Methods of Topographic Survey

What Is a Grid?
A surveying and mapping grid is a plane, rectangular mathematical matrix, usually oriented to the cardinal direction of north. A grid conforms to the curved surface of the earth, the geoid, usually at sea-level elevation. Thus, geodetic surveying, which takes into account the earth's curvature, is not required for working on a plane coordinate grid. A grid is anchored to the ground through survey monuments that are set in the ground and surveyed through conventional Weld survey techniques. Northing and easting values are arbitrarily assigned to a beginning control point, or they are derived from previously calculated and published tables for particular conformal mapping projections. The two most commonly used grids are the Lambert and the transverse Mercator. These grids, as projected onto the geoidal shape of the earth, comprise zones that are limited in west/east and south/north extent and that render the best plane surveying values.    
Azimuth orientation of a grid is usually accomplished by occupying the control point of origin with a surveying instrument and making repeat angular observations between a circumpolar star, such as Polaris, and a second monumented control point. Thus the derived azimuth is the basis for establishment of true north for the grid.    
The Theban Mapping Project Grid
Eight sets of observations of Polaris were completed on the evening of 16 June, 1978 with the theodolite occupying traverse point 14 and turning angular directions from Polaris to traverse point 15. However, it was decided to adopt the monumental axis of Karnak Temple as a "true" west/east azimuth (90 degrees clockwise from north). The result is that the TMP Grid is oriented 27 degrees, 02 minutes, and 23 seconds clockwise from true north.    
Traverse point 1 was arbitrarily assigned the values of North 100,000 meters and East 100,000 meters. These values were adopted to assure that negatives values would not enter into the grid. In addition, the Theban Necropolis was a considerable distance westerly, so there would not be any problem with confusing a northing value with one of easting, or vice versa.    
The Control Traverse
Traverse point 2 on the Karnak Temple baseline was first occupied by the theodolite. From there the survey began with a backsight on traverse point 1, which was around 400 meters easterly along the temple baseline and in the heart of the temple. Subsequently, measurements of distance and direction (angular - both horizontal and vertical) were made across the Nile, around the Valley of Kings, and back to the two points of beginning. This resulted in a 27-course (two more courses than desired), closed-loop traverse that was 13,809 meters long [17818].     17818
After the initial traverse was completed, control points were established in the Valley of the Kings. These were then used to set out further control points at the entrances of all visible tombs, to be used in the surveys of the tombs themselves [17819].     17819
Measurements of Control Traverse
Distances of each course were measured with a Wild DI-10 Distomat, which had a range of plus or minus 1,000 meters, depending on atmospheric conditions and the number of reflector prisms used for a single measurement. The DI-10 used invisible infrared lightwave propagation to a distant precise reflector and thence back to the DI-10's receiver and processor module. Nominal accuracy was one centimeter. All lines measured were on a slope from the transmitter at the theodolite to the reflector. The longest course, necessitated by the terrain and Welds of sugar cane, was 800 meters. A check line of 1200 meters was measured across the middle of the closed loop.    
In addition to measurements of horizontal directions, zenith angles were made along each course. These values were used in converting slope distances to horizontal values and in computing differences in elevation between the occupied station and the station being sighted. These horizontal values were further reduced to sea-level elevation, the datum where all coordinate values were calculated.    
Standards of Accuracy Used
A standard of accuracy requires concomitant Weld procedures, which were followed as rigorously as possible under conditions imposed by weather and personnel. To assure adequate and proper control for mapping topographical and planimetric features, such as tombs and temples, the standards adopted were second-order (modified):    
  • Number of courses between azimuth checks: 25 or less.
  • Azimuth closure not to exceed 3 sec/station.
  • Position closure after azimuth adjustment: 1:10,000.
  • Distance measurement accurate within 1:15,000.
  • Minimum distance to be measured with DI-10: 200 m.
  • Minimum number of direction observations with a one-second theodolite: 4 positions of circle.
  • Differential leveling-loop closure not to exceed 0.008 m multiplied by the square root of the loop length in km.
    Traverse Closure
    The total length of the 27-course control traverse was 13,809 meters. Azimuth closure approximated 1.5 seconds per angle, or direction, measured. This error of closure yielded an accuracy of 1:65,000. This closure easily met our second-order (modified) standard. Such accuracy is more than adequate for ground control of aerial photography and for archaeological Weld mapping. All calculations and adjustments were made and adjusted as required by the use of a Hewlett Packard HP-97 with an HP surveying program card.    
    Vertical Control
    Basis of Control
    Three bench marks were recovered from the 1920s Survey of Egypt, proved for agreement, and adopted for elevation control. One of the three bench marks is only a couple of hundred meters from the house of Howard Carter. Another is embedded in the side of an alabaster factory in al Qurna.    
    Vertical Measurements
    Elevations were determined by differential leveling and by trigonometric resolution of slope-distance measurements and zenith angles. Three-wire differential levels were run with a pendulum level. Each line was run ahead and back to form individual closed loops between each succeeding pair of turning points. In areas of marked relief, differences in elevation between traverse points were determined solely by trigonometric means.    
    Level rods were made from matched pairs of five-meter pocket tapes, which were affixed to wooden staffs. The four-meter level-rod staffs were made of wood that is similar to fir. Rod bubbles were essential for plumbing the rods in the typical desert winds. On two occasions, we were blown out by the force of the khamsin winds of late April. Iron livestock tether pins were used as turning pins and PK nails were used for "permanent" TPs.    
    All lines, both differential and trigonometric, were closed either in loops or upon other lines. The differential lines closed at second-order accuracies and the trigonometric lines closed within third-order values.    
    (Abridged and adapted from "Methods of Topographical Survey" by David A Goodman; first published in Atlas of the Valley of the Kings, edited by Kent R. Weeks.)    

    Published or last modified on: May 15, 2003
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