Error analysis on standing tree volume measurement by using electronic theodolites

In traditional forestry works, the compilation of volume tables by cutting down trees and using analytic timber volume estimations is faced of problems such as large destruction, high costs and low efficiency. Therefore, an estimation method was proposed. First, diameter at breast height and ground diameter were manually measured. Then, the horizontal angles and zenith distances at corresponding trunk positions of live standing trees were measured by using the approximate division of analytic timber based on an electronic theodolite. Finally, the timber volume was estimated by simulating mean sectional division volume as per summation of conical frustum. The measured data of standing timber volumes from poplar in Beijing were used as true data for examination. The errors of timber measurement from electronic theodolites were theoretically analyzed according to error propagation laws. Based on the four grades of electronic theodolite precision classification in China: I (DJ1), II (DJ2), III (DJ6) and IV (DJ15), the errors and the limit errors of root mean square error (RMSE) during measurements of tree height and timber volume were computed. Moreover, the differences and applicability of electronic theodolites with different precision levels were analyzed. The results showed that because of error propagation and accumulation, the errors of timber volumes measured by electronic theodolites with the same precision were larger than the errors of tree height. When timbers with different sizes were measured by electronic theodolites of the same precision level, the errors slightly changed along with the size of timbers. With the increased standard deviation in angle measurements by electronic theodolites, the errors in forest measurement also increased. When the standard deviation of electronic theodolites was ±0.5″, the RMSEs in measurements of tree height and timber volume were ±6.550 0×10-2 m and ±1.474×10-3 m3, respectively, while the relative errors were 0.44% and 0.73%, respectively. When the standard deviation of electronic theodolites was ±15.0″, the RMSEs in measurements of tree height and timber volume were ±8.927 5×10-2 m and ±4.385×10-3 m3, respectively, while the relative errors were 0.60% and 2.14%, respectively. Therefore, the existing I~IV electronic theodolites applied into tree measurements all conform to the precision requirement that relative errors do not exceed 3%~5%, and satisfy the requirements of different forestry works. ©, 2014, Chinese Society of Agricultural Machinery. All right reserved.