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<title>Potential temperature</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Potential temperature</span></span>

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<p>The <b>potential temperature</b> of a <a href="Air_parcel" class="mw-redirect" title="Air parcel">parcel</a> of fluid at pressure <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}">

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<annotation encoding="application/x-tex">{\displaystyle P}</annotation>

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</math></span><img src="./b4dc73bf40314945ff376bd363916a738548d40a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}" loading="lazy"></span> is the temperature that the parcel would attain if <a href="Adiabatic_process" title="Adiabatic process">adiabatically</a> brought to a standard reference pressure <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{0}}">

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<annotation encoding="application/x-tex">{\displaystyle P_{0}}</annotation>

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</math></span><img src="./671bd891701e0d6cfa6da0114a5dd64233b58709.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.547ex; height:2.509ex;" alt="{\displaystyle P_{0}}" loading="lazy"></span>, usually 1,000 hPa (1,000 mb). The potential temperature is denoted <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }">

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<annotation encoding="application/x-tex">{\displaystyle \theta }</annotation>

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</math></span><img src="./6e5ab2664b422d53eb0c7df3b87e1360d75ad9af.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }" loading="lazy"></span> and, for a gas well-approximated as <a href="Ideal_gas" title="Ideal gas">ideal</a>, is given by

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<annotation encoding="application/x-tex">{\displaystyle \theta =T\left({\frac {P_{0}}{P}}\right)^{R/c_{p}},}</annotation>

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</math></span><img src="./f6d406a44fe1b439c93712f9a89dcb32707aa1a7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:17.125ex; height:6.676ex;" alt="{\displaystyle \theta =T\left({\frac {P_{0}}{P}}\right)^{R/c_{p}},}" loading="lazy"></span></dd></dl>

<p>where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}">

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<annotation encoding="application/x-tex">{\displaystyle T}</annotation>

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</math></span><img src="./ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}" loading="lazy"></span> is the current absolute <a href="Temperature" title="Temperature">temperature</a> (in K) of the parcel, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}">

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<annotation encoding="application/x-tex">{\displaystyle R}</annotation>

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</math></span><img src="./4b0bfb3769bf24d80e15374dc37b0441e2616e33.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}" loading="lazy"></span> is the <a href="Specific_gas_constant" class="mw-redirect" title="Specific gas constant">specific gas constant</a> of air, and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{p}}">

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<annotation encoding="application/x-tex">{\displaystyle c_{p}}</annotation>

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</math></span><img src="./77463f4fbb953a6f1fe19d83708e553f6d21457f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.066ex; height:2.343ex;" alt="{\displaystyle c_{p}}" loading="lazy"></span> is the <a href="Specific_heat_capacity" title="Specific heat capacity">specific heat capacity</a> at a constant pressure.

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<annotation encoding="application/x-tex">{\displaystyle R/c_{p}=0.286}</annotation>

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</math></span><img src="./d8129c1a0a799d9ed5a829addaa0349032d2f3b7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.388ex; height:3.009ex;" alt="{\displaystyle R/c_{p}=0.286}" loading="lazy"></span> for air (meteorology). The reference point for potential temperature in the ocean is usually at the ocean's surface which has a water pressure of 0 dbar.<sup id="cite_ref-Talley_1-0" class="reference"><a href="#cite_note-Talley-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The potential temperature in the ocean doesn't account for the varying heat capacities of seawater, therefore it is not a conservative measure of heat content.<sup id="cite_ref-Talley_1-1" class="reference"><a href="#cite_note-Talley-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Graphical representation of potential temperature will always be less than the actual temperature line in a temperature vs depth graph.<sup id="cite_ref-Talley_1-2" class="reference"><a href="#cite_note-Talley-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

