A study published September 9, 2026, by C. Kotsakis of Aristotle University of Thessaloniki found that the solid Earth became slightly less flattened while the geoid’s flattening increased. The analysis used GNSS-derived vertical velocities recorded from 1997 through 2015, so its findings describe that study period.
The solid Earth and the geoid describe different things
The solid Earth is the physical, deformable planet; the geoid is an equipotential surface of Earth’s gravity field, shaped by the distribution of mass, including water. They describe different properties, so their flattening can change in opposite directions.
GNSS measurements track the geometric motion of stations on Earth’s surface. The geoid, by contrast, describes a gravity-defined surface. A shift in where mass sits can change the geoid even as the solid surface moves differently.
What the GNSS measurements found
The study analyzed vertical velocities from a final network of 886 GNSS stations. Mean polar uplift increased between the two periods, while equatorial vertical rates became increasingly negative, indicating subsidence of less than 1 millimeter per year in magnitude.
| Measure | 1997–2000 | 2011–2015 |
| Mean polar uplift | About 0.5 mm/year | Nearly 1 mm/year |
| Inferred J₂ rate | 0.8 × 10⁻¹⁰ per year | 2.7 × 10⁻¹⁰ per year |
J₂ is a coefficient describing a large-scale component of Earth’s gravity field associated with its flattening. The study found that its inferred rate increased across the two periods, alongside the opposing changes in solid-Earth and geoid flattening.
Why the two trends can move in opposite directions
Polar uplift and equatorial subsidence describe changes in the solid Earth’s geometry. The geoid reflects gravity and mass distribution instead. Because those are distinct measurements, less flattening of the solid Earth can occur alongside more flattening of the geoid.
The study’s GNSS analysis concerns vertical deformation, measured in millimeters per year. That is a different quantity from the horizontal movement of tectonic plates.
Ice loss is a plausible contributor
The study presents contemporary ice loss and the redistribution of meltwater toward lower latitudes as physically plausible contributors to the observed pattern. Losing ice can unload the crust beneath Greenland and Antarctica, while added water at lower latitudes can increase pressure on the ocean floor and contribute to equatorial subsidence.
