The length of the day (LOD), which has increased over the long term of

Earth's history The natural history of Earth concerns the development of planet Earth from its formation to the present day. Nearly all branches of natural science have contributed to understanding of the main events of Earth's past, characterized by consta ...

due to tidal effects, is also subject to fluctuations on a shorter scale of time. Exact measurements of time by

atomic clock An atomic clock is a clock that measures time by monitoring the resonant frequency of atoms. It is based on atoms having different energy levels. Electron states in an atom are associated with different energy levels, and in transitions betwee ...

s and

satellite laser ranging Satellite laser ranging (SLR) is a method to measure the distance to satellites in a geocentric orbit. It consists of an astronomical observatory equipped with a laser that sends ultrashort pulses of light. The pulses hit the satellite and boun ...

have revealed that the LOD is subject to a number of different changes. These subtle variations have periods that range from a few weeks to a few years. They are attributed to interactions between the dynamic

atmosphere An atmosphere () is a layer of gases that envelop an astronomical object, held in place by the gravity of the object. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A stellar atmosph ...

and Earth itself. The

International Earth Rotation and Reference Systems Service The International Earth Rotation and Reference Systems Service (IERS), formerly the International Earth Rotation Service, is the body responsible for maintaining global time and reference frame standards, notably through its Earth Orientation P ...

monitors the changes. In the absence of external torques, the total

angular momentum Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of Momentum, linear momentum. It is an important physical quantity because it is a Conservation law, conserved quantity – the total ang ...

of Earth as a whole system must be constant. Internal torques are due to relative movements and mass redistribution of Earth's core, mantle, crust, oceans, atmosphere, and

cryosphere The cryosphere is an umbrella term for those portions of Earth's surface where water is in solid form. This includes sea ice, ice on lakes or rivers, snow, glaciers, ice caps, ice sheets, and frozen ground (which includes permafrost). Thus, there ...

. In order to keep the

total angular momentum In quantum mechanics, the total angular momentum quantum number parametrises the total angular momentum of a given particle, by combining its orbital angular momentum and its intrinsic angular momentum (i.e., its spin). If s is the particle's ...

constant, a change of the angular momentum in one region must necessarily be balanced by angular momentum changes in the other regions. Crustal movements (such as

continental drift Continental drift is a highly supported scientific theory, originating in the early 20th century, that Earth's continents move or drift relative to each other over geologic time. The theory of continental drift has since been validated and inc ...

) or polar cap melting are slow secular (non-periodic) events. The characteristic coupling time between core and mantle has been estimated to be on the order of ten years, and the so-called 'decade fluctuations' of

Earth's rotation Earth's rotation or Earth's spin is the rotation of planet Earth around its own Rotation around a fixed axis, axis, as well as changes in the orientation (geometry), orientation of the rotation axis in space. Earth rotates eastward, in progra ...

rate are thought to result from fluctuations within the core, transferred to the mantle. The length of day (LOD) varies significantly even for time scales from a few years down to weeks (Figure), and the observed fluctuations in the LOD - after eliminating the effects of external torques - are a direct consequence of the action of internal torques. These short term fluctuations are very probably generated by the interaction between the solid Earth and the atmosphere. The length of day of other planets also varies, particularly of the planet

Venus Venus is the second planet from the Sun. It is often called Earth's "twin" or "sister" planet for having almost the same size and mass, and the closest orbit to Earth's. While both are rocky planets, Venus has an atmosphere much thicker ...

, which has such a dynamic and strong atmosphere that its length of day fluctuates by up to 20 minutes.

Observations

Any change of the axial component of the atmospheric

(AAM) must be accompanied by a corresponding change of the angular momentum of Earth's crust and mantle (due to the law of conservation of angular momentum). Because the

moment of inertia The moment of inertia, otherwise known as the mass moment of inertia, angular/rotational mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is defined relatively to a rotational axis. It is the ratio between ...

of the system mantle-crust is only slightly influenced by atmospheric pressure loading, this mainly requires a change in the

angular velocity In physics, angular velocity (symbol or \vec, the lowercase Greek letter omega), also known as the angular frequency vector,(UP1) is a pseudovector representation of how the angular position or orientation of an object changes with time, i ...

of the solid Earth; ''i.e.'', a change of LOD. The LOD can presently be measured to a high accuracy over integration times of only a few hours, and

general circulation model A general circulation model (GCM) is a type of climate model. It employs a mathematical model of the general circulation of a planetary atmosphere or ocean. It uses the Navier–Stokes equations on a rotating sphere with thermodynamic terms for ...

