What is the effect of large lakes and water reservoirs on Earth's rotation?

Moment of Inertia and Earth's Rotation

Definition of moment of inertia

The Earth, like any rotating body, possesses angular momentum that characterizes the quantity of motion related to its rotation. This angular momentum is written: \( L = I\,\omega \) where I is the Earth's moment of inertia and ω its angular velocity (the rotation speed around its axis). The moment of inertia measures how mass is distributed relative to the axis of rotation: the further the mass is from this axis, the higher I is.

In the general case, the moment of inertia of a body is defined by the integral: \( I = \int r^{2}\,dm \) where r is the distance between a mass element dm and the rotation axis. This expression shows that each mass portion contributes proportionally to the square of its distance from the axis: moving mass outward greatly increases I.

Relationship between moment of inertia and rotation speed

If the total angular momentum L remains constant, a change in the moment of inertia causes an inverse change in the angular velocity. In other words, if I increases, then ω decreases. This principle follows directly from the relationship: \( L = I\,\omega = \text{constant} \)

Thus, any modification in the distribution of Earth's masses, for example through large-scale constructions, can in theory influence the Earth's rotation speed — although, as we will see, the effect of a single structure remains far below the instrumental detection threshold.

Why do large dams change the Earth's rotation?

Mass redistribution by reservoirs

Large dams move immense quantities of water and thus change the distribution of Earth's mass. The Three Gorges Dam in China is the most commonly cited example: its reservoir can hold, according to estimates, between 39.3 and 40 billion cubic meters of water, at an average altitude of about 175 meters above sea level. This water stored at a higher altitude than the river's natural level ends up farther from the Earth's rotation axis, which very slightly modifies the planet's overall moment of inertia.

Other structures, such as the Itaipu Dam (Brazil/Paraguay) or the Tucuruí Dam (Brazil), produce the same type of effect, though of lesser magnitude individually.

Conservation of angular momentum

When large masses of water are moved to regions farther from the Earth's axis, the Earth's moment of inertia increases very slightly. However, in the absence of any significant external force capable of modifying the total angular momentum, this remains constant. Consequently, if I increases, the Earth must slow its rotation infinitesimally to maintain the same angular momentum. This slowdown translates into an infinitesimal increase in the length of the day.

Consequences: Slowing of Rotation

Lengthening of the day

A decrease in the Earth's angular velocity means that the Earth takes slightly longer to complete one rotation, resulting in a very minute lengthening of the day length.

Order of magnitude of the effect

The effect of a dam like the Three Gorges on the length of the day is extremely small. In 2005, geophysicists Benjamin Fong Chao (NASA's Goddard Space Flight Center) and Richard Gross (Jet Propulsion Laboratory) calculated that the complete filling of this reservoir would lengthen the day by 0.06 microseconds (6 × 10⁻⁸ seconds) and shift the geographic pole by about 2 centimeters. This calculation, originally published as a point of comparison with the effect of the 2004 Sumatra earthquake (which shortened the day by 2.68 microseconds), remains the most cited reference on the subject.

Order of magnitude to keep in mind: the smallest change in day length ever directly measured by space geodesy techniques (VLBI, GPS) is about 1 millisecond, i.e. 1000 microseconds. The theoretical effect of the Three Gorges Dam (0.06 microseconds) is therefore about 16,000 times too small to be isolated and measured individually: it is a result calculated from the mass and altitude of the water, not a direct measurement. Cumulatively across all the world's large dams, the effect also remains largely dominated by natural phenomena (tides, atmosphere, earthquakes) and by other anthropogenic processes such as groundwater pumping, presented below.

Dams and global sea level: a compensatory effect

A continental reservoir of 10,800 km³

Beyond Earth's rotation, large dams have a better-quantified and more significant effect: that of retaining water on the continents rather than allowing it to reach the oceans, which temporarily limits the rise in global sea level.

