Sayısal arazi modeli üzerine bir inceleme

Abstract

Fiziksel yeryüzü ya da fiziksel yeryüzünde meydana gelen her türlü olayla doğrudan ya da dolaylı olarak ilgilenen meslek grupları için, arazi öteden beri bir ilgi unsuru olmuştur. Bu kapsamda, topografya ya da değişik yüzeylerle ilgilenen insanların, özellikle bilgisayar teknolojisindeki gelişmelerden etkilenmesi kaçınılmaz olmuş, bunun sonucu olarak yüzeyin ya da arazinin daha iyi temsil edilebilmesi için yeni yöntemler ortaya çıkmış ve insanlığın kullanımına sunulmuştur. Bu çalışmada, çok sayıda mühendislik uygulaması için büyük önem taşıyan Sayısal Arazi Modeli oluşturmaya yönelik olarak geliştirilen SAM yazılımı ile, elde mevcut veriler ile sayısal arazi modeli oluşturulmaya ve elde edilen model irdelenmeye çalışılmıştır. Bu irdeleme yapılırken, değişik sayısal arazi modeli uygulamalarına yönelik olarak geliştirilen SAM yazılımının tüm imkan ve kabiliyetlerinden yararlanılmaya çalışılmış, böylece değişik interpolasyon yöntemlerinin değişik yüzey yapılarında nasıl tepki gösterdiği de belirlenmeye çalışılmıştır. Günümüzde sayısal arazi modeli ile sadece çıplak gözle görünebilen fiziksel yeryüzü ya da topografya anlaşılmadığı, değişik mühendislik çalışmalarının farklı verileri kullandığı bilindiğinden, bu çalışmada da topografya yarımda, daha çok jeodezi bilim dalında uygulama alam bulan yükseklik, jeoit yüksekliği, elipsoit yüksekliği, gravite anomalisi gibi büyüklüklerle çalışılmıştır. Çalışmada, test bölgelerindeki verilerin, bu veriler yardımıyla üretilen sayısal arazi modelinin doğruluğunu nasıl etkilediği incelenmiş ve interpolasyona yönelik öneriler ortaya konmuştur.