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

<p>The concept of potential temperature applies to any stratified fluid. It is most frequently used in the <a href="Atmospheric_sciences" class="mw-redirect" title="Atmospheric sciences">atmospheric sciences</a> and <a href="Oceanography" title="Oceanography">oceanography</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The reason that it is used

in both fields is that changes in pressure can result in warmer fluid residing under colder fluid – examples being dropping air temperature with altitude and increasing water temperature with depth in very deep ocean trenches and

within the ocean <a href="Mixed_layer" title="Mixed layer">mixed layer</a>. When the potential temperature is used instead, these apparently unstable conditions vanish as a parcel of fluid is invariant along its isolines. In the oceans, the potential temperature referenced to the surface will be slightly less than the in-situ temperature (the temperature that a water volume has at the specific depth that the instrument measured it in) since the expansion due to reduction in pressure leads to cooling.<sup id="cite_ref-Talley_1-3" class="reference"><a href="#cite_note-Talley-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The numeric difference between the in situ and potential temperature is almost always less than 1.5 degrees Celsius. However, it's important to use potential temperature when comparing temperatures of water from very different depths.<sup id="cite_ref-Talley_1-4" class="reference"><a href="#cite_note-Talley-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

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

<p>Potential temperature is a more dynamically important quantity than the actual temperature. This is because it is not affected by the physical lifting or sinking associated with flow over obstacles or large-scale atmospheric turbulence. A parcel of air moving over a small mountain will expand and cool as it ascends the slope, then compress and warm as it descends on the other side- but the potential temperature will not change in the absence of heating, cooling, evaporation, or condensation (processes that exclude these effects are referred to as dry adiabatic). Since parcels with the same potential temperature can be exchanged without work or heating being required, lines of constant potential temperature are natural flow pathways.

</p><p>Under almost all circumstances, potential temperature increases upwards in the atmosphere, unlike actual temperature which may increase or decrease. Potential temperature is conserved for all dry adiabatic processes, and as such is an important quantity in the <a href="Planetary_boundary_layer" title="Planetary boundary layer">planetary boundary layer</a> (which is often very close to being dry adiabatic).

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<p>Potential temperature is a useful measure of the static stability of the unsaturated atmosphere. Under normal, stably stratified conditions, the potential temperature increases with height,<sup id="cite_ref-Moore_3-0" class="reference"><a href="#cite_note-Moore-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {\partial \theta }{\partial z}}>0}</annotation>

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<p>and vertical motions are suppressed. If the potential temperature decreases with height,<sup id="cite_ref-Moore_3-1" class="reference"><a href="#cite_note-Moore-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {\partial \theta }{\partial z}}<0}</annotation>

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</math></span><img src="./954999df502b440856d057a8580b1392c0affc8c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:7.506ex; height:5.509ex;" alt="{\displaystyle {\frac {\partial \theta }{\partial z}}<0}" loading="lazy"></span></dd></dl>

<p>the atmosphere is unstable to vertical motions, and <a href="Atmospheric_convection" title="Atmospheric convection">convection</a> is likely. Since convection acts to quickly mix the atmosphere and return to a stably stratified state, observations of decreasing potential temperature with height are uncommon, except while vigorous convection is underway or during periods of strong <a href="Insolation" class="mw-redirect" title="Insolation">insolation</a>. Situations in which the <a href="Equivalent_potential_temperature" title="Equivalent potential temperature">equivalent potential temperature</a> decreases with height, indicating instability in saturated air, are much more common.

</p><p>Since potential temperature is conserved under adiabatic or <a href="Isentropic" class="mw-redirect" title="Isentropic">isentropic</a> air motions, in steady, adiabatic flow lines or surfaces of constant potential temperature act as <a href="Streamlines%2C_streaklines%2C_and_pathlines" title="Streamlines, streaklines, and pathlines">streamlines</a> or flow surfaces, respectively. This fact is used in <a href="Isentropic_analysis" title="Isentropic analysis">isentropic analysis</a>, a form of synoptic analysis which allows visualization of air motions and in particular analysis of large-scale vertical motion.<sup id="cite_ref-Moore_3-2" class="reference"><a href="#cite_note-Moore-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Potential_temperature_perturbations">Potential temperature perturbations</h2></div>

<p>The <a href="Atmospheric_boundary_layer" class="mw-redirect" title="Atmospheric boundary layer">atmospheric boundary layer</a> (ABL) potential temperature perturbation is defined as the difference between the potential temperature of the ABL and the potential temperature of the free atmosphere above the ABL. This value is called the potential temperature deficit in the case of a <a href="Katabatic" class="mw-redirect" title="Katabatic">katabatic</a> flow, because the surface will always be colder than the free atmosphere and the PT perturbation will be negative.

