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The Future of Vertical Geodetic Control

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The Future of Vertical Geodetic Control 1 The Future of Vertical Geodetic Control G. Steinberg H. Papo Survey of Israel Technion, Israel Institute of Technology Abstract The phenomenal progress made by motorized leveling in the past two decades has not changed the status of vertical geodetic control (VGC) worldwide. Only a few countries have been able to establish and to maintain (re-observe at reasonably short time intervals) their national VGC networks at first order accuracies. The establishment of a national VGC network by precise leveling has been indeed a technical possibility for many years and for some countries it has been even economically affordable. We claim that today those national VGC networks are not indispensable. Due to their many drawbacks such as high cost, slow pace, obstacle-crossing impotence and monumentation problems, we believe that they are going to be replaced in the near future by a more attractive alternative. The alternative we envision is a national VGC network based on GPS measurements which forms an integral part of a 3-D spatial network. The reference surface is the WGS84 (or any future equivalent) ellipsoid and thus the system of heights is ellipsoidal and not orthometric. We believe that the switch from orthometric (OVGC) to ellipsoidal (EVGC) height systems at the national (or at the continental or even at the worldwide) level is imminent and inevitable. OVGC networks may continue to be used in the future but that only in the form of floating islands with a limited geographical extent. Viable candidates for such orthometric islands are regions and projects where the use of orthometric heights remains mandatory. There are cases where the island can be ellipsoidal in character or in other words form a densification layer beneath the national EVGC network. Typical examples of such orthometric or ellipsoidal islands are urban areas, low-shore areas, sensitive water system projects etc. Each island maintains its own independent datum based on those points through which it is attached to the national EVGC network. In Israel we are already experimenting with the above flexible scheme of vertical control. The national EGVC network is composed of two layers: a primary layer of ten permanent GPS stations at distances of 30-90 kilometers and a secondary layer of 150 extremely well monumented points (the G1 geodynamic network) at distances of 10-20 km. Four orthometric islands based on the above secondary layer are at various stages of construction: The Mediterranean island: a narrow strip of land along the coast covering an area of 2000 km2; The Mount Carmel island: with 67 points over an area of 600 km2; 2 The City of Eilat island: by the coast of The Red Sea with 20 points over an area of 20 km2; The City of Modyin island: and its environs (still in the early stages of planning). 1. Introduction Over the years geodesy has been, and still is, very proud of its precise leveling technique that can produce elevation differences between distant points on the earth surface with an unsurpassed accuracy of fractions of a millimeter. The problem with leveling has never been its accuracy. The main problem associated with leveling is the technique itself which is notoriously time consuming, too expensive in terms of manpower and extremely cumbersome in having to cover literally step by step the distance between the end points. Motorized leveling has solved the slow-rate problem but the price remains prohibitively high, and still lengthy meandering is needed in order to cross mountains, wide rives or lakes. On top of the above problems related to the leveling technique, vertical crustal motions literally “slap us in the face” by rendering obsolete the heights of many points only a short time after their measurement and adjustment (see [3] as an example for difficulties in interpreting results of precise leveling). Vis-a-vis leveling, GPS as a geodetic tool has been advancing in the past 10 or 15 years by leaps and bounds. In terms of accuracy its progress has been impressive although in the vertical direction it is still at the mercy of chronic poor-geometry, insufficiently well resolved tropospheric delays, multipath and antenna focus variations. For the time being GPS can not compete with precise leveling as far as accuracy is concerned. But in all other respects it is a sure winner: it is fast, cheap, can easily bypass almost any obstacle. It only remains to see GPS make a significant improvement of accuracy in the “up” direction too. There is one additional problem which concerns not so much us - geodesists and surveyors - but rather the so called “consumers of heights”. Even if the ellipsoidal (GPS borne) heights were ten times more accurate, there are going to be users who would prefer the "good, old..." and familiar orthometric heights. "Sensitivity to transition" analyses of applicability of the ellipsoidal heights in various scientific and engineering