Using the Error-in-Variable Simultaneous Equations Approach to Construct Compatible Estimation Models of Forest Inventory Attributes Based on Airborne LiDAR

Airborne LiDAR has been extensively used for estimating and mapping forest attributes at various scales. However, most models have been developed separately and independently without considering the intrinsic mathematical relationships and correlations among the estimates, which results in the mathematical and biophysical incompatibility of the estimates. In this paper, using the measurement error model approach, the error-in-variable simultaneous equation (SEq) for airborne LiDAR-assisted estimations of four forest attributes (stand volume, V; basal area, G; mean stand height, H; and diameter at breast height, D) for four forest types (Chinese fir, pine, eucalyptus, and broad-leaved forest) is developed and compared to the independence models (IMs). The results indicated that both the SEqs and IMs performed well, and the rRMSEs of the SEqs were slightly larger than those of the IMs, while the increases in rRMSE were less than 2% for the SEqs. There were statistically significant differences (α = 0.05) in the means of the estimates between SEqs and IMs, even though their average differences were less than ±1.0% for most attributes. There were no statistically significant differences in the mean estimates between SEqs, except for the estimates of the D and G of the eucalyptus forest. The SEqs with H and G as the endogenous variables (EVs) to estimate V performed slightly better than other SEqs in the fir, pine, and broad-leaved forests. The SEq that used D, H, and V as the EVs for estimating G was best in the eucalyptus forests. The SEq ensures the definite mathematical relationship among the estimates of forest attributes is maintained, which is consistent with forest measurement principles and therefore facilitates forest resource management applications, which is an issue that needs to be addressed for airborne LIDAR forest parameter estimation.