Prezisyonlu elektromanyetik uzunluk ölçmelerinde atmosferik etkilerin ve ölçek hatalarının lokal ölçek parametreleri modeli ile giderilmesi

Abstract

Bu çalışmada, elektro magnetik uzaklık ölçerle ölçülen kenarların, atmosferik düzeltmelerinin hesaplanmasında kullanılan atmosferik modeller ve bu modellerin, kenar ölçme presizyonlarına etkileri araştırılmıştır. Bu amaçla, atmosferik modeller genel olarak incelenmiş ve daha sonra çevresel modeller olarak adlandırılan, Lineer Kırılma İndisi Modeli, Türbülans Transfer Modeli, Logaritmik Kırılma İndisi Modeli ve Lineer Kırılma İndisi Modeli ile atmosferik etkiler giderilmiş kenar ölçülerine ait en uygun Stokastik değerlerin belirlenmesi yöntemi incelenmiştir. Söz konusu çevresel atmosferik modellerin her biri si ile sadeleştirilmiş Taşkesti mikro jeodezik ağında, 1989 ve 1991.yıllarında Mekometre ME-5000 presizyonlu elektro-optik uzaklık ölçeri ile yapılan ölçüler değerlen dirilmiş ve her bir modele göre düzeltilen ölçülerle, mikro jeodezik ag, ayrı ayrı dengelenerek ag noktalarının, nokta konum presizyonları belirlenmiş ve stokastik model testine tabi tutulmuştur. Tüm hesap işlemlerinden sonra, elde edilen sonuçlar aşağıdaki biçimde özetlenebilir. Elde edilen nokta konum presizyonları birbirine çok yakındır. Signifikant bir fark yoktur. Bu durumda söz konusu ağda, hesaplanması en basit ve kolay olan Lineer Kırılma İndisi Modelinin kullanılması uygun olacaktır. v Söz konusu ağda, ölçme dalgaları yerden ortalama 120 metre yukarıdan geçmektedir. Atmosferik veriler ise yerden ortalama 10 metre yukarıda kaydedilmektedir. Bu nedenle, bulunan sonuç lineer kırılma indisi modelinin uygulanması için gereken koşullarla uyuşmaktadır.

