In atmospheric sciences (meteorology, climatology and related fields), the temperature gradient (typically of 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 degrees (on a particular temperature scale) per unit length. The SI unit is K/m (Kelvin per metre).

Mathematical description

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Assuming that the temperature T is an intensive quantity, i.e., a single-valued, continuous and differentiable function of three-dimensional space (often called a scalar field), i.e., that

$T=T(x,y,z)$

where x, y and z are the coordinates of the location of interest, then the temperature gradient is the vector quantity defined as

$$

\nabla T = \begin{pmatrix} {\frac{\partial T}{\partial x}}, {\frac{\partial T}{\partial y}}, {\frac{\partial T}{\partial z}} \end{pmatrix}

Physical interpretation

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Strictly speaking, the concept of temperature gradient is a local characterization of the air (more generally of the fluid under investigation). The temperature gradient is defined only at those spatial scales at which temperature (more generally fluid thermodynamics) itself is defined.

For most locations near the Earth's surface, the temperature gradient is a vector pointing rougly downwards, because the temperature changes most rapidly vertically, increasing downwards. The value of the strength (or norm) of the temperature gradient in the troposphere is typically of the order 6 mK/m (or 6 K/km). However,the temperature gradient is oriented upwards when there is an inversion or in the upper stratosphere, for instance.

The temperature gradient often has a small horizontal component, corresponding to the (comparatively much slower) rate of change with latitude, for instance. The horizontal temperature gradient is a 2-dimensional vector resulting from the projection of the temperature gradient onto a local horizontal plane. Again, near the Earth's surface, this horizontal temperature gradient is typically pointing towards the equator on average, but its particular orientation at any one time and place depends strongly on the weather situation. In the winter hemisphere, the average horizontal temperature gradient takes on values of the order of 10^-2 mK/m (or 1 K per 100 km). The horizontal temperature gradient in the summer hemisphere is usually even smaller.

Weather and climate relevance

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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)|precipitations]]). 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 poles and the equator by redistributing masses of warm and cold air (and water).

Meteorological fronts are regions where the horizontal temperature gradient may reach relatively high values, as these are boundaries between 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

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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

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• Gradient
• Adiabatic lapse rate

References

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• 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 0121394506.

• Robert G. Fleagle and Joost A. Businger (1980) An Introduction to Atmospheric Physics, Second Edition, Academic Press, International Geophysics Series, Volume 25, ISBN 0122603559.

• 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 012732951X.

External links

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• IPCC Third Assessment Report

Atmospheric dynamics | Climatology

Temperaturgradient | Pionowy gradient temperatury