enterprises have been made and published (see [1]). The bottom line has being that although the transition is not going to be easy, in the majority of cases it would be possible and even advantageous to use ellipsoidal (geometric) heights instead of ordinary orthometric (physical) heights. In this paper we are dealing not so much with the above "non-geodetic" problem but rather with the establishment of a novel and unorthodox system of vertical geodetic control. Miracles that were apparently commonplace in biblical times don’t happen any more. The inevitable transition from orthometric to ellipsoidal vertical control systems is just one such miracle which requires lots of work and patience from all those involved - geodesists as well as 3 their "customers" the consumers of heights (see [7]). In the next section we present schematically our vision of that future national ellipsoidal vertical geodetic control that will be based on GPS measurements alone. 2. The ellipsoidal alternative As an alternative to the existing national orthometric vertical control (NOVC) networks we propose to declare the ellipsoid (the WGS84 ellipsoid or any suitable equivalent) as the only reference surface needed to define the position of a control point in all 3 dimensions, including heights (above the ellipsoidal surface). The realization of a comprehensive and accurate ellipsoidal vertical geodetic control (EVGC) network based on GPS measurements does constitute an integral part of a 3-D spatial control network of any given country. As we all know, the above is not a vision anymore. GPS measurements backed up by the IGS permanent stations array have reached a level that makes it possible for any country to establish a nationwide GPS-borne 3-D geodetic control network. The time required for surveying and subsequent analysis is short and the cost is unbelievably low. As with the conventional horizontal and vertical control networks there is an advantage in constructing the EVGC net in a hierarchical order. Monumentation subtleties, optimal distances between points, types of GPS receivers and antennae, software sophistication, duration of measurement sessions - all have to be designed and coordinated in view of the well known principle of going “from the whole to the part”. A typical national EVGC network should consist of three to four control layers as follows: (a) The fundamental primary (datum) layer consists of points at distances of 100-250 km. Most or even all of those points should be permanent GPS stations. The datum of the fundamental layer should be based on fixed (nominal) ellipsoidal heights of those points. If kinematic or dynamic models of analysis are adopted, datum definition may become more complicated but still it is an easily manageable problem. Accuracy of the adjusted heights should be of the order of 6-8 mm. (b) The secondary layer consists of points 25-40 km apart, where relative accuracies in height are better than 1 cm. Location and monumentation of its points should be based on geometrical and geo-technical considerations. The first two layers are not intended for the occasional user but are there to provide control for lower level (densification) layers. (c) The third layer should consist of points at 6-10 km apart with relative accuracies still at the level of 1 cm. Due to the significantly shorter GPS vectors, a vertical accuracy of 1 cm can be obtained by relatively short GPS measurement sessions. Another characteristic that is 4 particularly important for the third layer of control is easy accessibility. An option that should be considered is to collocate between third layer control points and existing conventional vertical control points (particularly well monumented benchmarks). Whenever considered necessary, a lower (forth) layer of vertical control can be constructed to serve the specific needs for vertical control of a municipal area or that of a large industrial complex. Our proposal provides also a solution for height users who insist on having a forth layer of vertical control where heights are, however orthometric and not ellipsoidal. Such a mix- up is possible provided the boundaries of the "orthometric island" (OI) are clearly outlined and measurements and their processing are performed in a clear and consistent manner as proposed in the next section of this paper. Mixing physical (orthometric heights) and geometric (ellipsoidal heights) entities is not a new idea in Geodesy. In pre-1957 times (the first “sputnik” was put in orbit in 1957) national horizontal geodetic control networks were attached to the physical body of the earth by means of astronomical (physical) observations. In our vertical OI analogy each island will have its own independent datum - just as was the case in the past when each country had its own geodetic datum. 3. Orthometric islands Orthometric islands should be regarded as a temporary measure. They are intended to soften the shock of transition from the current orthometric heights system to the future ellipsoidal system.
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