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

<p>The <a href="Enthalpy" title="Enthalpy">enthalpy</a> form of the first law of <a href="Thermodynamics" title="Thermodynamics">thermodynamics</a> can be written as:

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<annotation encoding="application/x-tex">{\displaystyle dh=T\,ds+v\,dp,}</annotation>

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</math></span><img src="./a2280306e2b87a79421f2e4eab4a813c5cdd77cc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.37ex; height:2.509ex;" alt="{\displaystyle dh=T\,ds+v\,dp,}" loading="lazy"></span></dd></dl>

<p>where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dh}">

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<annotation encoding="application/x-tex">{\displaystyle dh}</annotation>

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</math></span><img src="./009d10a6e60a51483f875b809ea17244dd9b6021.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.555ex; height:2.176ex;" alt="{\displaystyle dh}" loading="lazy"></span> denotes the <a href="Enthalpy" title="Enthalpy">enthalpy</a> change, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}">

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<annotation encoding="application/x-tex">{\displaystyle T}</annotation>

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</math></span><img src="./ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}" loading="lazy"></span> the temperature, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ds}">

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<annotation encoding="application/x-tex">{\displaystyle ds}</annotation>

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</math></span><img src="./5f0fb36e4308227d3e4a1f809c2571ec02527100.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.306ex; height:2.176ex;" alt="{\displaystyle ds}" loading="lazy"></span> the change in <a href="Entropy" title="Entropy">entropy</a>, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v}">

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<annotation encoding="application/x-tex">{\displaystyle v}</annotation>

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</math></span><img src="./e07b00e7fc0847fbd16391c778d65bc25c452597.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}" loading="lazy"></span> the specific volume, and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}">

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<annotation encoding="application/x-tex">{\displaystyle p}</annotation>

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</math></span><img src="./81eac1e205430d1f40810df36a0edffdc367af36.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}" loading="lazy"></span> the pressure.

</p><p>For adiabatic processes, the change in entropy is 0 and the 1st law simplifies to:

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<annotation encoding="application/x-tex">{\displaystyle dh=v\,dp.}</annotation>

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</math></span><img src="./db163a4e135203c8e099df27f15e509b75dc25e7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.2ex; height:2.509ex;" alt="{\displaystyle dh=v\,dp.}" loading="lazy"></span></dd></dl>

<p>For approximately ideal gases, such as the dry air in the Earth's atmosphere, the <a href="Equation_of_state" title="Equation of state">equation of state</a>, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle pv=RT}">

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<annotation encoding="application/x-tex">{\displaystyle pv=RT}</annotation>

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</math></span><img src="./670f4e82b7916a685c7cff956e0ae877c8593952.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:8.885ex; height:2.509ex;" alt="{\displaystyle pv=RT}" loading="lazy"></span> can be substituted into the 1st law

yielding, after some rearrangement:

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<annotation encoding="application/x-tex">{\displaystyle {\frac {dp}{p}}={{\frac {c_{p}}{R}}{\frac {dT}{T}}},}</annotation>

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</math></span><img src="./3b4c268b98e83d659b5f6a26954acfad8cec4f3b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:13.557ex; height:5.843ex;" alt="{\displaystyle {\frac {dp}{p}}={{\frac {c_{p}}{R}}{\frac {dT}{T}}},}" loading="lazy"></span></dd></dl>

<p>where the <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dh=c_{p}dT}">

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<annotation encoding="application/x-tex">{\displaystyle dh=c_{p}dT}</annotation>

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</math></span><img src="./78624d06b4725b9d6e70b10e9aec8d944d482aac.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.571ex; height:2.843ex;" alt="{\displaystyle dh=c_{p}dT}" loading="lazy"></span> was used and both terms were divided by the product <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle pv}">

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</math></span><img src="./63d184b2526218a57f12947ff9cf57c1211b2e75.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:2.386ex; height:2.009ex;" alt="{\displaystyle pv}" loading="lazy"></span>

</p><p><a href="Integral" title="Integral">Integrating</a> yields:

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<annotation encoding="application/x-tex">{\displaystyle \left({\frac {p_{1}}{p_{0}}}\right)^{R/c_{p}}={\frac {T_{1}}{T_{0}}},}</annotation>

