Bolivia Salt Flat is not Flat

Monday, November 29, 2021 - 01:49 | Author: wabis | Topics: FlatEarth, Geodesy, Analysis
The Bolivia Salt Flat appears flat as far as we can see. So Flat Earther use this as proof that the earth is flat. Using UNAVCO GPS reference stations I can prove that the Bolivia Salt Flat curves exactly as predicted by the WGS84 Globe Model. It's not flat at all.

UNAVCO Reference Stations

Stations Bolivia Salt Flat

UNAVCO is a non-profit university-governed consortium that facilitates geoscience research and education using Geodesy and supports geoscience research around the world.

The UNAVCO GAGE Facility manages a community pool of high accuracy portable GPS/GNSS receiver systems that can be used for a range of applications. These complete systems – receivers, antennas, mounts, power and optional communications – can be deployed for days in episodic campaigns or for many months long-term investigations. Systems are also available for precision mapping applications.

This GPS/GNSS reference stations provide their location to sub cm accuracy in Earth Centered Earth Fixed (ECEF) cartesian coordinates. We can use the 3D positions of this stations to measure the curvature drop, or lack of, to find out whether the Salt Flat are as flat as they look, or curve according to the Globe Model.

The reference station AMDE is located on the Isla Incahuasi in the middle of the Bolivian Salt Flat. Three more stations, BDJC, BMWS and BLOV, are located around the Salt Flat, see Image.

Reference Station Data

The GPS locations of the following UNAVCO reference stations can be viewed and analyzed in my App Display Geo Data or downloaded in CSV format  2021-11-29 UNAVCO Reference Stations.zip .

Station X Y Z Lat/Long H ΔH
AMDE 2280008.627 -5539233.901 -2194098.501 -20.24161900  -67.62740400 3715.800 0.000
BDJC 2315256.507 -5569563.551 -2078385.509 -19.13178800  -67.42744100 3808.800 +93.000
BMWS 2234836.279 -5523178.606 -2278862.673 -21.05930135  -67.97033375 3727.091 +11.291
BLOV 2225593.314 -5577206.54 -2153730.805 -19.85361900  -68.24544900 3735.600 +19.800

All values except Lat/Long are given in meters.

UNAVCO Station AMDE
UNAVCO Station BDJC
UNAVCO Station BMWS
UNAVCO Station BLOV

Lat/Long are calculated from the X,Y,Z coordinates using the WGS84 globe model. They are not used for any of the following calculations. They are only provided to find the locations on any map. You can copy the values in the Lat/Long field and paste it in Google Earth to find the corresponding location.

How to find the Shape of the Earth

X,Y,Z and Lat,Long,H describe exactly the same location in 3D space in 2 different coordinate systems. If the earth is flat, than all locations lie on a flat plane in 3D space, no matter which coordinate system we use. If the earth is a globe, the locations lie all on the surface of a spheroid in any coordinate system. So we can use the 3D X,Y,Z coordinates to find out the shape the points lie on.

Using the X,Y,Z coordinates and vector algebra we can calculate the drop of the stations around the Salt Flat with respect to the station AMDE in the center of the Salt Flat. If the earth is flat then the calcultions will show no drop between the stations. If the earth is a globe, then the drop must match the prediction of the globe model. So lets see what the data leads to.

Drop Measurements and Calculations

The following table shows the drop calculations from the Station AMDE in the middle of the Salt Flat to the other 3 stations:

Station Azim Dist Chord Dist Surf REll REll+H Drop GPS Drop-ΔH Drop Pred ΔDrop ΔDrop%
BDJC 9.72° 124705.71 124707.72 6344128.34 6347844.14 1132.02 1225.02 1224.94 0.08 0.007%
BMWS 201.48° 97382.06 97383.01 6348083.11 6351798.91 735.19 746.48 746.50 -0.02 -0.003%
BLOV 304.49° 77669.01 77669.49 6369188.35 6372904.15 453.50 473.30 473.29 0.01 0.002%

The values in the yellow fields are the final Drop calculations from the GPS measurements, all with respect to the reference station AMDE. The values in the green fields are the predicted values for the WGS84 globe model. If the earth were flat, all the values in the yellow fields would be 0.

