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<div class="section" id="definitions">
<h1>Definitions</h1>
<div class="section" id="leading-dimensions">
<h2>Leading dimensions</h2>
<p>Many algorithms can be applied exactly the same to a variable even though it may have different dimension dependencies.
For instance, a density conversion can be the same algorithm for either <cite>density {}</cite>, <cite>density {time}</cite>,
<cite>density {latitude,longitude}</cite>, <cite>density {time,vertical}</cite>, etc.
The algorithm is just applied element-wise for each element in the dimensions that <cite>density</cite> depends on.
Such leading dimensions that can be handled element-wise are captured by a ‘:’ in the variable reference in the
definitions below.
Any dimensions that are significant for the conversion (for instance, the <cite>vertical</cite> dimension when integrating a
vertical profile to a total column) will still be mentioned explicitly and will map to an index in the symbol used for
the quantity (e.g. <span class="math notranslate nohighlight">\(\nu(:,i)\)</span>). If an algorithm has variables with a ‘:’ in the dimension specification then the
algorithm will contain a description of which combination of dimensions are supported for ‘:’.</p>
</div>
<div class="section" id="constants">
<h2>Constants</h2>
<table border="1" class="docutils">
<colgroup>
<col width="17%" />
<col width="25%" />
<col width="29%" />
<col width="28%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">symbol</th>
<th class="head">name</th>
<th class="head">unit</th>
<th class="head">value</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td><span class="math notranslate nohighlight">\(a\)</span></td>
<td>WGS84 semi-major axis</td>
<td><span class="math notranslate nohighlight">\(m\)</span></td>
<td><span class="math notranslate nohighlight">\(6378137.0\)</span></td>
</tr>
<tr class="row-odd"><td><span class="math notranslate nohighlight">\(b\)</span></td>
<td>WGS84 semi-minor axis</td>
<td><span class="math notranslate nohighlight">\(m\)</span></td>
<td><span class="math notranslate nohighlight">\(6356752.314245\)</span></td>
</tr>
<tr class="row-even"><td><span class="math notranslate nohighlight">\(c\)</span></td>
<td>speed of light</td>
<td><span class="math notranslate nohighlight">\(\frac{m}{s}\)</span></td>
<td><span class="math notranslate nohighlight">\(2.99792458\cdot10^{8}\)</span></td>
</tr>
<tr class="row-odd"><td><span class="math notranslate nohighlight">\(\frac{1}{f}\)</span></td>
<td>WGS84 inverse flatting</td>
<td> </td>
<td><span class="math notranslate nohighlight">\(298.257223563\)</span></td>
</tr>
<tr class="row-even"><td><span class="math notranslate nohighlight">\(g_{0}\)</span></td>
<td>mean earth gravity</td>
<td><span class="math notranslate nohighlight">\(\frac{m}{s^2}\)</span></td>
<td><span class="math notranslate nohighlight">\(9.80665\)</span></td>
</tr>
<tr class="row-odd"><td><span class="math notranslate nohighlight">\(g_{e}\)</span></td>
<td>earth gravity at equator</td>
<td><span class="math notranslate nohighlight">\(\frac{m}{s^2}\)</span></td>
<td><span class="math notranslate nohighlight">\(9.7803253359\)</span></td>
</tr>
<tr class="row-even"><td><span class="math notranslate nohighlight">\(g_{p}\)</span></td>