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</math></span><img src="./22aa88465ff2a5b091a68a9ec64ab8dfecc46714.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:17.323ex; height:6.676ex;" alt="{\displaystyle \left({\frac {p_{1}}{p_{0}}}\right)^{R/c_{p}}={\frac {T_{1}}{T_{0}}},}" loading="lazy"></span></dd></dl>

<p>and solving for <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{0}}">

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<annotation encoding="application/x-tex">{\displaystyle T_{0}}</annotation>

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</math></span><img src="./55b9e7d7b96196b5a6a26f4349caa3ac82fd67e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.412ex; height:2.509ex;" alt="{\displaystyle T_{0}}" loading="lazy"></span>, the temperature a parcel would acquire if moved adiabatically to the pressure level <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{0}}">

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<annotation encoding="application/x-tex">{\displaystyle p_{0}}</annotation>

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</math></span><img src="./2b969ada68a88e2aeba9a2d2096abaf1fd53c21d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:2.313ex; height:2.009ex;" alt="{\displaystyle p_{0}}" loading="lazy"></span>, you get:

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<annotation encoding="application/x-tex">{\displaystyle T_{0}=T_{1}\left({\frac {p_{0}}{p_{1}}}\right)^{R/c_{p}}\equiv \theta .}</annotation>

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</math></span><img src="./9bc95f75355ad92dbad2671edc819559cf7a9ca8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:23.088ex; height:6.676ex;" alt="{\displaystyle T_{0}=T_{1}\left({\frac {p_{0}}{p_{1}}}\right)^{R/c_{p}}\equiv \theta .}" loading="lazy"></span></dd></dl>

<div class="mw-heading mw-heading2"><h2 id="Potential_virtual_temperature">Potential virtual temperature</h2></div>

<p>The potential <a href="Virtual_temperature" title="Virtual temperature">virtual temperature</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta _{v}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \theta _{v}}</annotation>

</semantics>

</math></span><img src="./660bba2634de6a1eb78a6d9e4f5c7acc8c406b91.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.12ex; height:2.509ex;" alt="{\displaystyle \theta _{v}}" loading="lazy"></span>, defined by

</p>

<msub>

</mrow>

</msub>

<mrow>

<mrow>

<msub>

</mrow>

</msub>

</mrow>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \theta _{v}=\theta \left(1+0.61r-r_{L}\right),}</annotation>

</semantics>

</math></span><img src="./5a0fb8d1d9286fef0391b5d45215ecd29a9637cf.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.966ex; height:2.843ex;" alt="{\displaystyle \theta _{v}=\theta \left(1+0.61r-r_{L}\right),}" loading="lazy"></span></dd></dl>

<p>is the theoretical potential temperature of the dry air which would have the same density as the humid air at a standard pressure P<sub>0</sub>. It is used as a practical substitute for density in buoyancy calculations. In this definition <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \theta }</annotation>

</semantics>

</math></span><img src="./6e5ab2664b422d53eb0c7df3b87e1360d75ad9af.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }" loading="lazy"></span> is the potential temperature, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle r}</annotation>

</semantics>

</math></span><img src="./0d1ecb613aa2984f0576f70f86650b7c2a132538.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}" loading="lazy"></span> is the mixing ratio of water vapor, and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r_{L}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle r_{L}}</annotation>

</semantics>

</math></span><img src="./d659907b5127a343e50492dee25a6b33a77fbe86.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.4ex; height:2.009ex;" alt="{\displaystyle r_{L}}" loading="lazy"></span> is the mixing ratio of liquid water in the air.

</p>

<div class="mw-heading mw-heading2"><h2 id="Related_quantities">Related quantities</h2></div>

<p>The <a href="Brunt%E2%80%93V%C3%A4is%C3%A4l%C3%A4_frequency" title="Brunt–Väisälä frequency">Brunt–Väisälä frequency</a> is a closely related quantity that uses potential temperature and is used extensively in investigations of atmospheric stability.

