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<title>Temperature gradient</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Temperature gradient</span></span>

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<p>A <b>temperature gradient</b> is a <a href="Physical_quantity" title="Physical quantity">physical quantity</a> that describes in which direction and at what rate the <a href="Temperature" title="Temperature">temperature</a> changes the most rapidly around a particular location. The temperature <a href="Spatial_gradient" title="Spatial gradient">spatial gradient</a> is a <a href="Vector_quantity" title="Vector quantity">vector quantity</a> with <a href="Dimensional_analysis" title="Dimensional analysis">dimension</a> of temperature difference per unit <a href="Length" title="Length">length</a>. The <a href="International_System_of_Units" title="International System of Units">SI</a> <a href="Units_of_measurement" class="mw-redirect" title="Units of measurement">unit</a> is <a href="Kelvin" title="Kelvin">kelvin</a> per <a href="Meter" class="mw-redirect" title="Meter">meter</a> (K/m).

</p><p>Temperature gradients in the <a href="Earth's_atmosphere" class="mw-redirect" title="Earth's atmosphere">atmosphere</a> are important in the atmospheric sciences (<a href="Meteorology" title="Meteorology">meteorology</a>, <a href="Climatology" title="Climatology">climatology</a> and related fields).

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<div class="mw-heading mw-heading2"><h2 id="Mathematical_description">Mathematical description</h2></div>

<p>Assuming that the temperature <i>T</i> is an <a href="Intensive_quantity" class="mw-redirect" title="Intensive quantity">intensive quantity</a>, i.e., a single-valued, <a href="Continuous_function" title="Continuous function">continuous</a> and <a href="Derivative" title="Derivative">differentiable</a> <a href="Function_(mathematics)" title="Function (mathematics)">function</a> of three-dimensional space (often called a <a href="Scalar_field" title="Scalar field">scalar field</a>), i.e., that

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<annotation encoding="application/x-tex">{\displaystyle T=T(x,y,z)}</annotation>

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</math></span><img src="./4a4beaa2dc62ea81b8a8ebc8e63fa522be2d5808.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.821ex; height:2.843ex;" alt="{\displaystyle T=T(x,y,z)}" loading="lazy"></span></dd></dl>

<p>where <i>x</i>, <i>y</i> and <i>z</i> are the <a href="Cartesian_coordinate_system" title="Cartesian coordinate system">coordinates</a> of the location of interest, then the temperature gradient is the <a href="Vector_(geometric)" class="mw-redirect" title="Vector (geometric)">vector</a> quantity defined as

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<annotation encoding="application/x-tex">{\displaystyle \nabla T={\begin{pmatrix}{\frac {\partial T}{\partial x}},{\frac {\partial T}{\partial y}},{\frac {\partial T}{\partial z}}\end{pmatrix}}}</annotation>

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</math></span><img src="./e472b7e6a2234a0d756adcad3ab55e2fc2f00a5c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:21.041ex; height:4.843ex;" alt="{\displaystyle \nabla T={\begin{pmatrix}{\frac {\partial T}{\partial x}},{\frac {\partial T}{\partial y}},{\frac {\partial T}{\partial z}}\end{pmatrix}}}" loading="lazy"></span></dd></dl>

<div class="mw-heading mw-heading2"><h2 id="Physical_processes">Physical processes</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Meteorology">Meteorology</h3></div>

<p>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 <a href="Convection" title="Convection">convection</a> (a major process of <a href="Cloud" title="Cloud">cloud</a> formation, often associated with <a href="Precipitation_(meteorology)" class="mw-redirect" title="Precipitation (meteorology)">precipitation</a>).

<a href="Surface_weather_analysis" title="Surface weather analysis">Meteorological fronts</a> are regions where the horizontal temperature gradient may reach relatively high values, as these are boundaries between <a href="Air_mass" title="Air mass">air masses</a> with rather distinct properties.