<td>earth gravity at poles</td>
<td><span class="math notranslate nohighlight">\(\frac{m}{s^2}\)</span></td>
<td><span class="math notranslate nohighlight">\(9.8321849378\)</span></td>
</tr>
<tr class="row-odd"><td><span class="math notranslate nohighlight">\(GM\)</span></td>
<td>WGS84 earth’s gravitational
constant</td>
<td><span class="math notranslate nohighlight">\(\frac{m^3}{s^2}\)</span></td>
<td><span class="math notranslate nohighlight">\(3986004.418\cdot10^{8}\)</span></td>
</tr>
<tr class="row-even"><td><span class="math notranslate nohighlight">\(k\)</span></td>
<td>Boltzmann constant</td>
<td><span class="math notranslate nohighlight">\(\frac{kg m^2}{K s^2}\)</span></td>
<td><span class="math notranslate nohighlight">\(1.38064852\cdot10^{-23}\)</span></td>
</tr>
<tr class="row-odd"><td><span class="math notranslate nohighlight">\(N_A\)</span></td>
<td>Avogadro constant</td>
<td><span class="math notranslate nohighlight">\(\frac{1}{mol}\)</span></td>
<td><span class="math notranslate nohighlight">\(6.022140857\cdot10^{23}\)</span></td>
</tr>
<tr class="row-even"><td><span class="math notranslate nohighlight">\(p_{0}\)</span></td>
<td>standard pressure</td>
<td><span class="math notranslate nohighlight">\(Pa\)</span></td>
<td><span class="math notranslate nohighlight">\(101325\)</span></td>
</tr>
<tr class="row-odd"><td><span class="math notranslate nohighlight">\(R\)</span></td>
<td>universal gas constant</td>
<td><span class="math notranslate nohighlight">\(\frac{kg m^2}{K mol s^2}\)</span></td>
<td><span class="math notranslate nohighlight">\(8.3144598\)</span></td>
</tr>
<tr class="row-even"><td><span class="math notranslate nohighlight">\(T_{0}\)</span></td>
<td>standard temperature</td>
<td><span class="math notranslate nohighlight">\(K\)</span></td>
<td><span class="math notranslate nohighlight">\(273.15\)</span></td>
</tr>
<tr class="row-odd"><td><span class="math notranslate nohighlight">\(\omega\)</span></td>
<td>WGS84 earth angular velocity</td>
<td><span class="math notranslate nohighlight">\(rad/s\)</span></td>
<td><span class="math notranslate nohighlight">\(7292115.0\cdot10^{-11}\)</span></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="molar-mass">
<h2>Molar mass</h2>
<p>The following table provides for each species the molar mass <span class="math notranslate nohighlight">\(M_{x}\)</span> in <span class="math notranslate nohighlight">\(\frac{g}{mol}\)</span>.</p>
<p>See the documentation on the HARP data format for a description of all species.</p>
<table border="1" class="docutils">
<colgroup>
<col width="13%" />
<col width="88%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">name</th>
<th class="head">molar mass</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td>dry air</td>
<td>28.9644</td>
</tr>
<tr class="row-odd"><td>BrO</td>
<td>95.9034</td>
</tr>
<tr class="row-even"><td>BrO2</td>
<td>111.9028</td>
</tr>
<tr class="row-odd"><td>CCl2F2</td>
<td>120.9135</td>
</tr>
<tr class="row-even"><td>CCl3F</td>
<td>137.3681</td>
</tr>
<tr class="row-odd"><td>CCl4</td>
<td>153.822</td>
</tr>
<tr class="row-even"><td>CF4</td>
<td>88.00431</td>
</tr>
<tr class="row-odd"><td>CHClF2</td>
<td>86.4684</td>
</tr>
<tr class="row-even"><td>CH3Cl</td>
<td>50.48752</td>
</tr>
<tr class="row-odd"><td>CH3CN</td>
