (MS) eff  
Figure 1: Illustration of airborne and spaceborne lidar measurements. forest structures at this wavelength, because of the high reflectance of the vegetation. These effects distort the lidar profile and make it difficult to locate the ground echo (GE) and the canopy echo (CE). Doubling the fundamental frequency, the Nd:YAG laser emits at 532 nm but it is quite difficult to get the eye-safe condition with such a wavelength. Thus, a laser operating at an ultraviolet (UV) wavelength (355 nm) was used in our airborne lidar measurements, which is available with the Nd:YAG laser using a non-linear crystal by tripling the fundamental frequency. The use of the UV spectral domain leads to a significant reduction of the MS effects in the forest structures and relaxes the constraints for operating eye-safety measurements. In order to characterize a forest site, three key parameters were derived from lidar backscatter profiles: (1) tree top height (_TTH_), a basic parameter for forest studies which is calculated as the distance between the first return at the upper surface of the vegetation and the last return of the ground surface [25, 42]; (2) quadratic mean canopy height (_QMCH_), a structural parameter which can be used to evaluate the aboveground biomass [15, 42]; (3) extinction coefficient (\(\alpha\)), an optical property indicating forest characteristics (e.g., canopy density and forest category) closely related to the forest optical thickness (_FOT_). All the structural and optical parameters are linked to the lidar equation as shown in Section 2.2. An end-to-end simulator (EES) was specifically developed for this study, which is a powerful tool to simulate and analyze the performance of airborne and spaceborne lidar systems. It is composed of a direct model and an inverse model. The block diagram of EES is shown in Figure 2. From airborne lidar measurements (e.g., lidar profile _S_), forest parameters (_i.e._, _TTH\({}_{0}\), QMCH\({}_{0}\), \(\alpha_{0}\)_ in Figure 2) can be derived from the inverse model so as to initialize the direct model. Meanwhile, four types of external data (in the blue bloc of Figure 2) were used to provide additional necessary constraints to the direct model: (1) an instrument model, including instrumental parameters of the lidar system and related uncertainties; (2) an atmosphere model, which includes the atmospheric contributions (_i.e._, molecular, aerosol and cloud optical thickness); (3) surface characteristics, which provide the necessary surface information and identify forest and non-forest areas as well as forest types at the global scale; (4) an orbit model, in order to simulate the different possible orbits for spaceborne lidar systems. Lidar vertical profiles were simulated by the direct model. The main sources of noise were taken into account considering normal statistical distributions.