Geodesy and Coordinate Systems
This domain tests datums, projections, heights, and the grid-to-ground problem. Expect questions on NAD83 realizations, the California Coordinate System, scale and elevation factors, geoid models, and GNSS positioning.
Core rules
- NAD83 and its realizations, such as NAD83(2011), are the horizontal datum for California; NAD27 is legacy. NATRF2022 is replacing NAD83.
- Ellipsoid height h and orthometric height H differ by geoid separation N: H = h - N.
- The California Coordinate System 1983 uses six Lambert Conformal Conic zones. Scale factor varies with position, and convergence is the angle between grid north and true north.
- Grid distance equals ground distance times the combined factor. Combined factor equals scale factor times elevation factor.
- Elevation factor is approximately R/(R + H), where R is the Earth radius and H is the height above the ellipsoid.
- To go from grid to ground, divide by the combined factor.
Worked example
A ground distance is 1,000.000 ft. The scale factor is 0.99995, the elevation is 500 ft, and R is 20,906,000 ft. Elevation factor = 20,906,000 / 20,906,500 = 0.999976. Combined factor = 0.99995 x 0.999976 = 0.999926. Grid distance = 1,000.000 x 0.999926 = 999.926 ft. Dividing 999.926 by 0.999926 returns 1,000.000 ft.
Traps
- Applying scale factor but forgetting elevation factor.
- Using orthometric height where ellipsoid height is required.
- Mixing datum realizations or epochs.
- Reversing the convergence sign.
- Setting out grid distances as ground distances in construction.