Prezisyonlu nivelman ölçülerinde refraksiyon hatasının modellendirilmesi
Başlık çevirisi mevcut değil.
- Tez No: 46277
- Danışmanlar: PROF.DR. AHMET AKSOY
- Tez Türü: Yüksek Lisans
- Konular: Jeodezi ve Fotogrametri, Geodesy and Photogrammetry
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1995
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 73
Özet
ÖZET Bu çalışmada prezisyonlu nivelman ölçüsünü etkileyen ve nivelmandaki sistematik hatalardan biri olan refraksiyon hatası ele alınmıştır. Refraksiyon hatasının giderilmesi için literatürde adı geçen refraksiyon hata modelleri incelenmiş ve bunlara ait eşitlikler topluca sunulmuştur. Ulusal düzey kontrol ağlarındaki prezisyonlu nivelman ölçülerinin refraksiyon hataları nedeniyle düzeltilmesi için en uygun yöntemin“Isı Transfer Modeli”olduğu ortaya konmuş ve geçmiş yıllarda yapılmış (tarihi) nivelman ölçüleri ve günümüzde yapılmakta olan prezisyonlu nivelman ölçülerinin bu yöntemle düzeltilebileceği gösterilmiş ve uygulamada elde edilen sonuçlar ortaya konmuştur. vı
Özet (Çeviri)
SUMMARY STUDY ON THE CORRECTION OF PRECISE LEVELLING MEASUREMENTS FOR REFRACTION ERRORS Refraction causes leveled height differences to be too small. It is usually considered to be the largest known systematic error in levelling measurements, amounting to as much as a cm/km. In 1937, long before refraction was widely accepted as a significant error source, T.J. KUKKAMAKI developed a correction which proportionaly to the temperature difference, At, between heights of 0.5 m and 2.5 m, as the rod readings are generally on this range. At was to be measured, requiring extra effort and equipment. Few countries adopted the correction, but it is now realized that the correction is necessary, especially in the middle and lower latitudes. Removing refraction bias from levelling measurements requires a vertical temperature gradient (dt/dh). But if levelling measurements are old and vertical temperature gradient does not exist, one must use a temperature stratification model. The model described in this study, is based on historical records of solar radiation, sky cover, precipitation, and ground albedo from many locations in the conterminous Turkey. The average difference between predicted At and observed At is + 0.061°C, and -0.1 12°C for data sets from ANKARA and Gürün/SİVAS respectively. This modeling method can be adopted by any country with records of solar radiation. This modeling method is an important asset to levelling computations because it provides a means of eliminating extreme refraction bias in the absolute heights more reliable. An economic advantage is realized by eliminating the need to observe vertical temperature profiles during most levelling surveys. By considering this economic side of this method, new levelling measurements also can be corrected by the same way. A refraction correction for levelling was first developed by T.J. KUKKAMAKİ in 1937 (KUKKAMAKI, 1939). The correction for a single setup is R = -10“6. A. \~\.Ah.At (1) L is the sight lenght; Ah is the measured difference of elevation; and As is a function dependent on a assummed temperature function (t=a+b.hc), A may be assumed constant and is calculated as A = c c z2-zl rc”(zi+C-z2+j-Zo(Zi-Z2) 1+C (2) vnHere, R, Ah, and L are in meters, and At in degrees Kelvin, and ZQ is the height of the instrument, and z\ and Z2 are the heights of the line of sight on the fore and back rods, in meters. At is a difference in air temperature between two chosen heights, usually zı=0.5 m and Z2=2.50 m. Levelling refraction is proportional to the height difference observed at the instrument station and to the square of the sight lenght, thus accumulating most quickly on long gentle slope that can be found almost anywhere in Turkey. The inconsistencies in the levelling data caused by refraction error should be removed prior to the adjustment of level networks, crustal movements, and deformation investigation. The magnitudes of the vertical temperature gradient near the ground depends primarily on the intensity of solar radiation. Solar radiation at mid-latitudes is highly variable depending on season and time of day. This causes temperature gradients near the ground to fluctuate similarly. Thus the amount of refraction error in levelling surveys will generally depends on“when”the measurements were made. Rainfall, cloud cover, and ground refrectivity also have regional and temporal variations which influence vertical temperature gradients. To obtain the temperature difference, which can be expressed in terms of other meteorological factors, between two heights, the following equation is applied. At = t2-t1 = 3 H2,r nl/3 (Cp-p) -g (z21/3-z~,1/3)- 0.0038 (z2-Zl) (3) Where t0 is the air temperature at Zoin °K. The height Z©, would ordinarily be 1.60 m, g is the accelaration of gravity (m/sn2) (Cp.p) is a constant, 1200 J/m3.°K. The most important element is the upward sensible heat flux, H. This element can not be measured directly, and can be expressed by the following equation H= Sn-G-?iE (4) Where Sn is net radiation; it is possible to measure directly or express in terms of solar radiation measured in the meteorology station. G and XE are dependent on the precipitation, cloud cover, and the ground albedo. One can easily calculate mean values satisfying the results for G and AE. Solar radiation are observed with a pyronometer in meteorology stations. While levelling measurement are making, when solar radiation is needed, a predicted solar radiation is used for calculation of the sensible heat flux, H. Thus, a modelled temperature difference is found, and applied in the 1st equation. vmGiven that c= -1/3, and Z«, Z\, and Z2 are equal 1.60 m, 0.50 m, and 2.50 m respectively, the value A of the 1st eq is calculated as 1.48 x 102 and considered constant. All variation of predicted At with time and season is function of upward heat sensible heat flux, which in turn is primarily dependent on solar radiation. Solar radiation is dependent on time, place and season. Although preferable, it is not necessary to apply the refraction correction to At at every set up of the instrument in the levelling measurements. Instead, predicted At by the model is used for input to refraction formula (1). The correction is applied to the observed difference of elevation for the section of levelling, Ah', which is usually the sum of the height differences from several setups. Average sight lenght Lis substituted for the individual setup values. The total correction for a line is then _>2 R = -10“”A|^J At.Ah' (5) For c= -1/3, and Ah' in meters, (5) simplifies to R = C.L2.At.Ah' (6) Where R is in meters and C equals to -6.44x10-8, At in degrees Kelvin, and Lis in meters. In this study it is showed that the predicted temperature differences could be used for removal of refraction bias from old and new levelling measurements, made for construction of levelling networks and deformation investigations. On the application studies, the following procedure was applied to correction of levelling measurements for refraction errors: (i) Obtaining solar radiation, sky, cover, rainfall, temperature and albedo values observed in the meteorolgy satiations in Turkey. IX(ii) Modelling solar radiation for Turkey by a surface function, as Sr (,X) Cos (2n G/365) + F3 ((p,X,) Sin (2% G/365) (7) where Sr: monthly total daily mean solar radiation value at any station. (p,A,: longitude and latitude of the station. G: the number of day in the year from 21 december. Ff. the polynoms which are two dimensional function of j and 1. Ever$ polynom has (n+1)^ unknowns. Thus, the surface function has 3 (n+1)^ unknowns. The expansion of the polinoms is provided by the following serie. n n j j Fk= X I
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