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      Introduction to climate dynamics and climate modelling - Composition and temperature
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                <a href="index.html">Introduction to climate dynamics and climate modelling</a>
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            <h2>
              1.2.1 Composition and temperature
            </h2>
            <p>
            
              <a name="dry_air" href="glossary_d.html#dry_air">Dry air</a> is mainly composed of nitrogen (78.08% in volume), oxygen (20.95% in volume),
              argon (0.93% in volume) and to a lesser extent carbon dioxide<a name="footnote1"
              href="#footnote" id="tex2html2"><sup>1</sup></a> (380 ppm or 0.038% in
              volume). The remaining fraction is made up of various trace constituents such as
              neon (18 ppm), helium (5 ppm), methane<a name="tex2html2"
              href="#footnote" id="tex2html2"><sup>1</sup></a> (1.75 ppm), and krypton (1 ppm). In addition, a
              highly variable amount of water vapor is present in the air. This  ranges
              from approximately 0% in the coldest part of the atmosphere to as much as 5% in moist and
              hot regions. On average, water vapor accounts for 0.25% of the mass of the
              atmosphere.
            </p>
            <p>
              On a large-scale, the atmosphere is very close to <a href="glossary_h.xml#hydrostatic_equilibrium">hydrostatic equilibrium</a>, meaning
              that at a height <span class="textit">z,</span> the force due to the pressure
              <i>p</i> on a 1 m<sup>2</sup>
              horizontal surface balances the force due to the weight of the air above <i>z</i>. 
              The atmospheric pressure is thus at its maximum at the Earth's surface and the
              surface pressure <i>p</i><sub>s</sub> is directly related
              the mass of the whole air column at a particular location. Pressure then decreases
              with height, closely following an exponential law:
            </p>
            <div class="mathdisplay c1">
              <a name="eq1x01" id="eq1x01"></a><!-- MATH
 \begin{equation}
p\simeq p_{s} e^{{-z\mathord{\left/ {\vphantom {-z H}} \right. \kern-\nulldelimiterspace} H} }
\end{equation}
 -->
              <table class="equation" cellpadding="0" width="90%" align="center">
                <tr valign="middle">
                  <td nowrap="nowrap" align="center">
                    <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" 
                    overflow="scroll"><mi>p</mi><mo>&#x2243;</mo><msub><mi>p</mi><mi>s</mi></msub>
                    <msup><mi>e</mi><mrow><mo>-</mo><mi>z</mi><mo>/</mo><mi>H</mi></mrow></msup>
                    <mspace linebreak="newline"/></math>
                  </td>
                  <td nowrap="nowrap" class="eqno" width="10" align="right">
                    (<span class="arabic">1</span>.<span class="arabic">1</span>)
                  </td>
                </tr>
              </table>
            </div>
            <p>
              where <i>H</i> is a scale height (which is between 7 and 8 km
              for the lowest 100 km of the atmosphere). Because of this clear and monotonic
              relationship between height and pressure, pressure is often used as a vertical
              coordinate for the atmosphere. Indeed, pressure is easier to measure than height and
              choosing a pressure coordinate simplifies the formulation of some equations.
            </p>
            <p>
              The temperature in the <a name="tropposphere" href="glossary_t.html#troposphere">troposphere</a>, roughly the lowest 10 km of the atmosphere,
              generally decreases with height. The rate of this decrease is called the <a name="lapse_rate " href="glossary_l.xml#lapse_rate">lapse rate </a>
 <math xmlns="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mi>&#x0393;</mi></math>
:
            </p>
            <div class="mathdisplay c1">
              <a name="eq1x02" id="eq1x02"></a><!-- MATH
 \begin{equation}
{\it\Gamma }=-\frac{\partial T}{\partial z}
\end{equation}
 -->
              <table class="equation" cellpadding="0" width="90%" align="center">
                <tr valign="middle">
                  <td nowrap="nowrap" align="center">
                    <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" 
                    overflow="scroll"><mi>&#x0393;</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mo>
                    &#x2202;</mo><mi>T</mi></mrow><mrow><mo>&#x2202;</mo><mi>z</mi></mrow></mfrac>
                    <mspace linebreak="newline"/></math>
                  </td>
                  <td nowrap="nowrap" class="eqno" width="10" align="right">
                    (<span class="arabic">1</span>.<span class="arabic">2</span>)
                  </td>
                </tr>
              </table>
            </div>
            <p>
              where <span class="textit">T</span> is the temperature. The lapse rate depends mainly
              on the radiative balance of the atmosphere (see section <a href="chapter2_node3.xml">2.1.1</a>) and on 
              <a href="glossary_c.xml#convection">convection</a> as
              well as on the horizontal heat transport. Its global mean value is about 6.5
              K km<sup>-1</sup>, but
              <math xmlns="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mi>&#x0393;</mi></math> varies with the location and season.
            </p>
            <p>
              The lapse rate is an important characteristic of the atmosphere. For instance, it
              determines its vertical stability. For low values of the lapse rate, the atmosphere
              is very stable, inhibiting vertical movements. Negative lapse rates (i.e. temperature
              increasing with height), called temperature inversions, correspond to highly stable
              conditions. When the lapse rate rises, the stability decreases, leading in some 
              cases to vertical instability and <a href="glossary_c.xml#convection">convection</a>. The lapse rate is also
              involved in <a href="glossary_f.xml#feedback">feedbacks</a> playing an important role in the response of the climate system
              to a perturbation (see section <a href="chapter4_node7.html">4.2.1</a>).
            </p>
            <p>
At an altitude of about 10 km, a region of weak vertical temperature <a 
href="glossary_g.xml#gradient">gradients</a>, called the <a name="tropopause"
href="glossary_t.html#tropopause">tropopause</a>, separates the <a 
href="glossary_t.html#troposphere">troposphere</a> from the <a name="stratosphere"
href="glossary_s.xml#stratosphere">stratosphere</a> where the temperature 
generally increases with height until the stratopause at around 50 km (Fig. <a 
href="#image1x02">1.2</a>). Above the stratopause, temperature decreases strongly with height in the mesosphere, 
until the mesopause is reached at an altitude of about 80 km, and then increases 
again in the thermosphere above this height. The 
vertical <a href="glossary_g.xml#gradient">gradients</a> above 10 km are 
strongly influenced by the absorption of solar radiation by different 
atmospheric constituents and by chemical reactions driven by the incoming 
light. In particular, the warming in the stratosphere at heights of about 30-50 
km is mostly due to the absorption of ultraviolet <a 
href="glossary_r.html#radiation">radiation</a> by stratospheric <a 
name="ozone" href="glossary_o.xml#ozone">ozone</a>, which protects  life on 
Earth from this dangerous <a href="glossary_r.html#radiation">radiation</a>. 
</p>

