Mersin İli Toroslar İlçesi Örneğinde Lokal Datum Dönüşüm Parametrelerinin Belirlenmesi Üzerine Bir Çalışma

Abstract

Jeodezik çalışmaların anlamlı olabilmesi için koordinat sitemi ya da daha kapsamlı olarak datumlardan bahsetmek gerekmektedir. Bunun nedeni tüm jeodezik bilgilerin bu tanımlamalardan referans edilmesinden dolayıdır. Bu kapsamda çok çeşitli datumlar tanımlanmıştır. Ülkemizde yaygın olarak ED50 datumu, son yıllarda sıkça kullanılan ve bir bütünsellik imkanı verdiği için ilerleyen dönemlerde kullanılmak zorunda olunan ITRF96 datumudur. Bunların yanında bir diğer kullanılan koordinat sistemi de özellikle Belediyelerin sıkça kullandıkları lokal koordinat sistemi olan imar koordinat sistemidir. Kullanılan koordinat sistemlerindeki bu çeşitlilik, kullanıcılar arasında sorunsuz paylaşım sağlayacak ortak bir sistem oluşmasına engel olmaktadır. Özellikle resmi kurumlar arasında verilerin paylaşımında ve ortak kullanımında sorunlar yaşanmaktadır. Örneğin belediyelerin bir kısmı imar koordinat sistemi kullanmaktadır, kadastro kurumlarının önemli bir kısmı ise ED50 memleket koordinat sistemi kullanmaktadır. Belediyelerin Kadastro ile olan içiçe geçmiş çalışmaları, tevhid-ifraz 18.madde imar uygulamaları gibi, ortak koordinat sistemi kullanmaları gerektiğini açıkça göstermektedir. Fakat günümüzde halen bu problemler aşılabilmiş değildir. Bu problemler ise vatandaşların hukuksal haklarından biri olan taşınmaz mülkiyetleri ile ilgili olarak doğrudan doğruya işlem yapan kadastro ile vatandaşlar arasında ve vatandaşların kendi aralarında hukuksal davalara konu olabilmektedir. Böylesine ciddi bir konuda jeodezik verilerin sağlıklı olması hem kurumlar için hemde vatandaşlar için hayati bir önem taşımaktadır. Bu çalışmada, yukarıda bahsedilen konu kapsamında, çalışmanın olduğu bölge için uygun bir datum dönüşüm yöntemi tespit edilerek jeodezik verilerinin BÖHHBÜY’ne uygun hale getirilmesi amaçlanmaktadır. Bu çalışma kasamında 2 farklı datum dönüşümü yöntemi kullanılmıştır. Bunlar İki Boyutlu Helmert Benzerlik Dönüşümü ve Polinomlarla Dönüşüm yöntemidir. Çalışma kapsamındaki belediye sınırları içerisinde yapılan bu çalışmada, şu sonuçlara varılmıştır; bölge verilerinin datum dönüşümleri için 3 farklı dönüşüm yolu ortaya çıkmıştır, birincisi tüm bölge için bir adet dönüşüm parametresine sahip Helmert benzerlik dönüşümü, ikinci yol bölgenin 2 kısımdan oluştuğu ve tüm bölge için 2 adet dönüşüm parametrenin olduğu Helmert benzerlik dönüşümü, sonuncusu ise tüm bölge için tek parametreye sahip polinomlarla dönüşümdür. Bu 3 yöntemin hangisinin daha sağlıklı sonuçlar vereceğini tespit etmek için de 12 adet kontrol noktası seçilmiş ve bunlar her 3 yöntem ile dönüştürülüp çıkan sonuçların hata miktarları irdelenmiştir. Bu irdeleme sonucunda şu kanaate varılmıştır, her 3 dönüşüm yöntemi BÖHHBÜY’ne uygundur ancak bu yöntemlerin bölgede ki çalışma amacına uygun hizmet etmesi gerekmektedir. Yani örneğin bölgede bir bütünsellik gerekiyor ise polinomlarla dönüşüm yöntemi kullanılmalıdır, ya da çalışmalarda konum doğruluğu ön plana çıkıyor ise 2 kısımdan oluşan Helmert benzerlik dönüşümünün tercih edilmesi daha anlamlı olacaktır.

