$ 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.csv one row per site (22 rows)
- field_observations.csv per-station observations (220 rows, 10 per site)
- source.xlsx combined 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.