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      Introduction to climate dynamics and climate modelling - Heat transport
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            <h3>
              <a name="section215" id="section215"></a>
              2.1.5.2 Heat transport
            </h3>
            <p>
              Locally, heat storage by the climate system cannot compensate for the net
              radiative flux imbalance at the top of the atmosphere and, annually, the
              balance is nearly entirely achieved by heat transport from regions with a positive
              net radiative flux to regions with a negative net radiative flux. When the balance is
              averaged over latitudinal circles (<a href="glossary_z.html#zonal">zonal</a> mean), this corresponds to a <a name="meridional" href="glossary_m.xml#meridional">meridional</a> heat
              transport from equatorial to polar regions (Fig. <a href="#image054">2.17</a>). This poleward heat
              transport at a latitude <math xmlns="http://www.w3.org/1998/Math/MathML" overflow="scroll">
<mi>&#x03C6;</mi></math>
 can be estimated by
              integrating the net radiative balance at the top of the atmosphere from the South
              Pole to latitude <math xmlns="http://www.w3.org/1998/Math/MathML" overflow="scroll">
<mi>&#x03C6;</mi></math>
:
            </p>
            <div class="mathdisplay c1">
              <!-- MATH
 \begin{equation}
RT(\phi )=\int _{-\pi /2}^{\phi }\int _{0}^{2\pi }RF_{TOA} \left(\lambda ,\phi '\right) R^{2} \cos \phi 'd\lambda  d\phi '
\end{equation}
 -->
              <table class="equation" cellpadding="0" width="90%" align="center">
                <tr valign="middle">
                  <td nowrap="nowrap" align="center">
                    <math xmlns="http://www.w3.org/1998/Math/MathML" display="block" 
                    overflow="scroll"><mrow><mi>R</mi><mi>T</mi></mrow><mfenced><mi>&#x03C6;</mi>
                    </mfenced><mo>=</mo><munderover><mo>&#x222B;</mo><mrow><mo>-</mo><mi>&#x03C0;
                    </mi><mo>/</mo><mn>2</mn></mrow><mi>&#x03C6;</mi></munderover><munderover><mo>
                    &#x222B;</mo><mn>0</mn><mrow><mn>2</mn><mi>&#x03C0;</mi></mrow></munderover>
                    <mi>R</mi><msub><mi>F</mi><mrow><mi>T</mi><mi>O</mi><mi>A</mi></mrow></msub>
                    <mfenced close=")" open="(" separators=""><mi>&#x03BB;</mi><mi>,</mi><mi>
                    &#x03C6;</mi><mi>'</mi></mfenced><msup><mi>R</mi><mn>2</mn></msup><mi>cos</mi>
                    <mo>&#x2061;</mo><mi>&#x03C6;</mi><mi>'</mi><mi>d</mi><mi>&#x03BB;</mi><mi>
                    d</mi><mi>&#x03C6;</mi><mi>'</mi></math>
                  </td>
                  <td nowrap="nowrap" class="eqno" width="10" align="right">
                    (<span class="arabic">2</span>.<span class="arabic">31</span>)
                  </td>
                </tr>
              </table>
            </div>
            <p>
              The heat transport obtained is nearly zero at the equator, rising to more than 5
              PW at latitudes of about 35°, before declining again towards zero at the
              poles (Fig. <a href="#image054">2.17</a>). It can be divided into  an oceanic and an atmospheric
              contribution, the horizontal transport on continental surface being negligible. This
              shows that, except in tropical areas, the atmospheric transport is much larger than
              the oceanic transport.
            </p>
            <div align="center">
              <a name="image054" id="image054"></a><a name="517"></a>
              <table>
                <caption align="bottom"><p align="center">
                  <strong>Figure 2.17:</strong> The required total (RT) heat transport in PW (10<sup>15</sup>
                  W), needed to balance the net radiation imbalance
                  at the top of the atmosphere 
                  (in black) and the repartition of this transport in oceanic (blue) 
                  and atmospheric (red) contributions, accompanied with the associated 
                  uncertainty range (shaded). A positive value of the transport on the x 
                  axis corresponds to a northward transport. 
                  Figure from <a class="ref" href="chapter2_node16.html">Fasullo and Trenberth (2008)</a>. 
                  Copyright 2008 American Meteorological Society (AMS).
 </p></caption>

                <tr>
                  <td>
                    <div align="center">
                      <img  align="bottom" border="0" HEIGHT="350px" width="510px" src=
                      "./images/image(15).png" alt="Image image(15)" />
                    </div>
                  </td>
                </tr>
              </table>
            </div>
            <p>
              The energy can be transported as <a href="glossary_s.xml#sensible_heat">sensible heat</a> (<i>c</i><sub>p</sub><i>T</i>, which is related to <a name="internal_energy" href="glossary_i.xml#internal_energy">internal energy</a>), potential energy (<i>gz</i>), <a name="latent_heat" href="glossary_l.xml#latent_heat">latent heat</a> (<span class="MATH c2">Lq</span>) and kinetic
              energy (0.5 <i>u</i><sup>2</sup>) and is expressed per unit
              of mass as:
            </p>
            <div class="mathdisplay c1">
              <!-- MATH
 \begin{equation}
E=c_{p} T+gz+L_{v} q+0.5u^{2}
\end{equation}
 -->
              <table class="equation" cellpadding="0" width="90%" align="center">
                <tr valign="middle">
                  <td nowrap="nowrap" align="center">
                    <span class="MATH"><i>E</i> = <i>c</i><sub>p</sub><i>T</i> + <i>gz</i> +
                    <i>L</i><sub>v</sub><i>q</i> + 0.5<i>u</i><sup>2</sup></span>
                  </td>
                  <td nowrap="nowrap" class="eqno" width="10" align="right">
                    (<span class="arabic">2</span>.<span class="arabic">32</span>)
                  </td>
                </tr>
              </table>
            </div><br clear="all" />
            <p>
              where <i>z</i> is the altitude (or depth), <i>L</i><sub>v</sub> the latent heat of vaporisation of water,
              <i>q</i> the <a href="glossary_s.xml#specific_humidity">specific humidity</a> and <i>u</i> the velocity of the media. 