s of the atmosphere allow high precision determination of changes in AAM in the model. A comparison between AAM and LOD shows that they are highly correlated. In particular, one recognizes an annual period of LOD with an amplitude of 0.34 milliseconds, maximizing on February 3, and a semiannual period with an amplitude of 0.29 milliseconds, maximizing on May 8, as well as 10‑day fluctuations of the order of 0.1 milliseconds. Interseasonal fluctuations reflecting

El Niño EL, El or el may refer to: Arts and entertainment Fictional entities * El, a character from the manga series ''Shugo Chara!'' by Peach-Pit * Eleven (''Stranger Things'') (El), a fictional character in the TV series ''Stranger Things'' * El, fami ...

events and quasi-biennial oscillations have also been observed. There is now general agreement that most of the changes in LOD on time scales from weeks to a few years are excited by changes in AAM.

Exchange of angular momentum

One means of exchange of angular momentum between the atmosphere and the non-gaseous parts of Earth is evaporation and precipitation. The

water cycle The water cycle (or hydrologic cycle or hydrological cycle) is a biogeochemical cycle that involves the continuous movement of water on, above and below the surface of the Earth across different reservoirs. The mass of water on Earth remains fai ...

moves massive quantities of water between the oceans and the atmosphere. As the mass of water (vapour) rises its rotation must slow due to conservation of angular momentum. Equally when it falls as rain, its rate of rotation will increase to conserve angular momentum. Any net global transfer of water mass from oceans to the atmosphere or the opposite implies a change in the speed of rotation of the solid/liquid Earth which will be reflected in LOD. Observational evidence shows that there is no significant time delay between the change of AAM and its corresponding change of LOD for periods longer than about 10 days. This implies a strong coupling between atmosphere and solid Earth due to surface

friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Types of friction include dry, fluid, lubricated, skin, and internal -- an incomplete list. The study of t ...

with a time constant of about 7 days, the spin-down time of the

Ekman layer Ekman transport is part of Ekman motion theory, first investigated in 1902 by Vagn Walfrid Ekman. Winds are the main source of energy for ocean circulation, and Ekman transport is a component of wind-driven ocean current. Ekman transport occurs ...

. This spin-down time is the characteristic time for the transfer of atmospheric axial angular momentum to Earth's surface and vice versa. The zonal wind-component on the ground, which is most effective for the transfer of axial angular momentum between Earth and atmosphere, is the component describing rigid rotation of the atmosphere. The zonal wind of this component has the amplitude ''u'' at the equator relative to the ground, where ''u'' > 0 indicates superrotation and ''u'' < 0 indicates retrograde rotation with respect to the solid Earth. All other wind terms merely redistribute the AAM with latitude, an effect that cancels out when averaged over the globe. Surface friction allows the atmosphere to 'pick up' angular momentum from Earth in the case of retrograde rotation or release it to Earth in the case of superrotation. Averaging over longer time scales, no exchange of AAM with the solid Earth takes place. Earth and atmosphere are decoupled. This implies that the ground level zonal wind-component responsible for rigid rotation must be zero on the average. Indeed, the observed meridional structure of the climatic mean zonal wind on the ground shows westerly winds (from the west) in middle latitudes beyond about ± 30^o latitude and easterly winds (from the east) in low latitudes—the

trade wind The trade winds or easterlies are permanent east-to-west prevailing winds that flow in the Earth's equatorial region. The trade winds blow mainly from the northeast in the Northern Hemisphere and from the southeast in the Southern Hemisphere, ...

s—as well as near the poles (

prevailing winds In meteorology, prevailing wind in a region of the Earth's surface is a surface wind that blows predominantly from a particular Wind direction, direction. The dominant winds are the trends in direction of wind with the highest speed over a partic ...

).Murgatroyd, R.J., . The structure and dynamics of the stratosphere, in Coby G.A. (ed): ''The Global Circulation of the Atmosphere'', Roy. Met. Soc., London, p. 159, 1969 The atmosphere picks up angular momentum from Earth at low and high latitudes and transfers the same amount to Earth at middle latitudes. Any short term fluctuation of the rigidly rotating zonal wind-component is then accompanied by a corresponding change in LOD. In order to estimate the order of magnitude of that effect, one may consider the total atmosphere to rotate rigidly with velocity ''u'' (in m/s) without surface friction. Then this value is related to the corresponding change of the length of day (in milliseconds) as

u \approx 2.7 \Delta\tau.

The annual component of the change of the length of day of ms corresponds then to a superrotation of m/s, and the semiannual component of ms to m/s.

Observations

Exchange of angular momentum

See also

References

Further reading