Digital Terrain Model (DTM) has become almost a standard product in planning, production phases of mapping, surveying, civil engineering and many other disciplines. DTM can be defined simply as the digital representation of the terrain relief. In other words, DTM is an array of numbers that represent the spatial distribution of a set of properties of the topography. Although the abbreviation DTM includes in itself the word terrain, it represents today not only the topography as can be seen clearly, but also other entities such as gravity, gravity anomaly, gravity disturbance, temperature, pressure, magnetic field, etc., which can not be tangible to human beings. Today, almost all disciplines are in a way obliged to represent digitally the quantities, entities which are of concern to themselves. Therefore, the term DTM is generally followed by a short explanation defining the type of the entity being used. As DTM is utilized by a great number of disciplines, there exist different terms used to define numerical representation of the terrain, such as Digital Elevation Model (DEM), Digital Height Model (DHM), Digital Terrain Elevation Data (DTED), Digital Terrain Elevation Model (DTEM), Digital Ground Model (DGM). In addition to these terms, as DTM can be utilized to model also the surfaces other than terrain, the term Digital Surface Model (DSM) can also be addressed. The term DTM was for the first time used in 1950s by Prof. Charles L.Miller for the digital representation of the topography along which a highway construction was underway, and since then it has been used extensively by all professionals who are in this way or another closely related to surveying, civil engineering or other engineering branches that make use of terrain. Thus, DTM has been a subject of interest to mainly all professionals using computers that nowadays constitute the first and fundamental media to solve almost all kinds of scientific problems. The dramatic development in computer technology has widened the need and use of DTMs. High-speed computers with memories large enough to overcome huge numerical problems made it quite easy for engineers to plan, design and produce a good amount of work in a much shorter period. In this way, it became possible to store and manipulate a huge bulk of data in computers in a few minutes which previously took days and months when problems were solved manually without using computers. As defined before, DTM is the digital representation of the topography. However, nowadays, some scientists assume that the term DTM may be regarded as a model that includes also the techniques, software and methods as well as the coordinates of the points that constitute DTM (Figure 1). Figure 1. DTM Components The dotted part of Figure 1 indicates the new approach which is today accepted by some scientists. The numerical representation of the surface means that the three dimensional coordinates of the points that define the terrain are known to users. The coordinates may well be referenced either to a right hand rectangular coordinate system with the axis x, y, z which are all perpendicular to each other, or to ellipsoidal coordinates, or to another user-defined coordinate system. DTMs can be utilized to derive a wealth of information about the morphology of a land surface. It can be used in all areas where it is necessary to create, modify and display the surface in 3 dimension. The developments in hardware and software engineering have widened the use of DTMs in almost every field connected to surface. These fields can range from surveying, mapping where terrain is the main subject of production, to Geographical Information System (GIS), all earth-sciences like geology, magnetism, gravity field, civil-engineering, military applications, earthquake predictions, etc. The basic input data for the DTM surface specification are the coordinates of the surveyed (or otherwise determined) points which are usually randomly scattered (Figure 2). Figure 2. Randomly scattered data The position information for these points are collected via conventional surveying techniques, photogrammetric sampling using aerial photos or satellite images, or graphical methods by digitizing the existing maps. XI From randomly positioned data, height interpolation is carried out at certain grid points which are apart from each other with a fixed distance called grid interval (Figure 3). Figure 3. GriddedData Interpolation in DTMs is still one of the main concerns to users. There can be seen countless methods developed to construct DTM from sampling points. Still, quite a many scientists are trying to explore a new, untouched interpolation method which can well suit all kinds of terrain and meet the requirements of users. However, it is proved that any one of the methods that can be seen as the best solution for a problem may be found to be meaningless for another type of problem. This is why the number of prediction methods is still increasing continuously. All of the engineers who, in a way, are involved in DTM application agree that a unique prediction method that is acceptable to all contidions is not available. Therefore, different methods are offered for different type of surfaces. In this study, though the main area of interest is not the development or investigation of different prediction methods, three interplation methods are included in the software SAM prepared by the writer. These are;. Weighted Average,. Least Squares Prediction,. Multiquadric Equation In the weighted average method, the observation or sampling point is assigned a weight which is usully inversely proportional to the distance between itself and the prediction point. Equation (1) describes clearly the structure of the interpolation via weighted averages, ZWA *,= /=i /=1 i = !,...,« (1) where the distance d and the weight w are calculated as below; d = ,[ (Xj -xf +(yj -yf +Ö f2 =h (5) where the terrain is assumed to be the sum of paraboloid series. The constant 8 is taken arbitrarily. Apart from the prediction methods, there exist different modelling techniques, no matter what the prediction method is being applied. This study utilizes three different techniques;. Global,. Piecewise. Pointwise While producing digital terrain model, one may consider all sampling points and make the prediction globally only in one run. This is called global modelling. However, the structure of the terrain or the number of points may force the user to divide the whole area into sub-regions for ease of study. This approach is named as piecewise modelling. Another situation occur when one decides to use only a definite number within a fixed radius around the sampling point. In this case, each prediction point is computed by using different sets of sampling points, that is, pointwise. As shown also in this study, these techniques should be carefully considered. Xlll One of the drawbacks of the softwares producing digital terrain models is that all sampling points are compared with the prediction points. This is rather time consuming. In this study, a simple algorithm has been tried in order to save visiting all sampling points. As for the topography or any other surface, the density and the number of the available sampling points within the specified area, the coincidence of the locations at characteristic points of the terrain are all effective parameters on the digital terrain models. However, most of the time, most of the collected data are observed without the knowledge of the specialists who will handle the data. In any case, people who are engaged in digital terrain modelling are expected to create miracle and to produce a digital terrain model that meets all requirements of the users. Unfortunately, no predicted value can be better then its real value. Of course, there may be sometimes a chance to test the quality or the accuracy of the predicted value when there is a test data in hand. It is the only real occasion when the accuracy of the predicted value is valued in a realistic way. However, there is an inevitable need to derive some parameters that will give an idea of what is predicted, what the precision or accuracy is. Among the surfaces that await prediction, the topography is the most difficult one that can not be modelled ultimately. The solutions for other surfaces may be valid for all cases, this is not the case for the terrain itself. This study aims to make some offers for the test areas included here.