              The first term is often called <a name="sensible_heat" href="glossary_s.xml#sensible_heat">sensible
              heat</a>. The transport of kinetic energy is much weaker than the other transports and is generally
              neglected. In the atmosphere, the three remaining terms must be taken into account, but in the ocean 
              the transport of sensible heat is clearly dominant. Moreover, in some special cases, an additional term 
              representing the transport of latent heat by sea ice and icebergs must be considered for local or regional 
              analyses at high latitudes.
            </p>
            <p>
              In the tropics, the majority of the atmospheric poleward heat transport is achieved
              by the <a name="hadley_circulation" href="glossary_h.xml#hadley_cell">Hadley circulation</a>. By contrast, the mean circulation plays a much weaker role
              at mid to high latitudes where nearly all the transport is effected by <a name="eddies" href="glossary_e.xml#eddies">eddies</a>. In the
              ocean, both the wind-driven and deep-oceanic circulation are responsible for a
              significant part of the oceanic poleward heat transport, the latter having a dominant
              influence in the tropics. The role of the oceanic <a href="glossary_e.xml#eddies">eddies</a> is less well known, 
              but they can be significant in at least some regions (such as the Southern Ocean). 
            </p>
            <p>
              In addition to its dominant role in the reduction of the temperature contrast between
              the equator and the poles on Earth (compared to a planet without an ocean and an
              atmosphere), horizontal heat transport is also responsible for some temperature
              differences on a regional scale. This can be illustrated by analysing the departure
              of the local temperature from to the <a href="glossary_z.html#zonal">zonal</a> mean temperature. At first sight,
              Fig <a href="#image056">2.18</a> emphasises the mountainous area such as the Tibetan Plateau, the Rocky Mountains
              and Greenland, where the temperature is much lower than at other locations at the
              same latitude. However, the influence of the atmospheric circulation is also clearly
              apparent with, for instance, in cold areas such as north-east Canada. This is because 
              the dominant winds have a strong northerly component in this region, while the North 
              Atlantic is warmer, partly because of the south-westerly winds in this region 
              (see section <a href="chapter1_node5.html">1.2.2</a>). Over
              the ocean, the influence of the northward western boundary currents 
              (see section <a href="chapter1_node9.html">1.3.2</a>)
              results in generally warmer surface oceanic temperature at about <!-- MATH
 $30-40^\circ$
 -->
               30-40°N in the western part of the
              basin than in the eastern part (where the oceanic currents are generally bringing
              colder water from the North).
            </p>
            <div align="center">
              <a name="image056" id="image056"></a><a name="530"></a>
              <table>
                <caption align="bottom"><p align="center">
                  <strong>Figure 2.18:</strong> Difference between the annual mean surface
                  temperature and the <a href="glossary_z.html#zonal">zonal</a> mean temperature (computed as
                  the annual mean temperature measured at one particular point minus the mean
                  temperature obtained at the same latitude but averaged over all possible
                  longitudes). Data from the HadCRUT2 dataset <a class="ref" href="chapter2_node16.html">(Rayner et al., 2003)</a>.
                </p></caption>
                <tr>
                  <td>
                    <div align="center">
                      <img align="bottom" border="0" src=
                      "./images/image(16).png" alt="Image image(16)" />
                    </div>
                  </td>
                </tr>
              </table>
            </div>
            <p>
              The <a name="thermohaline_circulation" href="glossary_t.html#thermohaline_circulation">thermohaline circulation</a> is an additional source of longitudinal asymmetry as, in
              the Northern Hemisphere, <a name="deep_water_formation" href="glossary_d.html#deep_water_formation">deep water formation</a> only occurs in the North Atlantic
              and not in the North Pacific (see section <a href="chapter1_node9.html">1.3.2</a>). 
              The associated circulation transports
              cold water southward at great depths with the mass balance ensured by a corresponding northward
              transport of warmer water in the surface layer. This results in a net oceanic
              transport in the North Atlantic of about 0.8 PW at 
              <!-- MATH
 $30^\circ N$
 -->
               <span class="MATH">30<sup><tt>o</tt></sup><i></i></span>N, (i.e. more than twice the
              estimated transport in the wider Pacific at the same latitude). The <a href="glossary_t.html#thermohaline_circulation">thermohaline circulation</a> is also responsible for the northward oceanic heat transport at all
              latitudes in the Atlantic, even in the Southern Hemisphere.
            </p>
            <p>
              This oceanic heat transport contributes to the fact that higher temperatures 
              are observed in the North Atlantic than in other oceanic basins. Its influence 
              is particularly large in the Barents Sea, north of Norway. Thanks to the oceanic 
              heat transport, this area located north of  70°N (i.e., at the same latitude as 
              the northern part of Alaska) remains free of sea ice all year long. Climate model 
              calculations have shown that, if deep water formation was suppressed in the North 
              Atlantic, the temperature in the North Atlantic and in Western Europe would be reduced by about
              3°C at 45°N, while the annual mean temperature would decrease by more than 15° C in northern 
              Norway and the Barents Sea.
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