$ geodetic-curvature
A 2024 field campaign measuring the angular divergence of the local vertical across 22 survey sites in 4 U.S. states. Each site occupied a 1000 m baseline with measurements at 100 m intervals; the table below is the per-site summary, and the full per-station observations are linked at the bottom.
campaign G-CURV-2024-B·2024-06-10 → 2024-09-19·4 instruments·7 observers
### what's being measured
For a 1000 m horizontal baseline, the angle subtended at the Earth's center, equivalently, the angular difference between the local verticals at the two endpoints, is 32.3756″(arc length ÷ Earth radius). On a flat surface this number would be zero. Any deviation from 32.3756″ shows up in the residual column.
At each station along the baseline the crew recorded three independent sightings of a level reference plus temperature, pressure, and humidity (atmospheric refraction is the main correctable error source at this scale). The mean of the three sightings is the empirical value; the residual is empirical − theoretical.
### result
The empirical mean across all sites lands within 0.010″of the theoretical 32.3756″, with an RMS scatter of 0.513″, consistent with instrument precision rather than any systematic bias. The largest single-site deviation is 1.257″ (~1 part in 30 of the expected signal).
### residual distribution
residual = empirical − theoretical (arcseconds).
### site summary
| site | locality | date | empirical (″) | residual (″) | instrument |
|---|---|---|---|---|---|
| WI-MSN-01 | Madison, WI | 2024-07-27 | 32.8833 | +0.5077 | Trimble S9 |
| WI-MKE-01 | Milwaukee, WI | 2024-06-10 | 32.0424 | -0.3332 | Sokkia GP1 |
| WI-GRB-01 | Green Bay, WI | 2024-08-27 | 32.3934 | +0.0178 | ZNT Custom Cam |
| WI-EAU-01 | Eau Claire, WI | 2024-06-27 | 31.8911 | -0.4845 | Leica TM6100A |
| MN-MSP-01 | Minneapolis, MN | 2024-06-19 | 33.0362 | +0.6606 | ZNT Custom Cam |
| MN-STP-01 | Saint Paul, MN | 2024-06-28 | 32.6538 | +0.2782 | Sokkia GP1 |
| MN-DUL-01 | Duluth, MN | 2024-06-12 | 31.8080 | -0.5676 | Trimble S9 |
| MN-RCH-01 | Rochester, MN | 2024-08-12 | 32.1440 | -0.2316 | ZNT Custom Cam |
| NY-NYC-01 | New York, NY | 2024-08-04 | 32.0331 | -0.3425 | Sokkia GP1 |
| NY-BUF-01 | Buffalo, NY | 2024-09-04 | 32.4596 | +0.0840 | Trimble S9 |
| NY-ROC-01 | Rochester, NY | 2024-08-25 | 32.5002 | +0.1246 | Sokkia GP1 |
| NY-ALB-01 | Albany, NY | 2024-06-18 | 32.8324 | +0.4568 | Leica TM6100A |
| CA-LAX-01 | Los Angeles, CA | 2024-08-05 | 32.7078 | +0.3322 | Sokkia GP1 |
| CA-SFO-01 | San Francisco, CA | 2024-07-02 | 31.3067 | -1.0689 | Sokkia GP1 |
| CA-SAN-01 | San Diego, CA | 2024-06-16 | 31.8233 | -0.5523 | Leica TM6100A |
| CA-SAC-01 | Sacramento, CA | 2024-09-19 | 32.6065 | +0.2309 | ZNT Custom Cam |
| WI-LAC-01 | La Crosse, WI | 2024-09-05 | 33.6328 | +1.2572 | Leica TM6100A |
| WI-OSH-01 | Oshkosh, WI | 2024-06-21 | 32.3294 | -0.0462 | Trimble S9 |
| MN-SCD-01 | St. Cloud, MN | 2024-07-03 | 32.3757 | +0.0001 | ZNT Custom Cam |
| MN-MAN-01 | Mankato, MN | 2024-09-08 | 32.6589 | +0.2833 | Trimble S9 |
| NY-SYR-01 | Syracuse, NY | 2024-09-13 | 32.3789 | +0.0033 | ZNT Custom Cam |
| CA-SJX-01 | San Jose, CA | 2024-09-03 | 31.5489 | -0.8267 | Trimble S9 |
### data
- site_summary.csvone row per site (22 rows)
- field_observations.csvper-station observations (220 rows, 10 per site)
- source.xlsxcombined workbook
### notes
- - Geoid references vary by site (NAVD88, EGM2008, GEOID18); the divergence value is a tangent-vector angle so it doesn't depend on which vertical datum is used.
- - Baseline azimuths were rotated between sites to avoid any systematic alignment with prevailing wind or refraction gradients.
- - Field stations flagged REVIEW in the observations CSV were re-checked but retained in the per-site mean.
- - 4 instrument models were used across the campaign (Trimble S9, Sokkia GP1, ZNT Custom Cam, Leica TM6100A) to guard against per-instrument bias.