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Atmospheric Effects in Geodetic Levelling

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Atmospheric Effects in Geodetic Levelling GEODESY AND CARTOGRAPHY ISSN 2029-6991 print / ISSN 2029-7009 online 2012 Volume 38(4): 130–133 doi:10.3846/20296991.2012.755333 UDC 528.381 ATMOSPHERIC EFFECTS IN GEODETIC LEVELLING Aleš Breznikar1, Česlovas Aksamitauskas2 1Faculty of Civil and Geodetic Engineering, University of Ljubljana, Jamova 2, SI-1000 Ljubljana, Slovenia 2Department of Geodesy and Cadastre, Vilnius Gediminas Technical University, Saulėtekio al. 11, LT-10223 Vilnius, Lithuania E-mails: [email protected] (corresponding author); [email protected] Received 08 November 2012; accepted 12 December 2012 Abstract. The knowledge of physical processes and changes in the atmosphere is essential when addressing the fundamental problem, i.e. the accuracy of geodetic measurements. In levelling operations, all these changes are explained as the effect of refraction, which systematically distorts the results of levelling. Different ways of addres- sing the effect of refraction are represented based on the modelling of the vertical temperature gradient as the qu- antity that has the most influence on the refraction phenomenon. Keywords: atmospheric refraction, geodetic levelling, model of vertical temperature gradient. 1. Introduction 2. Known characteristics of levelling refraction Measurements in geodesy are mostly performed in the The principal knowledge about levelling refraction can field, under real atmospheric conditions. These measure- be summarized as follows: ments are therefore subjected to all the changes that oc- – On an inclined surface, the refraction systemati- cur in the atmosphere. The atmosphere is a highly inho- cally distorts the results of levelling; mogeneous medium, whose state is defined by a set of – The amount of refraction error is proportional to parameters that can quickly change, both spatially and the square of the length of the line of sight; temporarily. – The refraction effect increases with the increase of Today, the errors resulting from environmental the temperature gradient; impacts are the main reason why the measurement ac- – Under the influence of refraction, the height diffe- curacy is not even higher than it already is. The proper rence is reduced; evaluation of the individual parameters occurring in the – If a certain levelling line is levelled under the atmosphere, whose changes result in refraction effects, is same microclimatic conditions, the effects of ref- the main issue. Studying the atmospheric effects in geo- raction are not evident as deviations during the detic operations is an interdisciplinary activity, in which levelling in either direction, nor are they manifes- the problems are solved based on scientific achievements ted as deviations in the closure of loops; rather it in relevant scientific areas. functions as the systematic error of the rod scale. In levelling operations, too, invar levelling rods and The refraction error is manifested directly in the levelling instruments have reached a stage of develop- height error of individual benchmarks; ment which would have permitted even higher accuracy, – The effect of humidity is minimal and can be, in if it had not been limited by refraction. There are many most cases, neglected; problem domains where precise determination of the – On its way from the levelling instrument to the height difference between the stations on the Earth’s sur- level rod, the horizontal line of sight is deflected face is required. These problems are related to geophys- upwards, which is the result of the negative tem- ics, geodynamics, engineering geodesy and, indeed, pre- perature gradient in near-ground air layers. cise levelling. The refractive index of air along the levelling line of Today, refraction represents the main source of sight changes as a function of the quantities causing it to systematic errors in levelling. Particularly, the effects of change, hence resulting in the phenomenon of refraction refraction are analysed as part of national levelling net- (Mozzuchin 1999, 2010). work campaigns. In most of developed countries, in the The refractive index in the atmosphere is mostly in- national first-order levelling surveys corrections for re- fluenced by the following quantities: air temperature, air fraction effects are performed. pressure, and content of humidity and carbon dioxide 130 Copyright © 2012 Vilnius Gediminas Technical University (VGTU) Press Technika http://www.tandfonline.com/TGAC Geodesy and Cartography, 2012, 38(4): 130–133 131 (CO2). In ordinary levelling operations, mostly air mass This error also cannot be determined from the differ- in the range of 50 cm to 300 cm above ground is consid- ences in levelling in either direction; however, its effect ered; hence the studying of the values and changes of the is evident in the closure of levelling loops. In the level- influencing quantities in these layers is meaningful. ling loops that involve symmetrical slopes, the refraction The effect of air humidity is negligible since it repre- error will not be expressed as an error in levelling loop sents, at the most, less than 1/20 of the effect of tempera- closure. However, the effects of the part of the refrac- ture. The effect of carbon dioxide is even smaller. tion error resulting from the meteorological conditions Temperature and air pressure have the most signifi- during levelling will not be negligible. In levelling loops cant effect on the refractive index in the air layers where involving unsymmetrical slopes, the refraction error can levelling operations typically take place. be eliminated only partly. The non-eliminated part of the The amount of air pressure changes as a function of error results in non-closure of levelling loops, which is height. Generally speaking, air pressure decreases pro- frequently higher that the allowed deviation. portionally to the height above the ground. During the course of the day, the air pressure in a station changes 3. Ways of addressing the problem of refraction depending on the general weather conditions. However, There are several different approaches to the determina- these changes of air pressure are slow and, in general, tion of levelling refraction. Of the existing models solving minimal. Evidently, the systematic effect of air pressure the problem of levelling refraction, one can distinguish changes is eliminated in closed loops, while the effect of between three main groups (Heer 1983; Brunner 1984): minor, random changes of air pressure is also negligible. – Direct refraction models in which the corrections Temperature, along with its changes, is the main for refraction effect are calculated by taking into factor causing changes of the refractive index in the at- account the measured temperature differences mosphere. Hence the determination of the actual influ- and the selected equations for temperature chan- ence of levelling refraction depends on the use of as far ges near ground level, or, alternatively, the tempe- as possible realistic models describing temperature gra- rature changes serve for temperature gradient qu- dients in the air layers where lines of sight are captured antification. The temperature gradient is the input during levelling. of the model describing the physical changes in The changes of the refractive index are a function the atmospheric boundary layers. of both the absolute air temperature and the tempera- – Indirect refraction models where the corrections ture differences of the air layers where lines of sight are for refraction are also calculated based on the captured. Here, we must distinguish between two terms, size of the temperature gradient. In these cases, albeit the same quantity, i.e. temperature. The differ- the temperature gradient is expressed in relation ences in temperature can be relatively large at low tem- to meteorological and geometric parameters, as a peratures, and, vice versa, the differences can be minor function of height above the ground, tilted surfa- at high temperatures, depending on different factors. ce, zenith distance of the Sun and the height va- Therefore they should be dealt with separately, i.e. abso- riation of heat fluxes. In this case also, the tem- lute temperature and temperature gradients. perature gradient can be calculated based on the In almost all formulas for calculation of the cor- measurements of temperature. rection for levelling refraction, the size of the refractive – The statistical analysis of the levelling operations correction is proportional to the size of the temperature can estimate the individual types of errors; hence gradient. While the changes of other factors involved it is possible to assume the size of the error due to in levelling refraction do not significantly influence the the effects of refraction. change of refraction, the effect of temperature difference is great and can change the size of refractive effects by 3.1. Models of levelling refraction based on 100%, and even 200%. Temperature gradient in the ele- measurements of temperature differences vations of up to 3 m above the ground, i.e. in the range of The models for refraction error calculation originate ordinary levelling operations, can be negative, positive, from the common basis, which is expressed as the effect or equal to zero. Furthermore, temperature gradient can- of the temperature gradient on the refractive index of air not be considered as a random variable during the level- and the assumption that the isothermal layers are paral- ling operations. lel to the ground (Kakkuri 1984). The individual mod- The investigations
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