differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...

, the equivalent latitude is a Lagrangian coordinate . It is often used in

atmospheric science Atmospheric science is the study of the Atmosphere of Earth, Earth's atmosphere and its various inner-working physical processes. Meteorology includes atmospheric chemistry and atmospheric physics with a major focus on weather forecasting. Climat ...

, particularly in the study of stratospheric dynamics. Each isoline in a map of equivalent latitude follows the

flow velocity In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the f ...

and encloses the same area as the latitude line of equivalent value, hence "equivalent latitude." Equivalent latitude is calculated from

potential vorticity In fluid mechanics, potential vorticity (PV) is a quantity which is proportional to the dot product of vorticity and stratification. This quantity, following a parcel of air or water, can only be changed by diabatic or frictional processes. It i ...

, from passive tracer simulations and from actual measurements of atmospheric tracers such as

ozone Ozone (), or trioxygen, is an inorganic molecule with the chemical formula . It is a pale blue gas with a distinctively pungent smell. It is an allotrope of oxygen that is much less stable than the diatomic allotrope , breaking down in the lo ...

Calculation of equivalent latitude

The calculation of equivalent latitude involves creating a monotonic mapping between the values of equivalent latitude and the tracer it is based upon: higher values of the tracer map to higher values of equivalent latitude. A precise method is to assign a representative area to each of the tracer measurements, filling the entire globe. Thus, for a tracer field regularly gridded in longitude and latitude, grid points closer to the pole will take up a smaller area, in proportion to the cosine of the latitude. Now,

rank Rank is the relative position, value, worth, complexity, power, importance, authority, level, etc. of a person or object within a ranking, such as: Level or position in a hierarchical organization * Academic rank * Diplomatic rank * Hierarchy * H ...

all the tracer values then form the cumulative sum. The equivalent latitude from the area is given as: :

\phi = \sin^ \left ( \frac -1 \right )

where ''A'' is the area enclosed to the South (''A'' = 0 corresponds to the equivalent South Pole) and ''R'' is the radius of the Earth. This method generates a mapping that is as continuous as the data allows as opposed to binning which produces a coarse-grained mapping.

References

* * {{cite journal , author1=Neal Butchart , author2=Ellis E. Remsberg , title=The area of the stratospheric polar vortex as a diagnostic for tracer transport on an isentropic surface , journal=Journal of the Atmospheric Sciences , year=1986 , volume=43 , pages=1319–1339 , doi=10.1175/1520-0469(1986)043<1319:taotsp>2.0.co;2, doi-access=free Climatology Differential geometry Equivalence (mathematics)