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AN ADJUSTMENT OF PRECISE LEVELLING NETWORK BY ERROR FACTOR ASSUMPTION-FREE WEIGHTS

Christina Mickrenska, Vasil Cvetkov

Abstract

This paper discusses the relevance of the classical adjustment weights for the highest-order geometric levelling network. The commonly used weights are inversely proportional to the length of levelling lines. The argument behind this choice is the assumption that the accuracy of measured elevations is a function of the square root of the levelled route. Therefore, the longer the line, the less its weight in the adjustment of the network. However, there are often events where the measured elevations of long lines are more accurate than those of shorter ones. Thus, the classical weights do not correctly reflect the accuracy of the measured height differences and are a reason for incorrect final results and conclusions concerning the investigated processes by the adjusted network. Try to avoid this issue, we recommend weights that correspond to the actual line elevation accuracy. They are assumption-free weights regarding the factors that are supposed to form height differences uncertainty. Using the Jackknife procedure, we performed n-number independent adjustments of the Bulgarian Second Levelling network /1953-1957/, where n is the number of levelling lines in the network. We skipped a different levelling line in each adjustment and calculated the averages of the produced standard errors of the adjusted benchmark heights. We used these averages to define the proposed line height difference weights. The comparison between samples of the standard errors of the adjusted benchmark heights, obtained by the proposed weights and the classical ones, shows that the former produce more accurate results than the latter. The conclusion is made at a significance level higher than 90%. Furthermore, the differences between the adjusted benchmark heights by both approaches, regarding some benchmarks, go beyond 20 mm. These differences are too much when considering the recent vertical movements in Bulgaria or establishing a state height reference system. We recommend including the proposed weighting method in the specifications for levelling data processing. Their usage can likely increase the state levelling network accuracy, but also explain a part of the -mysterious- systematic deteriorations of the state and continental reference systems.

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Dimensions ID: pub.1195348443

DOI resolver: doi.org/10.5593/sgem2025/2.1/s08.10

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