This study is about datum transformation for the area which keeps within Mersin province and Toroslar Municipality boundaries. The topic of the thesis is about the geodetic problem between Toroslar Municipality and cadastre because of the coordinate systems. Thus, municipality and cadastre are using different coordinate system; this situation causes some problems about sharing geodetic data or information between people and public institutions, such as municipality and cadastre institutions. Therefore it is needed to establish joint data exchange way. There are too many geodetic application occurs between municipality and cadastre institution, land parcel processing for instance. This situation shows that it is necessary to use joint datum obviously. The aim of the Geodesy is to determine the geometric shape of earth precisely. This is possible to establish geodetic reference network on the earth. This network consist of ground control points which coordinates of positions can be determined precisely and accuracy. So, these geodetic infrastructure requires reference coordinate system which is called Geodetic Datum. Geodetic datum has a great importance in the geodetic applications to define coordinates mentioned before. Because it makes the geodetic data, which are coordinate informations, meaningful. This is because all of the geodetic informations and parameters are referred with respect to the datums. Basically, Geodetic Datum is a mathematical model which is defined on the ellipsoid of revolution and it can be projected on the plane with respect to the geodetic application locations and aim. It can be also defined as constant informations which is related origin plane or base plane which is used for determinations. In this case, it should be mentioned about Geodetic datum. Geodetic datum is positions information of the reference ellipsoid. This ellipsoid is the fittest to the earth geometric surface and shape in order to make geodetic calculations. Datum parameters informations defines coordinate system at the same time. There are too many geodetic datum , such as ED50, ITRF96 (International Terrestial Reference Frame), WGS84 (World Geodetic System). ED50 (European Datum) geodetic datum uses Hayford ellipsoid which is determined by John Fillmore Hayford, who is from America, in 1909. European Datum (Ed50) has been agreed on as an international ellipsoid by International Union of Geodesy and Geophysics (IUGG) in Madrid in 1924, and it is recommended to the countries especially which are at the begining of the applications about scientific researches and triangulation. ITRF96 (International Terrestial Reference Frame) is another gedetic datum like ED50 (European Datum) which is also used in Turkey. This datum uses GRS80 (Geodetic Reference System) ellipsoid . It has been agreed on as an reference ellipsoid by International Union of Geodesy and Geophysics (IUGG) in 1979.This ellipsoid is also selected as a reference ellipsoid for International Terrestial Reference Frame (ITRF).Since too many countries begins to use GRS80 ellipsoid as a base reference ellipsoid. In our country, ED50 (European Datum) and ITRF96 (International Terrestial Reference Frame) are generally being used as a geodetic datum as mentioned before. Since ITRF96 datum provides the unique coordinate system over the earth, and legal obligation , it is more used in from ED50 datum. On the other hand, municipality uses local datum generally. In this scope, there are many geodetic datum, and that means every datum has a different coordinate system. In this case, the datum transformation is needed to establish unique structure in geodetic coordinate system. This is because both local coordinates which is used for layout project for any engineering projects or municipality plans and geodetic coordinate system defined by countries for their applications, so it is obligated to define datums for every different scaled applications. In order to establish unique coordinate system for all different application mentioned before, it is necessary to repositioned to the same layout or reference coordinate system. For this reason, datum transformation is necessary. Datum parameters distinguish the datums from each other. For example, despite of many european countries use the same ellipsoid, they have different coordinate system, because of using different datum parameters. Another sample is about ED50 (European Datum), although many countries in Europe uses the ED50 datum and also Turkey, it is called as Turkish National Datum for Turkey , and it is called as European Datum for Europe. Coordinate transformation is the recalculation of the set of coordinates which is determined in any coordinate system. This process is consist of three steps which are shifting, rotation and scaling. In order to determine coordinate transformation parameters, it is necessary to have common control points which have well distributed and known coordinates in the both of two coordinate systems. According to the aim of datum transformations, it is possible to keep to the object properties after coordinate transformation. If the angle which is between points or shape of the geometry should be regarded, this datum transformation is called as “ similarity transformation ”. However, it can be also kept to object properties of length or area, such as Afin transformation. In this study, 2 Dimensional Helmert similarity used firstly, and 25 common control points were selected with respect to their geometric distribution. Before the transformation calculation, Pope (Tau) test for outliers was used to find out the outliers points and eliminate these outliers points from the common control points set. For this statistical test confidence interval was selected 0.05. Outliers points