## 2 Methodology
### Direct Model
#### 2.2.4 Platform Model  
**Airborne lidar**. The main characteristics of the lidar system ULICE are given in Table 3. The laser energy (\(E\)) is deliberately oversized (\(\sim\)7 mJ), which is compensated by optical densities (\(OD=3\)) at the reception, in order to limit the parasitic signal related to the sky radiance. The vertical sampling resolution (\(\Delta z\)) along the lidar line-of-sight depends on the sampling frequency of the digitizer card and the laser pulse duration. The Centurion laser has a laser pulse duration between 6 and 7 ns, so the sampling frequency is chosen between 100 and 500 MHz leading to vertical sampling between 0.3 and 1.5 m. The vertical sampling of 0.75 m was the one most frequently chosen for the acquisition the lidar profiles used in the simulations. The pulse repetition frequency (PRF) is defined on the basis of the footprint sampling density needed in the forest sites and the aircraft speed, which ranges from 5 to 100 Hz for a full-waveform lidar system and was chosen to be 20 Hz during the field campaigns [42]. The energy distribution of laser beam is Gaussian according to the calibration in the laboratory. It can be considered as homogeneous for airborne measurements with small footprints (\(<\)5 m), but has to be taken into account for spaceborne measurements with lager footprints. The laser footprint size at the ground level is defined by the laser beam divergence and the platform altitude. Airborne lidar measurements were performed for flight altitude close to 350 m agl. According to the divergence of the laser, it leads to footprints between 2 and 5 m in diameter over the temperate forests, and \(\sim\)10 m in diameter for tropical forests. These profiles can be further recombined to simulate profiles in a compatible footprint of a spaceborne lidar.  
**Spaceborne lidar systems**. Lidar systems have been already embedded onboard the satellites. Even though none of their purposes is to detect and sample forests, some instrumental parameters and the orbits of the main spaceborne lidar missions can be considered as the references for our simulations. Four missions were chosen and will be considered: the Geoscience Laser Altimeter System (GLAS) onboard the past mission ICESat (Ice, Cloud, and land Elevation Satellite) to detect ice-elevation changes in Antarctica and Greenland [52]; the future Climate Mission MERLIN (Methane Remote Sensing Lidar Mission) with the payload of a Methane Integrated Path Differential Absorption (IPDA) LIDAR emitting at 1645 nm, dedicated to the measurements of the greenhouse gas Methane [53]; the near-future ADM-Aeolus (Atmospheric Dynamics Mission Aeolus) mission carrying the Atmospheric Laser Doppler Instrument (ALADIN) for global wind profile observations [54]; the current CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations) mission carrying the Cloud-Aerosol LIdar with Orthogonal Polarization (CALIOP) to improve the understanding of the role of aerosols and clouds in the Earth's climate system [55]. The International Space Station (ISS) is also considered as a potential platform for a future spaceborne canopy lidar system, an example of recent mission CATS (Cloud-Aerosol Transport System) for the atmospheric purpose is given at [56].  
Actual parameters of these referenced spaceborne lidar missions were found out through research papers [53, 57, 58, 59, 60], and are given in Table 3. As they were not designed for forest studies, the sampling vertical resolution (\(\Delta z\)) for CALIPSO, MERLIN, and ADM-Aeolus missions is too large. Their parametersare then modified for a 0.75 m resolution as the one of our airborne lidar ULICE. The \(\Delta\)z of the ICESat mission keeps its own value since one of its targets is the surface study.