Quasiperiodicity is the property of a
system
A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its open system (systems theory), environment, is described by its boundaries, str ...
that displays irregular
periodicity. Periodic behavior is defined as recurring at regular intervals, such as "every 24 hours". Quasiperiodic behavior is almost but not quite periodic. The term used to denote oscillations that appear to follow a regular pattern but which do not have a fixed period. The term thus used does not have a precise definition and should not be confused with more strictly defined mathematical concepts such as an
almost periodic function or a
quasiperiodic function.
Climatology
Climate oscillations that appear to follow a regular pattern but which do not have a fixed period are called ''quasiperiodic''.
[''The meteorological glossary: 2d ed.'' 1930. Meteorological Office, Great Britain. "Certain phenomena which recur more or less regularly but without the exactness of truly periodic phenomena are termed quasi-periodic."]
Within a
dynamical system
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models ...
such as the ocean-atmosphere system, oscillations may occur regularly when they are forced by a regular external forcing: for example, the familiar winter-summer cycle is forced by variations in sunlight from the (very close to perfectly) periodic motion of the Earth around the Sun. Or, like the recent
ice age
An ice age is a long period of reduction in the temperature of Earth's surface and atmosphere, resulting in the presence or expansion of continental and polar ice sheets and alpine glaciers. Earth's climate alternates between ice ages, and g ...
cycles, they may be less regular but still locked by external forcing. However, when the system contains the potential for an oscillation, but there is no strong external forcing to be
phase-locked to, the "period" is likely to be irregular.
The canonical example of quasiperiodicity in climatology is
El Niño–Southern Oscillation (ENSO).
[ ENSO is highly consequential for ]wheat
Wheat is a group of wild and crop domestication, domesticated Poaceae, grasses of the genus ''Triticum'' (). They are Agriculture, cultivated for their cereal grains, which are staple foods around the world. Well-known Taxonomy of wheat, whe ...
cultivation in Australia.[ Models to predict and thereby assist adaptation to ENSO have a large potential benefit to Australian wheat farmers.][
This review cites this study:
] In the modern era, it has a "period" somewhere between four and twelve years and a peak spectral density around five years.
See also
* Nonlinear resonance
* Quasiperiodic function
* Quasiperiodic motion
* Quasi-periodic oscillations
* Quasiperiodic tiling
* Seasonality
References
Systems theory
Dynamical systems
Wave mechanics
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