## 5 Discussion  
[PERSON] et al. [24] estimated the vertical _LAI_ distributions from the Laser Vegetation Imaging Sensor (LVIS) large-footprint waveforms based on the GORT model. Our study indicated that the forest foliage profile could be accurately estimated using the GORT model and simulated airborne small-footprint full-waveform LiDAR data. Therefore, the physics-based method used in this study is an efficient foliage profile retrieval method to use when waveform LiDAR data are available. To improve the foliage profile estimation accuracy and minimize the data acquisition costs, the effects of data acquisition conditions on the forest foliage profile estimation were explored, including the scanning angle, flying altitude, and pulse density. Previous studies have found that when the scanning angle increased, the amount of echo from the ground decreased [28; 30; 40]. Similarly, the analysis of the influence of the scanning angle on the foliage profile estimation in this study found that when the scanning angle increased, airborne LiDAR acquired a similar return energy from the upper canopy, more return energy from the lower canopy, and less ground return energy. Therefore, when the scanning angle was larger, the foliage area index derived from the GORT model was slightly smaller at the upper canopy and larger at the lower canopy. This result occurs because when using a large scanning angle, the path length through the canopy is longer than in near nadir measurements with a small scanning angle [29]. Thus, more emitted pulses were intercepted by the lower canopy, and fewer echoes backscattered from the ground were detected. [PERSON] et al. [30] simulated the influence of the LiDAR scanning angle on the estimation of canopy height and closure related metrics. The results indicated that these metrics changed quickly when the scanning angle increased from 0\({}^{\circ}\) to 20\({}^{\circ}\), and they changed slightly when the scanning angle increased from 20\({}^{\circ}\) to 30\({}^{\circ}\). [PERSON] et al. [29] studied the effect of the scanning angle on the accuracy of an ALS-based forest inventory, and they found that a narrower scanning angle (30\({}^{\circ}\)) led to more accurate results than a wider scanning angle (40\({}^{\circ}\)). Similarly, the accuracy assessments in this study found that the estimated foliage profile at the scanning angle of 20\({}^{\circ}\) was nearest to the simulated foliage profile, and the estimated total _LAI_ at the scanning angle of 20\({}^{\circ}\) was the most accurate. Therefore,  
Figure 16: The _RMS_Es of the foliage profiles (**a**) and the _Diff_s of the total _LAI_ (**b**) at pulse densities from 0.25 pulse/m\({}^{2}\) to eight pulses/m\({}^{2}\) (the scanning angle and flying altitude are 20\({}^{\circ}\) and 2000 m, respectively). the optimal scanning angle for the forest foliage profile estimation was 20\({}^{\circ}\). The sensitivity analyses found that the optimal scanning angle for foliage profile retrieval at plot level is independent of the flying altitude and pulse density when the flying altitude increased from 1000 m to 4000 m and the pulse density increased from 0.25 pulse/m\({}^{2}\) to four pulses/m\({}^{2}\). In addition, a combination of multiple scanning angles can improve the foliage profile estimation accuracy, such as the combinations of 15\({}^{\circ}\) and 25\({}^{\circ}\) and 15\({}^{\circ}\) and 30\({}^{\circ}\) scanning angles. Of course, more accurate foliage profile estimation methods for combining multiple scanning angles should be explored in future research. Increasing the flying altitude can enlarge the observation area while retaining the same flying time, thereby decreasing the cost of data acquisition [41]. When the flying altitude was increased, the footprint size was enlarged and the pulse density was decreased, so the return energy was affected. [PERSON] et al. [42] found that the flying altitude had no effect on the estimation of mean height and volume. A study by [PERSON] et al. [43] also reached similar conclusions.