- Pressure gradient
In atmospheric sciences (

meteorology ,climatology and related fields), the**pressure gradient**(typically of air, more generally of anyfluid ) is a physical quantity that describes in which direction and at what rate thepressure changes the most rapidly around a particular location. The pressure gradient is a dimensional quantity expressed in units of pressure per unit length. The SI unit is pascal permetre (Pa/m).**Mathematical description**Assuming that the pressure "p" is an

intensive quantity , i.e., a double-valued, continuous and differentiable function of three-dimensional space (often called ascalar field ), i.e., that:$p=p(x,y,z)$

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

:$abla\; p\; =\; egin\{pmatrix\}\{frac\{partial\; p\}\{partial\; x,\; \{frac\{partial\; p\}\{partial\; y,\; \{frac\{partial\; p\}\{partial\; zend\{pmatrix\}$

**Physical interpretation**Strictly speaking, the concept of pressure gradient is a "local" characterization of the air (more generally of the fluid under investigation). The pressure gradient is defined only at those spatial scales at which pressure (more generally

fluid dynamics ) itself is defined.Within

planet aryatmosphere s (including the Earth's), the pressure gradient is a vector pointing roughly downwards, because the pressure changes most rapidly vertically, increasing downwards. The value of the strength (or norm) of the pressure gradient in thetroposphere is typically of the order 9 Pa/m (or 90 hPa/km).The pressure gradient often has a small but critical horizontal component, which is largely responsible for the

wind circulation. The**horizontal pressure gradient**is a 2-dimensional vector resulting from the projection of the pressure gradient onto a local horizontal plane.Near the

Earth's surface , this horizontal pressure gradient is typically pointing towards high pressureair mass es (anticyclone s), its particular orientation at any one time and place depends strongly on the weather situation. At mid-latitude s, the typical horizontal pressure gradient may take on values of the order of 10^{-2}Pa/m (or 10 Pa/km), although rather higher values occur within meteorological fronts.**Weather and climate relevance**Differences in air pressure between different locations are critical in weather forecasting and climate. As indicated above, the pressure gradient constitutes one of the main forces acting on the air to make it move as wind. Note that the pressure gradient force points from high towards low pressure zones, it is thus oriented in the opposite direction from the pressure gradient itself.

Sound waves andshock wave s are events that can induce very large pressure gradients, but these are often transitory disturbances.**Day to day experiences and health issues**Our

ear s detect and interpret sound waves; as such they are delicate, sensitive organs to measure pressure gradients. Excessive pressure gradients can hurt or damage theauditory system . By contrast, pressure alone does not have quite the same effect: divers can reach significant depths under water (and thus experience very large pressures) without damage, provided appropriate and necessary precautions are taken.**ee also***

Gradient

*Isobar

*Geopotential height

*Geostrophic wind

*Primitive equations

*Temperature gradient **References*** Edward N. Lorenz (1967) "The nature and theory of the general circulation of atmosphere", World Meteorological Organization, Publication No. 218, Geneva, Switzerland.

* 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.* 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*]

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