大光斑激光雷达数据已广泛应用于森林冠层高度提取，但通常仅限于地形坡度小于20°的平缓地区。在地形坡度大于20°的陡峭山区,地形引起的波形展宽使得地面回波和植被回波信息混合在一起，给森林冠层高度提取带来巨大挑战。本文利用激光雷达回波模型和地形信息，提出了一种模型辅助的坡地森林冠层高度反演算法。该方法以激光雷达回波信号截止点为参考，定义了波形高度指数H50和H75，使用激光雷达回波模型与已知地形信息模拟裸地的激光雷达回波，将裸地回波信号截止点与森林激光雷达回波信号截止点对齐，利用裸地回波计算常用的波形相对高度指数RH50和RH75，对森林冠层高度进行反演。并与高斯波形分解法和波形参数法的反演结果进行了比较。研究结果表明：(1)利用所提取的波形指数RH50和RH75对胸高断面积加权平均高(Lorey’s height)进行了估算，在坡度小于20°时，高斯波形分解法、波形参数法和模型辅助法的估算结果与实测值线性拟合的相关系数(R²)分别为0.70，0.78和0.98，对应的均方根误差(RMSE)分别为2.90 m,2.48 m和0.60 m,模型辅助法略优于其他两种方法；(2)在坡度大于20°时，高斯波形分解法、波形参数法和模型辅助法的R²分别为0.14，0.28和0.97，相应的RMSE分别为4.93 m,4.53 m和0.81 m,模型辅助法明显优于其他两种方法；(3)在0°—40°时，模型辅助法对Lorey’s height估算结果与实测值的R²为0.97，RMSE为0.80 m。本研究提出的模型辅助法具有更好的地形适应性，在0°—40°的坡度范围内具备对坡地森林冠层高度反演的潜力。

Full waveform data of large-footprint LiDAR are widely used to retrieve global or regional forest canopy heights. However, most studies have focused on forests on relatively flat terrains where the slope is smaller than 20°. Estimating the canopy height of hillside forest stands over mountainous areas with large relief remains a challenge. A model-assisted method is proposed to estimate canopy heights of hillside forest stands by using LiDAR waveforms and overcome the effect of terrains. The adaptability of the method in 0° to 40° is evaluated.
We propose a new method and redefine the height index. First, the LiDAR waveform of bare ground is simulated according to given terrain slopes. Second, the LiDAR waveforms of a forest stand and bare ground are aligned according to their signal ending points. Finally, the heights of quarter energy points (i.e., H50 and H75) of the LiDAR waveform of forests are defined relative to the signal ending points, and the heights of quarter energy points (i.e., Hg50 and Hg75) of the LiDAR waveform of bare ground are defined relative to the signal ending points. The relative height indices (i.e., RH50 and RH75) of the forest LiDAR waveform are defined as the difference in the corresponding index of the simulated waveform of forest and bare ground, namely, RH50=H50 - Hg50 and RH75=H75 - Hg75. The newly defined RH50 and RH75 are used to estimate forest canopy heights. The model-assisted method is validated within 0° to 40° terrain slopes and compared with Gaussian decomposition and edge-extent methods.
(1) Within the 0° to 20° terrain slopes, the accuracies of estimating forest canopy heights using Gaussian decomposition, edge-extent, and proposed model-assisted methods are R²=0.70, 0.78, and 0.98 and root-mean-square error (RMSE)=2.90 m, 2.48 m, and 0.60 m, respectively. The performance of the proposed method is slightly better than that of the two other methods. (2) Within the 22° to 40° terrain slopes, the accuracies of estimating forest canopy heights using Gaussian decomposition, edge-extent, and proposed model-assisted methods are R²=0.14, 0.28, and 0.97 and RMSE=4.93 m, 4.53 m, and 0.81 m, respectively. The proposed model-assisted method is superior to the two other methods. (3) The estimation accuracy of the model-assisted method within the 0° to 40° terrain slopes is R²=0.97 and RMSE=0.80 m. This model can overcome the effect of the terrain and maintain high accuracy. The method will be further validated using spaceborne LiDAR data in future research.
The proposed method can correct the effect of slope over hillsides, and the relative height indices extracted by this method are insensitive to terrain slopes. The proposed method shows a potential for use in the accurate estimation of forest canopy heights over hillsides.