全站仪测量立木胸径树高及材积的误差分析

立木材积表是常用的森林调查数表，胸径、树高和材积的测量精度直接影响到编制材积表的精度，该文以全站仪无损测量立木的原理和误差传播理论为基础，推导了测算胸径、树高、材积误差的数学模型，研究了各立木因子间的相关性及其误差变化规律。结果表明：树干各分段高度与分段直径间存在弱相关性，树干总材积的误差受各分段材积的方差和相邻两段材积间的协方差影响。全站仪立木因子测量理论误差材积大于树高和胸径，其中胸径、树高和材积的平均相对误差分别为0.070%、0.023%和0.235%，说明全站仪无损测量立木的理论精度均远高于不同目标的林业调查及编制材积表的精度要求，对大范围的林业生产实践有着现实意义。

Error analysis of measuring diameter at breast height and tree height and volume of standing tree by total station

Abstract: Diameter at breast height (DBH), tree height and volume are the most significant factors in forestry investigation. The measurement precision of DBH and tree height directly affects the accuracy of individual volume. In traditional forestry works, cutting down trees and using analytic timber are for compiling the volume tables, which are yet faced with the problems such as high consumption, low efficiency and large destruction. In recent years, the emergence of the modern instruments gradually lays the foundation for achieving high precision nondestructive standing tree measurements. Total station is a kind of precise tool that can be used to measure distance and angle and to process data automatically. And it will be widely used in forestry production practice and scientific research in the future because of the high measurement accuracy, so studying the accuracy of measuring trees has practical significance for the forestry work. Calculating DBH, tree height and volume by measuring zenith angles, horizontal angles and distance from the center of the instrument to the tree is the principle of measuring standing trees by using total station. Based on the theory of measuring DBH, tree height and volume of standing tree by total station and taking the variance and covariance of measurement factors into consideration, the research deduced the mathematical models to calculate the error of DBH, height and volume of standing tree according to error propagation laws. We chose larches in Beijing as the experimental samples, and analyzed 10 sample groups of different sizes for the difference of relative errors. The results show: 1) There are correlations between the height and the diameter of random tree section, and the value range of correlation coefficient is (0, 0.3); besides, the variance and covariance of these 2 factors affect the error of each segment volume; furthermore, the error of total volume is affected not only by the variance of each section volume, but also by the covariance between 2 adjacent segments'' volumes, and the value range of correlation coefficient is (0.5,0.7); 2) The relative error of DBH, tree height and volume decreases with the increase of the sample size when the different samples are measured by total station. For 10 groups of samples, the relative error of DBH reduces from 0.108% to 0.052%, that of tree height reduces from 0.051% to 0.012% and that of volume reduces from 1.104% to 0.053%. And the average relative error of DBH, tree height and volume is 0.070%, 0.023% and 0.235% respectively. The relative error of DBH and height measurement is less than that of volume when the same sample is measured. The accuracies of DBH are much higher than the DBH measurement standard for national forest resource continuous investigation. The accuracies of tree height and volume of all samples are also much higher than the forest investigation standard for which tree height and volume measurement errors ought to be less than 3%-5%. Volume measurement error is required to be less than 3% for establishing volume tables, so using total station to collect the samples of various specifications can also meet the accuracy of volume tables. In conclusion, total station can satisfy the different needs of forestry survey.