In a landmark study published in 2008 in the journal Science, Benjamin Fong Chao and colleagues Y. H. Wu and Y. S. Li reconstructed the history of artificial reservoir filling worldwide. They estimate that about 10,800 cubic kilometers of water have been stored on the continents over the last century, reducing the global sea level rise by about 30 millimeters, at an average rate of −0.55 mm per year over the last half-century. Once this effect is subtracted, the "natural" sea level rise appears surprisingly constant, at around +2.46 mm per year over at least 80 years, while raw data suggested a much more irregular evolution.

A reassessed sea level rise

This result clearly illustrates the scale difference between the two phenomena: the effect of dams on Earth's rotation (fraction of a microsecond) is purely theoretical and not individually measurable, while their cumulative effect on sea level (tens of millimeters) is directly observable in space geodesy time series.

Groundwater pumping and Earth's pole drift

Pole drift finally explained

Another anthropogenic phenomenon related to the redistribution of water on the Earth's surface has proven to be much more measurable than the effect of dams on day length: the drift of the Earth's rotation pole due to massive groundwater pumping.

In 2016, a study by Surendra Adhikari and Erik Ivins (NASA's Jet Propulsion Laboratory), published in Science Advances, showed that continental water movements (glacier melt, variations in groundwater storage) largely explain the observed drift of the rotation pole since 1899, including an east-west oscillation unexplained for over a century.

Groundwater pumping as the primary cause

This line of inquiry was further explored in 2023 by a team led by Ki-Weon Seo (Seoul National University), published in Geophysical Research Letters. By modeling approximately 2,150 gigatons of groundwater extracted between 1993 and 2010 for agriculture, industry, and domestic consumption, then released into the water cycle, the researchers were able to reproduce the actually observed drift of the Earth's pole: about 80 centimeters eastward over this 17-year period, at a speed of about 4.36 cm per year. According to this study, groundwater pumping is the most significant climatic contribution to the observed polar drift, ahead of the melting of the Greenland and Antarctic ice sheets over the period considered.

Be careful not to confuse the two phenomena: day length (lengthening of the time of one rotation, expressed in microseconds) and polar drift or polar motion (displacement of the rotation axis relative to the Earth's crust, expressed in centimeters) are two distinct manifestations of the conservation of angular momentum. Dams, like groundwater pumping, affect both, but in very different proportions: the effect on polar drift is now measurable, unlike the effect on day length.

What physical phenomena affect the Earth's rotation?

Natural phenomena

• Very powerful earthquakes can modify the distribution of Earth's mass: the 2004 Sumatra earthquake (magnitude 9) thus shortened the day by 2.68 microseconds.
• Earth and ocean tides, caused by the gravitational attraction of the Moon and the Sun, have a dominant effect on Earth's rotation over the long term (lengthening the day by about 1.7 milliseconds per century).
• Convective currents and other movements in the Earth's mantle and core can displace large internal masses, slightly modifying the Earth's moment of inertia.
• Isostatic adjustments, such as post-glacial rebound after the melting of polar ice caps, modify mass distribution and can affect Earth's rotation and polar drift.
• Seasonal variations in atmospheric and oceanic mass produce variations in day length on the order of a millisecond over a year, far greater than the effect of dams.

Anthropogenic phenomena

• Groundwater pumping redistributes water mass from the continents to the oceans and constitutes, according to the most recent studies, the most significant and best-measured anthropogenic contribution to the Earth's polar drift.
• The melting of large ice masses due to climate change redistributes water from the poles to the oceans, which modifies the moment of inertia and also contributes to polar drift.
• Large dams, such as the Three Gorges or Itaipu, move colossal quantities of water to higher altitudes; their effect on day length remains theoretical and not individually measurable, but their cumulative effect on global sea level is well documented.

In summary: Impacts of human activities

Beyond local social and environmental consequences (population relocation, submersion of archaeological sites), large dams have a theoretical effect, but not individually measurable, on the rotation speed of our planet.

This reasoning pedagogically illustrates how large-scale human actions can, in principle, influence the physical properties of our planet, but ultimately it is other, more discreet effects such as groundwater pumping or cumulative storage in reservoirs that leave a truly measurable imprint on sea level and the Earth's polar drift.