Temperature gradient
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2008-01-18T10:55:07Z
Leptictidium
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In atmospheric sciences ([[meteorology]], [[climatology]] and related fields), the '''temperature gradient''' (typically of [[Earth's atmosphere|air]], more generally of any [[fluid]]) is a physical quantity that describes in which direction and at what rate the [[temperature]] changes the most rapidly around a particular location. The temperature gradient is a dimensional quantity expressed in [[Units of measurement|units]] of degrees (on a particular temperature scale) per unit length. The [[International System of Units|SI]] unit is [[kelvin]] per [[metre]] (K/m).
==Mathematical description==
Assuming that the temperature ''T'' is an [[intensive quantity]], i.e., a single-valued, [[Continuous function|continuous]] and [[Derivative|differentiable]] [[Function (mathematics)|function]] of three-dimensional space (often called a [[scalar field]]), i.e., that
:<math>T=T(x,y,z)</math>
where ''x'', ''y'' and ''z'' are the [[Cartesian coordinate system|coordinates]] of the location of interest, then the temperature gradient is the [[Vector (spatial)|vector]] quantity defined as
:<math>
\nabla T = \begin{pmatrix}
{\frac{\partial T}{\partial x}},
{\frac{\partial T}{\partial y}},
{\frac{\partial T}{\partial z}}
\end{pmatrix}</math>
==Weather and climate relevance==
Differences in air temperature between different locations are critical in weather forecasting and climate. The absorption of solar light at or near the planetary surface increases the temperature gradient and may result in [[convection]] (a major process of [[cloud]] formation, often associated with [[Precipitation_(meteorology)|precipitation]]). Similarly, on a global and annual basis, the dynamics of the atmosphere (and the oceans) can be understood as attempting to reduce the large difference of temperature between the [[Geographical pole|poles]] and the equator by redistributing masses of warm and cold air (and water).
[[Surface weather analysis|Meteorological fronts]] are regions where the horizontal temperature gradient may reach relatively high values, as these are boundaries between [[Air mass|air masses]] with rather distinct properties.
Clearly, the temperature gradient may change substantially in time, as a result of diurnal or seasonal heating and cooling for instance.
==Day to day experiences and health issues==
Other places where noticeable temperature gradients can be experienced include the entrance (or exits) of air conditioned shops in the summer, or the entrance of caves and other protected or poorly ventilated areas.
Rapid changes in temperature (in space or time) may cause discomfort and, in extreme cases, heat or cold stresses.
==See also==
* [[Gradient]]
* [[Adiabatic lapse rate]]
==References==
* Edward N. Lorenz (1967) ''The nature and theory of the general circulation of atmosphere'', World Meteorological Organization, Publication No. 218, Geneva, Switzerland.
* M. I. Budyko (1978) ''Climate and Life'', Academic Press, International Geophysics Series, Volume '''18''', ISBN 0-12-139450-6.
* Robert G. Fleagle and Joost A. Businger (1980) ''An Introduction to Atmospheric Physics'', Second Edition, Academic Press, International Geophysics Series, Volume '''25''', ISBN 0-12-260355-9.
* David Miller (1981) ''Energy at the Surface of the Earth: An Introduction to the Energetics of Ecosystems'', Academic Press, International Geophysics Series, Volume '''29'''.
* John M. Wallace and Peter V. Hobbs (2006) ''Atmospheric Science: An Introductory Survey'', Second Edition, Academic Press, International Geophysics Series, ISBN 0-12-732951-X.
==External links==
* [http://www.grida.no/climate/ipcc_tar/wg1/index.htm IPCC Third Assessment Report]
[[Category:Atmospheric dynamics]]
[[Category:Climatology]]
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