Leveling
Differential Leveling: Height of Instrument Method
Summary
Differential leveling measures height differences by reading a staff on a known point (backsight) and on the next point (foresight). The height of instrument is the known elevation plus the backsight; each new elevation is that height minus the foresight. A run between two benchmarks is checked with ΣBS − ΣFS and its misclosure is distributed in proportion to distance.
Definition
Differential leveling: determining the height difference between points from horizontal sight readings on vertical staffs.
- HI = Elev + BS
- Elev = HI − FS
- Check: ΣBS − ΣFS = ΔH
- Allowance ≈ C·√K mm (K in km)
Height of instrument method
Turning points (TP) carry the height forward: each TP receives a foresight from one setup and a backsight from the next.
Misclosure and allowance
Closing on a second benchmark gives the misclosure = observed − known. Allowances are usually C·√K millimetres, with K the run length in kilometres and C depending on order, for example about 4 mm to 12 mm. Use your specification.
Adjustment
For a single run, distribute the misclosure in proportion to the cumulative distance (or number of setups) to each point. For networks of runs, use least squares weighted by 1/distance.
Good practice
- Balance backsight and foresight distances to cancel collimation and curvature errors.
- Keep sights short in heat shimmer.
- Use a change plate and keep the staff vertical.
- Run two-way (forward and back) for control.
Worked example
Leveling from BM1 (100.000 m) to BM2 (known 101.250 m):
| Point | BS | HI | FS | Elevation |
|---|---|---|---|---|
| BM1 | 1.523 | 101.523 | 100.000 | |
| TP1 | 2.104 | 102.640 | 0.987 | 100.536 |
| TP2 | 1.876 | 103.174 | 1.342 | 101.298 |
| BM2 | 1.928 | 101.246 |
| Point | Cum. distance (m) | Observed | Correction | Adjusted |
|---|---|---|---|---|
| BM1 | 0 | 100.000 | +0.0000 | 100.000 |
| TP1 | 120 | 100.536 | +0.0013 | 100.537 |
| TP2 | 255 | 101.298 | +0.0028 | 101.301 |
| BM2 | 365 | 101.246 | +0.0040 | 101.250 |
Step by step
- Set up. Set up midway between the benchmark and the first turning point.
- Backsight. Read the staff on the benchmark; compute HI.
- Foresight. Read the staff on the turning point; compute its elevation.
- Move forward. Move the instrument; backsight the same turning point.
- Close. Finish on a known benchmark and compute the misclosure.
- Check and adjust. Verify ΣBS − ΣFS, compare with allowance, distribute the misclosure.
FAQ
Why balance sight lengths?
Equal backsight and foresight distances cancel the effect of a tilted line of sight (collimation error) and most of the curvature and refraction effect.
What is a turning point?
A temporary, stable point on which the staff is held for a foresight from one setup and a backsight from the next.
Can GNSS replace leveling?
GNSS gives ellipsoidal heights. Converting to orthometric heights needs a geoid model, and the result is usually less precise than careful leveling over short distances.
Related tools and articles
Tools
- Field Visit SurveyRecord and check field observations.
- Survey CalculatorsInverse, area, intersection, resection and more.
Articles
- BenchmarksReference topic
- Survey ErrorsReference topic
- Vertical CRSReference topic
- Least Squares Adjustment for SurveyorsLeast squares adjustment finds the coordinates that minimize the weighted sum of squared observation residuals…
References
- NOAA National Geodetic Survey. Geodetic Leveling, NOAA Manual NOS NGS 3, 1981.
- Ghilani, C. D. & Wolf, P. R. Elementary Surveying: An Introduction to Geomatics, 15th ed., Pearson, 2018 (traverse computations and adjustments).
- Uren, J. & Price, W. F. Surveying for Engineers, 5th ed., Palgrave Macmillan, 2010.
Cite this page
GeoCAD Bridge. “Differential Leveling: Height of Instrument Method.” GeoCAD Bridge Knowledge Center, updated 2026-10-05. https://www.geocadbridge.com/knowledge/survey-leveling/