{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T20:03:37Z","timestamp":1775592217972,"version":"3.50.1"},"reference-count":23,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,3,14]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Despite being in use for more than 150 years, the error accumulation in precise levelling has not yet been completely clarified. It is believed that the error accumulation in this method is proportional to the square root of the levelling length. The first goal of this article is to demonstrate that this belief is not always scientifically proven. The second aim is to show that it is likely that a better adjustment decision will be missed if inverse distance weighting with a power parameter equal to one is automatically applied. Using linear regression analysis the measuring data of the Second Levelling of Finland is analysed. An inadequacy of the relationship between the absolute values of the differences between both measurements of the elevations in the levelling lines and their length is shown, which is due to heteroscedasticity. In order to obtain a homoscedastic model, the other two models are constructed. Based on the regression analysis results, the network is adjusted using three types of weights. The adjustment with traditional weights has produced significantly greater mean errors of the nodal benchmarks than both variants based on weights, which are functions of the absolute values of the line elevations.<\/jats:p>","DOI":"10.1515\/jogs-2022-0148","type":"journal-article","created":{"date-parts":[[2023,3,14]],"date-time":"2023-03-14T17:05:43Z","timestamp":1678813543000},"source":"Crossref","is-referenced-by-count":6,"title":["Two adjustments of the second levelling of Finland by using nonconventional weights"],"prefix":"10.1515","volume":"13","author":[{"given":"Vasil","family":"Cvetkov","sequence":"first","affiliation":[{"name":"Department of Geodesy, Tochnost Ltd , Stephan Stambolov 50 , Bankya, Sofia-city , 1320 , Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2023,3,14]]},"reference":[{"key":"2023041008053871462_j_jogs-2022-0148_ref_001","unstructured":"Adam, J., W. Augath, F. Brouwer, G. Engelhardt, W. Gurtner, B. G. Harsson, et al. 1999. \u201cStatus and development of the european height systems.\u201d In Geodesy beyond 2000: The challenges of the first decade. IAG General Assembly, Birmingam. July 19 \u2013 30 1999."},{"key":"2023041008053871462_j_jogs-2022-0148_ref_002","unstructured":"Angelov, A. 2017. Geodetic methods in the study for deformation process of high buildings and engineering facilities, Monographic, 1 (uacg.bg), (in Bulgarian)"},{"key":"2023041008053871462_j_jogs-2022-0148_ref_003","unstructured":"Cvetkov, V. 2022a. Discrepancies and misclosures in the third levelling of Bulgaria, Vol. 55, No. 1, p. 195\u2013201. Annual of the University of Architecture, Civil Engineering and Geodesy, Sofia. 14-G-3.pdf (uacg.bg)."},{"key":"2023041008053871462_j_jogs-2022-0148_ref_004","unstructured":"Cvetkov, V. 2022b. Accumulation of the discrepancies [D] along the Balkan Mountains crossing lines 26, 31, 35, 37 in the Third Levelling of Bulgaria, Vol. 55, No. 1, p. 203\u201311. Annual of the University of Architecture, Civil Engineering and Geodesy, Sofia. 15-G-4.pdf (uacg.bg)."},{"key":"2023041008053871462_j_jogs-2022-0148_ref_005","unstructured":"Cvetkov, V. 2022c. An attempt at explaining of the absolute discrepancies |D| accumulated between the fundamental bench marks of the First and the Second order in the Third Levelling of Bulgaria by some regression models, Vol. 55, No. 2, p. 275\u201382. Annual of the University of Architecture, Civil Engineering and Geodesy, Sofia. 4-G1.pdf (uacg.bg)."},{"key":"2023041008053871462_j_jogs-2022-0148_ref_006","doi-asserted-by":"crossref","unstructured":"Enman, S. and V. Enman. 1984. \u201cSystematic errors in leveling of mountainous areas.\u201d Bulletin G\u00e9od\u00e9sique 58, 475\u201393.","DOI":"10.1007\/BF02523695"},{"key":"2023041008053871462_j_jogs-2022-0148_ref_007","unstructured":"Gekov, D. and V. Tzvetkov. 2005a. \u201cThe problem about choice of weights in the adjustment of precise leveling networks.\u201d In Proceedings of the International Symposium on Modern Technologies, Education and Professional Practice in Geodesy and Related Fields, p. 290\u20136, Sofia (in Bulgarian)."},{"key":"2023041008053871462_j_jogs-2022-0148_ref_008","unstructured":"Gekov, D. and V. Tzvetkov. 