<td>41.05192</td>
</tr>
<tr class="row-even"><td>CH3OH</td>
<td>32.04186</td>
</tr>
<tr class="row-odd"><td>CH4</td>
<td>16.0425</td>
</tr>
<tr class="row-even"><td>CO</td>
<td>28.0101</td>
</tr>
<tr class="row-odd"><td>COF2</td>
<td>66.0069</td>
</tr>
<tr class="row-even"><td>COS</td>
<td>60.0751</td>
</tr>
<tr class="row-odd"><td>CO2</td>
<td>44.0095</td>
</tr>
<tr class="row-even"><td>C2H2</td>
<td>26.0373</td>
</tr>
<tr class="row-odd"><td>C2H2O2</td>
<td>58.036163</td>
</tr>
<tr class="row-even"><td>C2H6</td>
<td>30.0690</td>
</tr>
<tr class="row-odd"><td>C2H3NO5</td>
<td>121.04892</td>
</tr>
<tr class="row-even"><td>C3H8</td>
<td>44.09562</td>
</tr>
<tr class="row-odd"><td>C5H8</td>
<td>68.11702</td>
</tr>
<tr class="row-even"><td>ClNO3</td>
<td>97.4579</td>
</tr>
<tr class="row-odd"><td>ClO</td>
<td>51.4524</td>
</tr>
<tr class="row-even"><td>HCHO</td>
<td>30.026</td>
</tr>
<tr class="row-odd"><td>HCOOH</td>
<td>46.0254</td>
</tr>
<tr class="row-even"><td>HCN</td>
<td>27.0253</td>
</tr>
<tr class="row-odd"><td>HCl</td>
<td>36.4609</td>
</tr>
<tr class="row-even"><td>HF</td>
<td>20.006343</td>
</tr>
<tr class="row-odd"><td>HNO2</td>
<td>47.013494</td>
</tr>
<tr class="row-even"><td>HNO3</td>
<td>63.0129</td>
</tr>
<tr class="row-odd"><td>HNO4</td>
<td>79.0122</td>
</tr>
<tr class="row-even"><td>HOCl</td>
<td>52.4603</td>
</tr>
<tr class="row-odd"><td>HO2</td>
<td>33.00674</td>
</tr>
<tr class="row-even"><td>H2O</td>
<td>18.0153</td>
</tr>
<tr class="row-odd"><td>H2O_161</td>
<td>1.00782503207 + 15.99491461956 + 1.00782503207</td>
</tr>
<tr class="row-even"><td>H2O_162</td>
<td>1.00782503207 + 15.99491461956 + 2.0141017778</td>
</tr>
<tr class="row-odd"><td>H2O_171</td>
<td>1.00782503207 + 16.99913170 + 1.00782503207</td>
</tr>
<tr class="row-even"><td>H2O_181</td>
<td>1.00782503207 + 17.9991610 + 1.00782503207</td>
</tr>
<tr class="row-odd"><td>H2O2</td>
<td>34.01468</td>
</tr>
<tr class="row-even"><td>IO</td>
<td>142.903873</td>
</tr>
<tr class="row-odd"><td>NH3</td>
<td>17.03056</td>
</tr>
<tr class="row-even"><td>NO</td>
<td>30.00610</td>
</tr>
<tr class="row-odd"><td>NOCl</td>
<td>65.4591</td>
</tr>
<tr class="row-even"><td>NO2</td>
<td>46.00550</td>
</tr>
<tr class="row-odd"><td>NO3</td>
<td>62.0049</td>
</tr>
<tr class="row-even"><td>N2</td>
<td>28.01340</td>
</tr>
<tr class="row-odd"><td>N2O</td>
<td>44.0129</td>
</tr>
<tr class="row-even"><td>N2O5</td>
<td>108.0104</td>
</tr>
<tr class="row-odd"><td>OClO</td>
<td>67.4518</td>
</tr>
<tr class="row-even"><td>OH</td>
<td>17.00734</td>
</tr>
<tr class="row-odd"><td>O2</td>
<td>32.000</td>
</tr>
<tr class="row-even"><td>O3</td>
<td>47.99820</td>
</tr>
<tr class="row-odd"><td>O3_666</td>
<td>15.99491461956 + 15.99491461956 + 15.99491461956</td>
</tr>
<tr class="row-even"><td>O3_667</td>
<td>15.99491461956 + 15.99491461956 + 16.99913170</td>
</tr>
<tr class="row-odd"><td>O3_668</td>
<td>15.99491461956 + 15.99491461956 + 17.9991610</td>
</tr>
<tr class="row-even"><td>O3_686</td>
<td>15.99491461956 + 17.9991610 + 15.99491461956</td>
</tr>
<tr class="row-odd"><td>O4</td>
<td>63.9976</td>
</tr>
<tr class="row-even"><td>SF6</td>
<td>146.0554</td>
</tr>
<tr class="row-odd"><td>SO2</td>
<td>64.0638</td>
</tr>
</tbody>
</table>
</div>
</div>
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