## 5 Discussion  
Our proposed method for retrieving forest VFP and LAI is based on physical principle, rather than based on a statistical regression, which is currently a preferential method by modelers. In addition, our method used more information provided by GLAS products compared with the previous methods only using received waveform information and solved a problem of existing methods, which will likely improve the accuracy of VFP and LAI estimation. Although there is a limitation that we cannot provide accurate ground reflectance as input, the analysis in Section 4.4 has shown that it has a small effect on the result. Overall, our research provided a new perspective for retrieving the VFP and LAI  
To test the performance of our method, we used ground-based data to validate our method. However, there were some limitations in our validation process. First, the different times of GLAS data acquisition and TRAC measurements will introduce errors. As shown in the comparison scattering plot (Figure 7c), the comparison points were roughly distributed on both sides of the 1:1 line, which may have been caused by the above reason. Second, due to the limitations of the field measurement equipment, we were unable to obtain the LAD profile data through measurement; therefore, we used photos of the sites along the observation footprints as a reference to evaluate the rationality and accuracy of the VFP but did not conduct a quantitative evaluation. Regardless, the quantitative evaluation of the VFP has been addressed by a variety of virtual scenes. In view of the limitation in the validation of this work, future studies should place an emphasis on field data collection to ensure that the measurement time is consistent with the satellite LiDAR data. We also extended our method to Heilonggiang Province. For this province-level LAI inversion, there was an error source, which may come from landcover information provided by the GlobeLand30 landcover product. Our research focused on forests, so the non forest-covered GLAS data had to be filtered out. In Saihanba National Forest Park, we selected forest-covered GLAS data by visual interpretation of high-resolution images and on site investigation. However, this strategy is challenging to conduct in large study areas, such as those at the province level, because of time and labor costs. Here, we adopted an effective strategy to select the forest-cover GLAS data that used the high-resolution land-cover product to filter out the non forest cover GLAS data. The GlobeLand30 product has an accuracy of 83% at a global scale [42]; therefore, the misclassification of landcover types in the GlobeLand30 product may lead to errors in the LAI inversion in Heilongjiang Province. For example,  
Figure 16: An example of a LAD profile derived from GLAS data with different values of \(\rho_{g}\). the low LAI values (e.g., LAI < 1) shown in Figure 11 may not have resulted from the GLAS observations of the forest because of the misclassification of land-cover types. Due to the lack of available validation datasets at the province level, we therefore limited the assessment of the GLAS LAI differences in Heilongjiang Province by using the MODIS LAI product. The result showed a weak correlation between the two; the reason is that our method did not consider canopy clumpiness. For any given effective LAI value, the error in the true LAI varied linearly with the clumping index. Previous studies have used a strategy that builds a clumping index look-up table by assigning each land cover class an average clumping index from coarse resolution clumping index products such as MODIS or Polarization and Directionality of the Earth's Reflectance (POLDER) to revise this error. However, this simple and crude method does not take into account the difference in the level of clumping of the same landcover type, so it may introduce error. In addition, the scale effect, which is caused by the direct application of coarse-resolution products to high-resolution products, needs to be considered [58].