2005b. \u201cLimits for differences in values of forward and backward heights between nodal bench marks in levelling lines.\u201d In Proceedings of the International Symposium on Modern Technologies, Education and Professional Practice in Geodesy and Related Fields, p. 297\u2013304, Sofia (in Bulgarian)."},{"key":"2023041008053871462_j_jogs-2022-0148_ref_009","doi-asserted-by":"crossref","unstructured":"Gruber, T., C. Gerlach, and R. Haagmans. 2012, \u201cIntercontinental height datum connection with GOCE and GPS-levelling data.\u201d Journal of Geodetic Science 2, 4, 270\u201380, 10.2478\/v10156-012-0001-y.","DOI":"10.2478\/v10156-012-0001-y"},{"key":"2023041008053871462_j_jogs-2022-0148_ref_010","doi-asserted-by":"crossref","unstructured":"Hayden, T., B. Amjadiparvar, E. Rangelova, and M.G. Sideris. 2012, \u201cEstimating Canadian vertical datum offsets using GNSS\/levelling bench mark information and GOCE global geopotential model.\u201d Journal of Geodetic Science 2, 4, 257\u201369. 10.2478\/v10156-012-0008-4.","DOI":"10.2478\/v10156-012-0008-4"},{"key":"2023041008053871462_j_jogs-2022-0148_ref_011","unstructured":"K\u00e4\u00e4ri\u00e4inen, E. 1953. On the recent uplift of the Earth\u2019s crust in Finland, Publications of the Finnish Geodetic Institute No. 42, Helsinki."},{"key":"2023041008053871462_j_jogs-2022-0148_ref_012","unstructured":"K\u00e4\u00e4ri\u00e4inen, E. 1966. The Second Levelling of Finland in 1935\u20131955. Publications of the Finnish Geodetic Institute No. 61, Helsinki."},{"key":"2023041008053871462_j_jogs-2022-0148_ref_013","doi-asserted-by":"crossref","unstructured":"Kotsakis, C. and K. Katsambalos. 2010. \u201cQuality analysis of global geopotential models at 1542 GPS\/levelling bench marks over the Hellenic Mainland\u201d Survey Review 42, 318, 327\u201344. 10.1179\/003962610X12747001420500.","DOI":"10.1179\/003962610X12747001420500"},{"key":"2023041008053871462_j_jogs-2022-0148_ref_014","doi-asserted-by":"crossref","unstructured":"Kowalczyk, K. and J. Rapinski. 2013. \u201cEvaluation of levelling data for use in vertical crustal movements model in Poland.\u201d Acta Geodynamica et Geomaterialia, 10(4, 172), 401\u201310. 10.13168\/AGG.2013.0039.","DOI":"10.13168\/AGG.2013.0039"},{"key":"2023041008053871462_j_jogs-2022-0148_ref_015","unstructured":"Lehmuskoski, P. 1996. 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Applied Regression Analysis: A Research Tool, 2nd edn. New York: Springer.","DOI":"10.1007\/b98890"},{"key":"2023041008053871462_j_jogs-2022-0148_ref_019","unstructured":"Saaranen, V., P. Lehmuskoski , M. Takalo, and P. Rouhiainen. 2021. The Third Precise Levelling of Finland, FGI Publications No. 161, Kirkkonummi, The third precise levelling of finland (helsinki.fi)."},{"key":"2023041008053871462_j_jogs-2022-0148_ref_020","unstructured":"Sacher, M., J. Ihde, G. Liebsch, and J. M\u00e4kinen. 2008. \u201cEVRF2007 as Realization of the European Vertical Reference System.\u201d Presented at the Symposium of the IAG Sub-commission for Europe (EUREF) in Brussels, June 18\u201321 2008."},{"key":"2023041008053871462_j_jogs-2022-0148_ref_021","unstructured":"Takalo, M. 1978. Measuring method for the Third Levelling of Finland, Reports of the Finnish Geodetic Institute No. 78, 3, Helsinki."},{"key":"2023041008053871462_j_jogs-2022-0148_ref_022","unstructured":"Takalo, M. 1997. Automated calibration of precise levelling rods, Reports of the Finnish Geodetic Institute No. 97, 3, Kirkkonummi."},{"key":"2023041008053871462_j_jogs-2022-0148_ref_023","unstructured":"Takalo, M. 1999. Verification of automated calibration of precise levelling rods in Finland, Reports of the Finnish Geodetic Institute No. 99, 7, Kirkkonummi."}],"container-title":["Journal of Geodetic Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/jogs-2022-0148\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/jogs-2022-0148\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,10]],"date-time":"2023-04-10T08:05:55Z","timestamp":1681113955000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/jogs-2022-0148\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,1]]},"references-count":23,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,3,14]]},"published-print":{"date-parts":[[2023,3,14]]}},"alternative-id":["10.1515\/jogs-2022-0148"],"URL":"https:\/\/doi.org\/10.1515\/jogs-2022-0148","relation":{},"ISSN":["2081-9943"],"issn-type":[{"value":"2081-9943","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,1]]},"article-number":"20220148"}}