The Carolina Bays are shallow elliptical depressions on unconsolidated soil that originated as penetration funnels from secondary impacts of glacier ice boulders ejected by an extraterrestrial impact on the Laurentide Ice Sheet (Zamora, 2017). Since the Carolina Bays are conic sections, it is often necessary to fit them with ellipses.

LiDAR image of Carolina Bays near Bowmore, NC. Three bays have been fitted with ellipses.

In many cases, it is possible to fit the ellipses by observation and trial-and-error, but it is desirable to be able to fit the ellipses by identifying points along the perimeter and using a least squares method to fit the ellipses[5]. Ben Hammel and Nick Sullivan-Molina [2] have developed a Python routine for least squares fitting of an ellipse based on a publication of Halir and Flusser[3]. The program **ellipse.py** from the Github package had to be modified to output the coefficients of the polynomial for the ellipse.

I created a program called **CBellipse.py** to read a file of latitude/longitude pairs as listed in GitHub. The coordinates were changed to meters relative to the southmost and westmost positions so that the ellipse would be in the first quadrant. The procedure for converting the coordinates to meters recognizes that one degree of latitude is equal to 10,000,000 meters/90 degrees or 111,111 meters/degree. The distance in meters between degrees of longitude depends on the latitude. The program uses the cosine of the minimum latitude in the coordinate pairs and multiplies by 111,111.

LiDAR image of the Tulsa Basin. The coordinates of the rim are given in the next image.

**The Tulsa Basin.** An elliptical basin found using LiDAR images near the Oxley Nature Center in Tulsa, Oklahoma has led to a surprising archaeological discovery. The lines carved on the west side of the Tulsa Basin are aligned with the sunrise during the solstices and the equinoxes. The Tulsa Basin is probably the best ancient solar observatory in the United States.

Results of processing the coordinate pairs of the Tulsa Basin

LiDAR image of Carolina Bays near Bowmore, NC.

The LiDAR visualization tool by Michael Davias [4] integrates with Google Earth and makes it possible to position the crosshairs of a pushpin along the rim of the bay in order to display a panel from which the coordinates for the latitude and longitude may be copied.

Results of processing the coordinate pairs of a Carolina Bay near Bowmore, NC

A second program called **driver2d.py** performs the functions of **CBellipse.py**, but it adds the capability of entering x,y coordinates from a digitized image instead of latitude and longitude by specifying *2D as a comment at the beginning of the data file.

The ellipse may be overlaid on the original image using PowerPoint or an image editor.

- Origin of the Carolina Bays
- Elliptical Shape of the Carolina Bays
- W.F. Prouty - Ellipticity of the Carolina Bays
- Carolina Bay Deformations
- The Nebraska Rainwater Basins
- Geological Exploration of the Carolina Bays
- Estimate of the water ejected by an extraterrestrial impact
- The Carolina Bays as evidence of a cosmic impact

YouTube video: The Carolina Bays as evidence of a cosmic impact. (44 minutes)

- A. Zamora, A model for the geomorphology of the Carolina Bays, Geomorphology, 282, 209–216. (2017), DOI 10.1016/j.geomorph.2017.01.019 https://doi.org/10.1016/j.geomorph.2017.01.019
- Ben Hammel, & Nick Sullivan-Molina. (2020, March 21). bdhammel/least-squares-ellipse-fitting: v2.0.0 (Version v2.0.0). Zenodo. http://doi.org/10.5281/zenodo.3723294
- Least Squares fitting of ellipses, python routine based on the publication Halir, R., Flusser, J.: 'Numerically Stable Direct Least Squares Fitting of Ellipses' https://github.com/bdhammel/least-squares-ellipse-fitting/tree/v2.0.0
- LiDAR Visualization Tool for Google Earth by Michael Davias. https://ovoidbasinsurvey.cintos.org/
- Python program for fitting ellipses to the Carolina Bays by the least squares method. Source code and documentation: https://github.com/citpeks/Carolina-Bays-least-squares-ellipse-fitting

© Copyright - Antonio Zamora