were subtracted from common points by using Pope test for outliers. After detecting outliers points, transformation process was repeated. This iterative calculation was proceeded. Common points which residuals values are greater than 14 cm were also subtracted from common points set. At the end of the transformation calculation, 4 transformation parameters were determined. These parameters are 2 shifting, 1 rotation and 1 scale factor. According to the end of the datum transformation calculations, it was identified that distributed common control points remained did not cover all the study area; middle of the area has not any common control points. Therefore, 2D Helmert transformation was considered for two parts. One of them is transformation parameters which are used for middle of the area, and second one is transformation parameters which are used for all the study area. In the other words, two transformations can be used with respect to the location of the points or objects. For example, if the object or point is in the middle of the study area that means the “middle transformation parameters” will be used. On the other hand, if it is in the rest of the middle of the study area, that means the “transformation parameters for whole area” will be used. In order to find out the transformation parameters for the middle of the study area, all of the 2D Helmert transformation calculations were repeated. That means, Pope (Tau) test for outliers and another coordinate transformation functions were used. So, datum transformation parameters were also determined for middle of the study area. Second datum transformation methods used for this study is Polynomial coordinate transformation method. According to the surface of study area and number of the control points, second degree polynomial function was used in the calculations. First of all, common control points coordinates have to be converted from projected coordinates (X,Y) to the geographical coordinates (latitude, longitude). This is necessary, because polynomial transformation determination indicates the polynomial function calculation. Therefore, geographical coordinates (latitude, longitude) define the surface in mathematical notation. For the polynomial calculations, outlier common points detected by using Pope (Tau) statistical test for outliers, so that; this process was repeated two times. After second test for outliers, it was not found any outlier point in the common points set. In the polynomial coordinate transformation calculation, polynomial coefficients were determined as datum transformation parameters. Thus, coordinates which are in the second can be calculated using these polynomial coefficients by means of polynomial functions. These parameters consist of two sub parameters which are for latitude and longitude. These are called “a coefficients” and “b coefficients”. So far, 3 coordinate transformations ways were determined for study area. In order to find out which transformation way is accurate and precise, 12 new common control points were selected for test points. These 12 test points were transformed using three coordinate transformation way. Thus, after this transformation of 12 test points, residuals value for each 12 test points was calculated. Root mean square error of these test points were calculated using residuals (correction) values. Using of the variety different datum, prevent to establish joint data exchange way. This situation causes some problems about sharing geodetic data or information between people and public institutions, such as municipality and cadastre institutions. There are too many geodetic applications occur between municipality and cadastre institution, land parcel processing for instance. This situation shows that it is necessary to use joint datum obviously. These problems mentioned above can also cause some legal issues between people and cadastre institutions which make process over the land parcels being legal rights of the people. In the serious subject mentioned before, geodetic datum has very seriously importance for the public institutions and people. According to the subject mentioned above, the goal of the study is determine the datum transformation methods and to optimize the municipality geodetic data with respect to the “Large Scale Map and Map Information Production Regulation” (LSMMIPR). In summary, two datum transformations have been used in this study. These are 2D Helmert Similarity Datum Transformation and second one is Polynomial Transformation. In this study, which covers the municipality boundaries, some conclusions have been reached. These are about transformation methods. There are three different ways for transforming. One of them is the Helmert transformation which has only one transformation parameters for whole area, and second one is the Helmert transformation which has two transformation parameters for middle and whole area, and last one is polynomial transformation. 12 test control points have been selected to determine which transformation methods give reliable transformation results. After that these 12 test points were transformed by three transformation ways and calculated the result of the transformation errors. After the calculation, it has been decided that these three transformation ways are reliable with respect to the “Large Scale Map and Map Information Production Regulation” (LSMMIPR). As a result, three datum transformation methods mentioned before should be used with respect to the aim of the applications in this area. For example, if the application is needed precision, Helmert methods, which have two transformation parameters, should be used. However, if the applications are needed integrity, polynomial transformation should be used for this study area.