Azim
Azimuth direction of the Station as seen from AMDE. Azim is used to calculate the ellipsoid radius REll along this direction.
Dist Chord
Chord distance d from AMDE location R to a point Q below the other station P at the same elevation as AMDE:
$d = | \vec Q - \vec R |$ with $\vec Q = \vec P - \Delta H \cdot \hat z_\mathrm{P}$ and $\hat z_\mathrm{P}$ is the unit vector perpendicular to the ellipsoid surface at P. The components of $\vec R$ and $\vec P$ are the (x,y,z) coordinates of the locations.
Dist Surf
Distance s along the surface calculated from Dist Chord $d$:
$s = 2R\ \mathrm{asin}(d/2R)$ with $R = R_\mathrm{Ell}+H$
REll
Ellipsoid radius in the direction Azim. The radius of curvature of the WGS84 reference ellipsoid, which is the basis of GPS, depends on the direction you measure.
REll+H
Because all stations are at an elevation of 3715.8 m or slightly above, this height has to be added to the ellipsoid radius. This radius is used to calculate the expected Drop Pred.
Drop GPS
Drop in reality, calculated by the App Display Geo Data from the GPS data of the stations, using vector algebra.
Drop-ΔH
Because the stations are at slightly higher elevations with respect to the station AMDE, the differences in the elevations have to be subtracted from the measured Drop GPS values to get the Drop of each station with respect to the same elevation as the AMDE station. The tilt of the ΔH at the drop location with respect to the AMDE station is taken into account:
$x_\mathrm{H} = x - \Delta H \ \cos(s/R)$, where $x$ = Drop GPS, $\Delta H$ = difference in elevation between 2 stations, $s$ = surface distance between 2 stations and $R = R_\mathrm{Ell}+H$.
Drop Pred
Expected Drop calculated for an ellipsoid radius $R = R_\mathrm{Ell}+H$:
$x_{pred} = R\ (1 - \cos(s/R))$
ΔDrop, ΔDrop%
Difference of measured Drop-ΔH from GPS data to expected Drop Pred, absolute and relative in %.

To correctly predict the Drop for the globe model, we have to know the radius of curvature between the reference stations.

The WGS84 Globe Model describes the earth as an oblate spheroid, the so called Reference Ellipsoid. Contrary to a sphere, an ellipsoid has not only one radius. In fact the radius of curvature depends not only on latitude, but also on the direction it is measured. To get an accurate drop value prediction, we have to use the directional radius between 2 stations, increased by the elevation of the station AMDE. The calculation of the Azim direction and the directional radius is very complicated. I used my WGS84 Calculator for that.

Result and Conclusion

As we can see, there is a measured Drop Drop-ΔH between the stations. The Bolivia Salt Flat curves exactly as predicted by the official Globe Model WGS84.

The Bolivian Salt Flat show a Drop in every direction as predicted by the Globe Model. The Earth is NOT FLAT.

Bonneville Salt Flats

There is another salt lake in Utah, the Bonneville Salt Flats. I have the GPS data from a car driving along Rte 80 recording 1274 data points (thanks Jesse). They clearly show the curvature of the earth too. There are even images and a video showing this curvature:

Calculating the Drop from GPS Data

We can use the GPS (x,y,z) coordinates of 2 reference stations and vector algebra to calculate the drop between the stations. Lets label the AMDE reference station vector $\vec R$ and one of the other stations vector $\vec P$. The vector from $\vec R$ to $\vec P$ is then simply $\vec p = \vec P - \vec R$. The drop x of P with respect to R is the component of $\vec p$ projected onto the direction $\hat r$ of the vector $\vec R$. We can get the projection using the scalar product:

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