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<div class="section" id="column-volume-mixing-ratio-derivations">
<h1>column volume mixing ratio derivations</h1>
<ol class="arabic">
<li><p class="first">column volume mixing ratio from column number density</p>
<table border="1" class="docutils">
<colgroup>
<col width="12%" />
<col width="33%" />
<col width="20%" />
<col width="34%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">symbol</th>
<th class="head">description</th>
<th class="head">unit</th>
<th class="head">variable name</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td><span class="math notranslate nohighlight">\(c\)</span></td>
<td>total column number density of total air</td>
<td><span class="math notranslate nohighlight">\(\frac{molec}{m^2}\)</span></td>
<td><cite>column_number_density {:}</cite></td>
</tr>
<tr class="row-odd"><td><span class="math notranslate nohighlight">\(c_{x}\)</span></td>
<td>total column number density for air
component x (e.g. <span class="math notranslate nohighlight">\(c_{O_{3}}\)</span>)</td>
<td><span class="math notranslate nohighlight">\(\frac{molec}{m^2}\)</span></td>
<td><cite><species>_column_number_density {:}</cite></td>
</tr>
<tr class="row-even"><td><span class="math notranslate nohighlight">\(\nu_{x}\)</span></td>
<td>column volume mixing ratio of
quantity x with regard to total air</td>
<td><span class="math notranslate nohighlight">\(ppv\)</span></td>
<td><cite><species>_column_volume_mixing_ratio {:}</cite></td>
</tr>
</tbody>
</table>
<p>The pattern <cite>:</cite> for the dimensions can represent <cite>{latitude,longitude}</cite>, <cite>{time}</cite>, <cite>{time,latitude,longitude}</cite>,
or no dimensions at all.</p>
<div class="math notranslate nohighlight">
\[\nu_{x} = \frac{c_{x}}{c}\]</div>
</li>
<li><p class="first">column volume mixing ratio dry air from column number density</p>
<table border="1" class="docutils">
<colgroup>
<col width="16%" />
<col width="28%" />
<col width="19%" />
<col width="37%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">symbol</th>
<th class="head">description</th>
<th class="head">unit</th>
<th class="head">variable name</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td><span class="math notranslate nohighlight">\(c_{dry\_air}\)</span></td>
<td>total column number density of dry air</td>
<td><span class="math notranslate nohighlight">\(\frac{molec}{m^2}\)</span></td>
<td><cite>dry_air_column_number_density {:}</cite></td>
</tr>
<tr class="row-odd"><td><span class="math notranslate nohighlight">\(c_{x}\)</span></td>
<td>total column number density for air
component x (e.g. <span class="math notranslate nohighlight">\(c_{O_{3}}\)</span>)</td>
<td><span class="math notranslate nohighlight">\(\frac{molec}{m^2}\)</span></td>
<td><cite><species>_column_number_density {:}</cite></td>
</tr>
<tr class="row-even"><td><span class="math notranslate nohighlight">\(\bar{\nu}_{x}\)</span></td>
<td>column volume mixing ratio of
quantity x with regard to dry air</td>
<td><span class="math notranslate nohighlight">\(ppv\)</span></td>
<td><cite><species>_column_volume_mixing_ratio_dry_air {:}</cite></td>
</tr>
</tbody>
</table>
<p>The pattern <cite>:</cite> for the dimensions can represent <cite>{latitude,longitude}</cite>, <cite>{time}</cite>, <cite>{time,latitude,longitude}</cite>,
or no dimensions at all.</p>
<div class="math notranslate nohighlight">
\[\bar{\nu}_{x} = \frac{c_{x}}{c_{dry\_air}}\]</div>
</li>
<li><p class="first">column volume mixing ratio from column mass mixing ratio</p>
<table border="1" class="docutils">
<colgroup>
<col width="13%" />
<col width="34%" />
<col width="18%" />
<col width="35%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">symbol</th>
<th class="head">description</th>
<th class="head">unit</th>
<th class="head">variable name</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td><span class="math notranslate nohighlight">\(M_{air}\)</span></td>
<td>molar mass for total air</td>
<td><span class="math notranslate nohighlight">\(\frac{g}{mol}\)</span></td>
<td><cite>molar_mass {:}</cite></td>
</tr>
<tr class="row-odd"><td><span class="math notranslate nohighlight">\(M_{x}\)</span></td>
<td>molar mass for air component x</td>
<td><span class="math notranslate nohighlight">\(\frac{g}{mol}\)</span></td>
<td> </td>
</tr>