</p>

<ul><li><a href="Wet-bulb_potential_temperature" title="Wet-bulb potential temperature">Wet-bulb potential temperature</a></li>

<li><a href="Atmospheric_thermodynamics" title="Atmospheric thermodynamics">Atmospheric thermodynamics</a></li>

<li><a href="Conservative_temperature" title="Conservative temperature">Conservative temperature</a></li>

<li><a href="Equivalent_potential_temperature" title="Equivalent potential temperature">Equivalent potential temperature</a></li></ul>

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

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</style><cite id="CITEREFTalley2011" class="citation book cs1">Talley, Lynne D. (2011). <a rel="nofollow" class="external text" href="https://www.sciencedirect.com/book/9780750645522/descriptive-physical-oceanography"><i>Descriptive Physical Oceanography</i></a> (Sixth ed.). Boston: Elsevier. pp. <span class="nowrap">29–</span>65. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9780750645522</bdi>.</cite></span>

</li>

<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFStewart2008" class="citation book cs1">Stewart, Robert H. (September 2008). "6.5: Density, Potential Temperature, and Neutral Density". <a rel="nofollow" class="external text" href="https://www.academia.edu/download/35363446/book.pdf"><i>Introduction To Physical Oceanography</i></a> <span class="cs1-format">(PDF)</span>. Academia. pp. <span class="nowrap">83–</span>88<span class="reference-accessdate">. Retrieved <span class="nowrap">March 8,</span> 2017</span>.</cite></span>

</li>

<li id="cite_note-Moore-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-Moore_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Moore_3-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Moore_3-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFDr._James_T._Moore_(Saint_Louis_University_Dept._of_Earth_&_Atmospheric_Sciences)1999" class="citation web cs1">Dr. James T. Moore (Saint Louis University Dept. of Earth & Atmospheric Sciences) (August 5, 1999). <a rel="nofollow" class="external text" href="http://rams.atmos.colostate.edu/at540/fall03/isen.pdf">"Isentropic Analysis Techniques: Basic Concepts"</a> <span class="cs1-format">(PDF)</span>. COMET COMAP<span class="reference-accessdate">. Retrieved <span class="nowrap">March 8,</span> 2017</span>.</cite></span>

</li>

</ol></div></div>

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

<ul><li>M K Yau and R.R. Rogers, <i>Short Course in Cloud Physics, Third Edition</i>, published by Butterworth-Heinemann, January 1, 1989, 304 pages. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9780750632157</bdi> <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-7506-3215-1</bdi></li></ul>

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

<ul><li><a rel="nofollow" class="external text" href="http://scienceworld.wolfram.com/physics/PotentialTemperature.html">Eric Weisstein's World of Physics</a> at Wolfram Research</li></ul>

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</style><div id="Meteorological_data_and_variables132" style="font-size:114%;margin:0 4em">Meteorological data and variables</div></th></tr><tr><th scope="row" class="navbox-group" style="background-color: skyblue;width:1%">General</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Adiabatic_process" title="Adiabatic process">Adiabatic processes</a></li>

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

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

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

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

<li><a href="Solar_radiation" class="mw-redirect" title="Solar radiation">Surface solar radiation</a></li>

<li><a href="Surface_weather_analysis" title="Surface weather analysis">Surface weather analysis</a></li>

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

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

<li><a href="Wind_shear" title="Wind shear">Wind shear</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="background-color: skyblue;width:1%"><a href="Condensation" title="Condensation">Condensation</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Cloud" title="Cloud">Cloud</a></li>

<li><a href="Cloud_condensation_nuclei" title="Cloud condensation nuclei">Cloud condensation nuclei (CCN)</a></li>

<li><a href="Convective_condensation_level" title="Convective condensation level">Convective condensation level (CCL)</a></li>

<li><a href="Lifting_condensation_level" title="Lifting condensation level">Lifting condensation level (LCL)</a></li>

<li><a href="Precipitable_water" title="Precipitable water">Precipitable water</a></li>

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

<li><a href="Water_vapor" title="Water vapor">Water vapor</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="background-color: skyblue;width:1%"><a href="Atmospheric_convection" title="Atmospheric convection">Convection</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Convective_available_potential_energy" title="Convective available potential energy">Convective available potential energy (CAPE)</a></li>

<li><a href="Convective_inhibition" title="Convective inhibition">Convective inhibition (CIN)</a></li>

<li><a href="Convective_instability" title="Convective instability">Convective instability</a></li>

