The secular variation of a time series is its long-term non-periodic variation (see Decomposition of time series). Whether something is perceived as a secular variation or not depends on the available timescale: a secular variation over a time scale of centuries may be part of a periodic variation over a time scale of millions of years. Natural quantities often have both periodic and secular variations. Secular variation is sometimes called secular trend or secular drift when the emphasis is on a linear long-term trend.
The term secular variation is used wherever time series are applicable in economics, operations research, biological anthropology, astronomy (particularly celestial mechanics) such as VSOP (planets) etc.
In astronomy, secular variations are contrasted with periodic phenomena. In particular, astronomical ephemerides use secular to label the longest-lasting or non-oscillatory perturbations in the motion of planets, as opposed to periodic perturbations which exhibit repetition over the course of a time frame of interest. Solar System ephemerides are essential for the navigation of spacecraft and for all kinds of space observations of the planets, their natural satellites, stars and galaxies.
Most of the known perturbations to motion in stable, regular, and well-determined dynamical systems tend to be periodic at some level, but in many-body systems, chaotic dynamics result in some effects which are one-way (for example, planetary migration).
In the Solar System
Secular phenomena create variations in the orbits of the Moon and the planets. The solar emission spectrum and the solar wind are undergoing secular trends due to migration through the galactic plane, leading to effects that may impact on climate and cause extinction events.
Depending on what time frames are considered, perturbations can appear secular even if they are actually periodic. An example of this is the precession of the Earth's axis considered over the time frame of a few hundred or thousand years. When viewed in this time frame the so-called "precession of the equinoxes" can appear to mimic a secular phenomenon since the axial precession takes 25,771.5 years and monitoring it over a much smaller timeframe appears to simply result in a "drift" of the position of the equinox in the plane of the ecliptic of approximately one degree every 71.6 years, influencing the Milankovitch cycles.
Secular variation also refers to long-term trends in the orbits of the planets Mercury to Neptune. Several attempts have from time to time been undertaken to analyze and predict such gravitational deviations from ordinary satellite orbits. Others are often referred to as post keplerian effects.
Geomagnetic secular variation
Geomagnetic secular variation refers to changes in the Earth's magnetic field. The field has variations on time scales from milliseconds to millions of years, but rapid changes mostly come from currents in the ionosphere and magnetosphere. The secular variation is the changes over periods of a year or more, reflecting changes in the Earth's core. Phenomena associated with this secular variation include geomagnetic jerk, westward drift and geomagnetic reversals.
A secular trend has been observed in the age of onset of puberty (menarche/first menstruation and beginning of breast development) of girls around the world beginning roughly 4 months earlier each decade. This is largely believed to be caused by nutritional changes in children over time.
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