</p><p>Clearly, the temperature gradient may change substantially in time, as a result of diurnal or seasonal heating and cooling for instance. This most likely happens during an <a href="Inversion_(meteorology)" title="Inversion (meteorology)">inversion</a>. For instance, during the day the temperature at <a href="Lithosphere" title="Lithosphere">ground level</a> may be cold while it's warmer up in the atmosphere. As the day shifts over to night the temperature might drop rapidly while at other places on the land stay warmer or cooler at the same <a href="Elevation" title="Elevation">elevation</a>. This happens on the <a href="West_Coast_of_the_United_States" title="West Coast of the United States">West Coast of the United States</a> sometimes due to geography.

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<div class="mw-heading mw-heading3"><h3 id="Weathering">Weathering</h3></div>

<p>Expansion and contraction of rock, caused by temperature changes during a <a href="Wildfire" title="Wildfire">wildfire</a>, through <a href="Weathering#Thermal_stress" title="Weathering">thermal stress weathering</a>, may result in <a href="Thermal_shock" title="Thermal shock">thermal shock</a> and subsequent structure failure.

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<div class="mw-heading mw-heading2"><h2 id="Indoor_temperature">Indoor temperature</h2></div>

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</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Thermal_destratification_in_buildings" class="mw-redirect" title="Thermal destratification in buildings">Thermal destratification in buildings</a></div>

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<ul><li><a href="Atmospheric_temperature" title="Atmospheric temperature">Atmospheric temperature</a> for gradient of Earth's atmosphere</li>

<li><a href="Geothermal_gradient" title="Geothermal gradient">Geothermal gradient</a></li>

<li><a href="Gradient" title="Gradient">Gradient</a></li>

<li><a href="Lapse_rate" title="Lapse rate">Lapse rate</a></li>

<li><a href="Weak_temperature_gradient_approximation" title="Weak temperature gradient approximation">Weak temperature gradient approximation</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFEdward_N._Lorenz1967" class="citation book cs1">Edward N. Lorenz (1967). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/naturetheoryofge0000lore"><i>The Nature and Theory of the General Circulation of the Atmosphere</i></a></span>. Publication No. 218. Geneva, Switzerland: World Meteorological Organization.</cite></li>

<li><cite id="CITEREFM._I._Budyko1978" class="citation book cs1">M. I. Budyko (1978). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/climatelife00mibu"><i>Climate and Life</i></a></span>. International Geophysics Series. Vol. 18. Academic Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-12-139450-6</bdi>.</cite></li>

<li><cite id="CITEREFRobert_G._FleagleJoost_A._Businger1980" class="citation book cs1">Robert G. Fleagle; <a href="Joost_A._Businger" class="mw-redirect" title="Joost A. Businger">Joost A. Businger</a> (1980). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=6oIuAAAAIAAJ"><i>An introduction to atmospheric physics</i></a>. International Geophysics Series. Vol. 25. Academic Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-12-260355-9</bdi>.</cite></li>

<li><cite id="CITEREFDavid_Miller1981" class="citation book cs1">David Miller (1981). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/energyatsurfaceo0000mill"><i>Energy at the surface of the earth : an introduction to the energetics of ecosystems</i></a></span>. Academic Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-08-095460-8</bdi>.</cite></li>

<li><cite id="CITEREFJohn_M._WallacePeter_V._Hobbs2006" class="citation book cs1">John M. Wallace; Peter V. Hobbs (2006). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=HZ2wNtDOU0oC"><i>Atmospheric Science: An Introductory Survey</i></a>. Elsevier. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-08-049953-6</bdi>.</cite></li></ul>

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<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="http://www.grida.no/climate/ipcc_tar/wg1/index.htm">IPCC Third Assessment Report</a></li>

<li><a rel="nofollow" class="external text" href="http://visualdaq.com/DaqPlaner/">Pictorial Representation of Temperature Gradient (Tools)</a>.</li></ul>

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