<li><a href="Convective_momentum_transport" title="Convective momentum transport">Convective momentum transport</a></li>

<li><a href="Conditional_symmetric_instability" title="Conditional symmetric instability">Conditional symmetric instability</a></li>

<li><a href="Convective_temperature" title="Convective temperature">Convective temperature (<i>T</i><sub>c</sub>)</a></li>

<li><a href="Equilibrium_level" title="Equilibrium level">Equilibrium level (EL)</a></li>

<li><a href="Free_convective_layer" title="Free convective layer">Free convective layer (FCL)</a></li>

<li><a href="Hydrodynamical_helicity#Meteorology" title="Hydrodynamical helicity">Helicity</a></li>

<li><a href="K-index_(meteorology)" title="K-index (meteorology)">K Index</a></li>

<li><a href="Level_of_free_convection" title="Level of free convection">Level of free convection (LFC)</a></li>

<li><a href="Lifted_index" title="Lifted index">Lifted index (LI)</a></li>

<li><a href="Maximum_parcel_level" title="Maximum parcel level">Maximum parcel level (MPL)</a></li>

<li><a href="Bulk_Richardson_number" title="Bulk Richardson number">Bulk Richardson number (BRN)</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="background-color: skyblue;width:1%"><a href="Temperature" title="Temperature">Temperature</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Dew_point" title="Dew point">Dew point (<i>T</i><sub>d</sub>)</a></li>

<li><a href="Dew_point_depression" title="Dew point depression">Dew point depression</a></li>

<li><a href="Dry-bulb_temperature" title="Dry-bulb temperature">Dry-bulb temperature</a></li>

<li><a href="Equivalent_temperature" title="Equivalent temperature">Equivalent temperature (<i>T</i><sub>e</sub>)</a></li>

<li><a href="Forest_fire_weather_index" title="Forest fire weather index">Forest fire weather index</a></li>

<li><a href="Haines_Index" title="Haines Index">Haines Index</a></li>

<li><a href="Heat_index" title="Heat index">Heat index</a></li>

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

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

<li><a href="Relative_humidity" class="mw-redirect" title="Relative humidity">Relative humidity (RH)</a></li>

<li><a href="Mixing_ratio" title="Mixing ratio">Mixing ratio</a></li>

<li><a href="Equivalent_potential_temperature" title="Equivalent potential temperature">Equivalent potential temperature (<i>θ</i><sub>e</sub>)</a></li>

<li><a href="Sea_surface_temperature" title="Sea surface temperature">Sea surface temperature (SST)</a></li>

<li><a href="Temperature_anomaly" title="Temperature anomaly">Temperature anomaly</a></li>

<li><a href="Thermodynamic_temperature" title="Thermodynamic temperature">Thermodynamic temperature</a></li>

<li><a href="Vapor_pressure" title="Vapor pressure">Vapor pressure</a></li>

<li><a href="Virtual_temperature" title="Virtual temperature">Virtual temperature</a></li>

<li><a href="Wet-bulb_temperature" title="Wet-bulb temperature">Wet-bulb temperature</a></li>

<li><a href="Wet-bulb_globe_temperature" title="Wet-bulb globe temperature">Wet-bulb globe temperature</a></li>

<li><a href="Wet-bulb_potential_temperature" title="Wet-bulb potential temperature">Wet-bulb potential temperature</a></li>

<li><a href="Wind_chill" title="Wind chill">Wind chill</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="background-color: skyblue;width:1%"><a href="Pressure" title="Pressure">Pressure</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Atmospheric_pressure" title="Atmospheric pressure">Atmospheric pressure</a></li>

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

<li><a href="Barotropic" class="mw-redirect" title="Barotropic">Barotropicity</a></li>

<li><a href="Pressure_gradient" title="Pressure gradient">Pressure gradient</a></li>

<li><a href="Pressure-gradient_force" title="Pressure-gradient force">Pressure-gradient force (PGF)</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="background-color: skyblue;width:1%"><a href="Velocity" title="Velocity">Velocity</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Maximum_potential_intensity" title="Maximum potential intensity">Maximum potential intensity</a></li></ul>

</div></td></tr></tbody></table></div></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-01-06" href="https://en.wikipedia.org/wiki/?title=Potential_temperature&oldid=1267769771">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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