            <div align="center">
              <a name="image1x02" id="image1x02"></a><a name="192"></a>
              <table>
                <caption align="bottom"><p align="center">
<strong>Figure 1.2:</strong> Idealised <a href="glossary_z.html#zonal">
zonal</a> mean temperature (in <span class= "MATH"><sup><tt>o</tt></sup></span>
C) in the atmosphere as a function of the height (or of the pressure). The 
dashed lines represent schematically the location of the tropopause, 
stratopause and mesopause. This figure was published in Atmospheric science: 
an introductory survey, <a class="ref" href="chapter1_node17.html">Wallace and Hobbs, International Geophysics Series 92, 
Copyright Elsevier (Academic Press) 2006</a>. </p></caption>

                <tr>
                  <td>
                    <div align="center">
                      <img align="bottom" border="0" src=
                      "./images/image1x02.jpg" alt="Image image1x02" />
                    </div>
                  </td>
                </tr>
              </table>
            </div>
            <p>
              Atmospheric <a  name="specific_humidity" href="glossary_s.xml#specific_humidity">specific humidity</a> also displays a characteristic vertical profile with
              maximum values in the lower levels and a marked decrease with height. As a
              consequence, the air above the tropopause is nearly dry. This vertical distribution
              is mainly due to two processes. First, the major source of atmospheric water vapour
              is evaporation at the surface. Secondly, the warmer air close to the surface 
              can contain a much larger quantity of water before it becomes saturated than the colder air further away; 
              saturation that leads to the formation of water or ice droplets, clouds and eventually precipitation.
            </p>
            <p>
              At the Earth’s surface, the temperature reaches its maximum in equatorial regions (Fig.
              <a href="#image1x03x04">1.3</a>) because of the higher
              incoming radiations (see section <a href="chapter2_node6.html">2.1.4</a>). In those regions, the temperature is
              relatively constant throughout the year. Because of the much stronger seasonal cycle
              at mid and high latitudes, the north-south gradients are much larger in winter than
              in summer. The distribution of the surface temperature is also influenced by
              atmospheric and oceanic heat transport as well as by the thermal inertia of the ocean
              (see section <a href="chapter2_node7.xml">2.1.5</a>). Furthermore, the role of topography is important, with a
              temperature decrease at higher altitudes associated with the positive lapse rate in
              the troposphere.
            </p>
            <div align="center">
              <a name="image1x03x04" id="image1x03x04"></a><a name="472"></a>
              <table>
                <caption align="bottom"><p align="center">
                  <strong>Figure 1.3:</strong> Surface air temperature (in <span class=
                  "MATH"><sup><tt>o</tt></sup></span>C) averaged over (a) December, January, and February
                  and (b) June, July, and August. Data source: Brohan et al. (2005).
                  <a href="http://www.cru.uea.ac.uk/cru/data/temperature/">http://www.cru.uea.ac.uk/cru/data/temperature/</a>
                </p></caption>
                <tr>
                  <td>
                    <div class="c1">
                      <img align="bottom" border="0" src=
                      "./images/image1x03.png" alt="Image image1x03" />
                    </div>
                  </td>
                </tr>
                <tr>
                  <td>
                    <div class="c1">
                      <img align="bottom" border="0" src="./images/image1x04.png" alt=
                      "Image image1x04" />
                    </div>
                  </td>
                </tr>
              </table>
              <br/>
            </div>
             <a href="#footnote1" name="footnote"><sup>1</sup></a> The concentrations of carbon dioxide and methane are 
             changing quickly (see section <a href="chapter2_node10.html">2.3</a>).
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