In this study, various models for atmospheric refrac tive index of air between standard atmosphere and atmosphere in the conditions of temparature, presure, humidity, wind velocity and cloud rate at time of measurement, have been discussed for analysing which model is the most suitable one to calculate atmospheric effects on Electro Magnetic Dxstance Measurements. Over the past decade or so considerable research attention has been paid to solving the main problem limiting the attainable accuracy of medium-to longrange electronic distance measurement (EDM). That problem being the deter mination of the integral refractive index along the EDM wave path. The observing procedure most commonly adopted for refractive index determination involves the measurement of temparature, humidity and pressure at each endpoint of an EDM line. The mean of the two endpoint values is then assumed to be equal to the integral value. But usually it is not equal to the integral valve. That is why, scientists have been improved some different atmospheric models to get the best result according to integral value. In this case, various models for atmospheric correc tion are called peripheral atmospheric refractive index mo dels. The mean reason of preparing this study was to get decision about the mentioned models. For this aim, some peripheral atmospheric models which are linear Refractive Index Model, Turbulent Transfer Model, Logorithmic Refrac tive Index Model and calculation of ideal stochastic values for distance measurements which are corrected by linear refractive index model, are applied to Teskesti micro geo detic network measurements. vn Two periods of Taskesti micro geodetic network measurements which are done in 1989 and 1991, are chosen as the data grups to calculate each peripheral atmospheric model to compare them to eachather to get final conclusion. It was expected that after all calculations, we could get exact result about the models to say the best model for Taskesti micro geodetic metwork's conditions. For our pur pose, peripheral atmospheric models which are selected for the calculations, can be explained as follows. The representative refractive index of a line is computed from meteorological observations taken at one or both terminals of the line.. For lines in excess of a few kilometers and whenever high accuracy is required, t, p and t1 are measured at both endpoints and the refractive indices are computed separately for both terminals. The mean ref ractive index is then used to correct the measured distance. In case of taking meteorological observations at both end- point, procedure may be simplifed by taking the mean value of the endpoint meteorological measurements, before calcu lating the refractive index once. This process is called linear refractive index model. Small errors are introduced in the process due to the non-linearity of the refractive index equations. There errors are sufficiently small to be ignored in most cases. Briefly, model is based on meteoro logical measurements t, p and t1 endpoint and refractive index can be formuled as follow; e = E'-0.43(t-t') 755 Torr where; E'=10(237!lt: +0-6609) t ; dry bulb temparature (°C) t'; wet bulb temparature (°C) p ; atmospheric pressure (Torr) e ; partial water vapour pressure (Torr) E ; saturation water vapour pressure over water (Torr) and finally refractive index can be presented; nt=l+ Ngr. P l+P(0.817-0.0133.t)10-6 + (_n pc^p e) 720.755 1+at 10~6 a = 273.15 Vlll Where; n..; refractive index Ngr; grup refractive index of the instrument. The EDM reduction formula, for lineer refractive index, dn=d(no~nt) Where, d is measured distance and nois refractive index for instrument. The second atmospheric model which is used in this study, can be summerized as follow. The Turbulent Transfer Model is proposed as an atmospheric model for electro magnetic distance measurements reduction which is applicable during periods when an uns table turbulent regime has developed in the atmospheric boundary layer. In such conditions, two principal regions are distinquistable in the convective boundary layer. Above the unstable surface layer of height L lies an adia- batic layer of well mixed air where the prevailing tempara- ture gradient is in accordance with the dry adiabatic lapse rate. In the context of refraction modeling, such meteoro logical conditions are considered the optimum for electro magnetic distance measurements. The term stability, refers to the behavior of a small parcel of air when moved, e.g., upward from an initial position, with no exchange of heat. When the parcel of air has adjusted to the pressure at the new height, its density compared with the surrounding air will either tend to push it back down, or to drive it further upward. Because the density differences are mainly dependent upon temparatures, stability can be described in terms of temparature. The potential temparature 0 of the air parcel is defined as that temparature which it would take up if brought adiabatically to a standart pressure. Unstable atmospheric stratification prevails during sunny weather conditions. The mean potential temparature gradient can be expressed by the appropriate equation for composite convection Au= 0.027 H2/3 where, H= 450.C.w.sin a and H is the sensible heat flux, IX C, cloud rate w, wind velocity a, the height of the sun during the observations. The EDM reduction formula for unstable conditions dc can be derived by dc=3.10"6Au.d(Nm/Tm) |hr~1//3- | / hx"1//3dx|+dn o where, Tm is mean value of temparature ( K),Pm is mean value of pressure (m bar) and dn is reduction for linear refractive index model and Nm =(0.2696 Ngo Pm-llem) /Tm where, Ngo is the grup refractive index, em is the vapour pressures, quoted are means of observations at the two end points. As it is shown, the difference between linear refractive index model and TTM model is only the value of (dc) reduction. In this study, also it is purpose to determine this difference, if it is significant. The third model is Logarithmic refractive index model. If we explain it brief ly^ the refractive index of air is given by general equation, (ti-hA) N=NA.e~ c and if it is put applicable form, Log N=log NA- ^, hB-hA (1-k),2 2 " 12R and here, and ci hB-hB LogNA-LogNB NB-NA k= -6.38 hB-hA The parameters which have been consisted by formula, hB,hA^ are the heights of two endpoint and N is the refractive index. Finally, the reduction for distance in logarithmic refractive index. can be explaned by formula? d£=d(n -n) o -6 here, n is obtained by (N.10 -1). The model is improved for specially the field which has L profile between the x points. And it gives best result if the measurements are done on water surface. Beside, these three atmospheric refractive index models in this study, we used another method to calculate the stochastic values of the measurements which are done by EDM ME-5000, instead of using fixed values which are given for instrument by production company. In this method, we used distance measurements which are corrected for atmospheric effects by linear refractive index model. The distance between two points, measured with an electro-optic device is given by d= IfH- " k t with the following meaning of the symbols : 1= number of wave-lenghts contained between the points V= light speed in standard atmosphere f= modulation frequency k= additive constant nij.= relative refractive index of air between standard atmosphere and atmosphere in the conditions of temparature and pressure at time of measurement The main idia to apply this method is, according to the law of error propagation, getting differencial effects of the parameters which are held in function, on basic function. By this way, it is possible to calculate the variance of a distance measurements. This method is applied just for EDM mekometer 5000, because of using some constants according to instrument. After the short explanations of whole model, here, according to final calculations to compare models eachother, it is obtained that linear refractive index model is the best atmospheric model to determine the atmospheric effects on electro magnetic distance measurements in Taşkesti micro geodetic network. Also, calculations showed that given properties for linear refractive index model are acceptable due to geometric position of Taşkesti geodetic test network!. And, after the comparison of position errors of points, between applied models, it is clear that the best position errors for points are obtained by linear refractive index model.