Measurement and Geodesy
This domain tests the relationships among the ellipsoid, the geoid, and vertical datums, plus the correction logic behind leveling and electronic distance measurement. Expect questions on height systems, curvature and refraction, EDM constants, and how accuracy is expressed in standards.
Heights and reference surfaces
- Orthometric height H, ellipsoid height h, and geoid undulation N are related by H = h - N. GNSS gives h; converting to a NAVD 88-type orthometric height requires a geoid model and a datum transformation.
- NAD83 is a horizontal datum referenced to the GRS80 ellipsoid; NAVD 88 is a vertical datum of orthometric heights.
- Deflection of the vertical is the angle between the ellipsoid normal and the gravity vertical. It affects astronomic azimuths and long plumb-line reductions, and it is why the geoid is not a level surface everywhere.
- Published heights change when networks are readjusted, when a new geoid model is adopted, or when land subsidence is measured.
Leveling and distance measurement
- Differential leveling reduces random error when sight lengths are balanced: curvature, refraction, and collimation errors cancel between equal back and forward sights.
- Combined curvature and refraction correction: C and R = 0.0206 times D squared with D in thousands of feet (feet); in metric, 0.0675 times K squared with K in kilometers (meters).
- EDM work must account for prism constant, additive constant, meteorological correction (temperature, pressure, humidity), instrument scale, and reduction of slope distance to horizontal and to the ellipsoid.
- Precision is repeatability (small standard deviation); accuracy is closeness to the true value. A network accuracy stated at 95 percent confidence is not the same as an instrument's repeatability.
Worked example
A GNSS observation gives an ellipsoid height h of 250.00 m at a monument where the geoid model gives N = -32.00 m. Then H = h - N = 250.00 - (-32.00) = 282.00 m. The negative undulation means the geoid lies about 32 m below the ellipsoid at that location, so the orthometric height is larger than the ellipsoid height. Sign discipline matters: a wrong sign produces a 64 m blunder that looks like a legitimate number.
Traps that cost marks
Adding N instead of subtracting it; applying a curvature and refraction correction to a balanced level run where it cancels; leaving an EDM slope distance unreduced; ignoring an instrument-to-prism constant mismatch; quoting a repeatability figure as the accuracy of a coordinate; mixing a geoid model built for one vertical datum with a height from another.