<tr class="row-even"><td><span class="math notranslate nohighlight">\(q_{x}\)</span></td>
<td>column mass mixing ratio of quantity x
with regard to total air</td>
<td><span class="math notranslate nohighlight">\(\frac{kg}{kg}\)</span></td>
<td><cite><species>_column_mass_mixing_ratio {:}</cite></td>
</tr>
<tr class="row-odd"><td><span class="math notranslate nohighlight">\(\nu_{x}\)</span></td>
<td>column volume mixing ratio of quantity x
with regard to total air</td>
<td><span class="math notranslate nohighlight">\(ppv\)</span></td>
<td><cite><species>_column_volume_mixing_ratio {:}</cite></td>
</tr>
</tbody>
</table>
<p>The pattern <cite>:</cite> for the dimensions can represent <cite>{latitude,longitude}</cite>, <cite>{time}</cite>, <cite>{time,latitude,longitude}</cite>,
or no dimensions at all.</p>
<div class="math notranslate nohighlight">
\[\nu_{x} = q_{x}\frac{M_{air}}{M_{x}}\]</div>
</li>
<li><p class="first">column volume mixing ratio dry air from column mass mixing ratio dry air</p>
<table border="1" class="docutils">
<colgroup>
<col width="16%" />
<col width="30%" />
<col width="16%" />
<col width="38%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">symbol</th>
<th class="head">description</th>
<th class="head">unit</th>
<th class="head">variable name</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td><span class="math notranslate nohighlight">\(M_{dry\_air}\)</span></td>
<td>molar mass for dry air</td>
<td><span class="math notranslate nohighlight">\(\frac{g}{mol}\)</span></td>
<td> </td>
</tr>
<tr class="row-odd"><td><span class="math notranslate nohighlight">\(M_{x}\)</span></td>
<td>molar mass for air component x</td>
<td><span class="math notranslate nohighlight">\(\frac{g}{mol}\)</span></td>
<td> </td>
</tr>
<tr class="row-even"><td><span class="math notranslate nohighlight">\(\bar{q}_{x}\)</span></td>
<td>column mass mixing ratio of quantity x
with regard to dry air</td>
<td><span class="math notranslate nohighlight">\(\frac{kg}{kg}\)</span></td>
<td><cite><species>_column_mass_mixing_ratio_dry_air {:}</cite></td>
</tr>
<tr class="row-odd"><td><span class="math notranslate nohighlight">\(\bar{\nu}_{x}\)</span></td>
<td>column volume mixing ratio of quantity x
with regard to dry air</td>
<td><span class="math notranslate nohighlight">\(ppv\)</span></td>
<td><cite><species>_column_volume_mixing_ratio_dry_air {:}</cite></td>
</tr>
</tbody>
</table>
<p>The pattern <cite>:</cite> for the dimensions can represent <cite>{latitude,longitude}</cite>, <cite>{time}</cite>, <cite>{time,latitude,longitude}</cite>,
or no dimensions at all.</p>
<div class="math notranslate nohighlight">
\[\bar{\nu}_{x} = \bar{q}_{x}\frac{M_{dry\_air}}{M_{x}}\]</div>
</li>
<li><p class="first">stratospheric column volume mixing ratio dry air from stratospheric column mass mixing ratio dry air</p>
<table border="1" class="docutils">
<colgroup>
<col width="14%" />
<col width="27%" />
<col width="14%" />
<col width="44%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">symbol</th>
<th class="head">description</th>
<th class="head">unit</th>
<th class="head">variable name</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td><span class="math notranslate nohighlight">\(M_{dry\_air}\)</span></td>
<td>molar mass for dry air</td>
<td><span class="math notranslate nohighlight">\(\frac{g}{mol}\)</span></td>
<td> </td>
</tr>
<tr class="row-odd"><td><span class="math notranslate nohighlight">\(M_{x}\)</span></td>
<td>molar mass for air component x</td>
<td><span class="math notranslate nohighlight">\(\frac{g}{mol}\)</span></td>
<td> </td>
</tr>
<tr class="row-even"><td><span class="math notranslate nohighlight">\(\bar{q}_{x}\)</span></td>
<td>stratospheric column mass mixing ratio
of quantity x with regard to dry air</td>
<td><span class="math notranslate nohighlight">\(\frac{kg}{kg}\)</span></td>
<td><cite>stratospheric_<species>_column_mass_mixing_ratio_dry_air {:}</cite></td>
</tr>
<tr class="row-odd"><td><span class="math notranslate nohighlight">\(\bar{\nu}_{x}\)</span></td>
<td>stratospheric column volume mixing ratio
of quantity x with regard to dry air</td>
<td><span class="math notranslate nohighlight">\(ppv\)</span></td>
<td><cite>stratospheric_<species>_column_volume_mixing_ratio_dry_air {:}</cite></td>
</tr>
</tbody>
</table>
<p>The pattern <cite>:</cite> for the dimensions can represent <cite>{latitude,longitude}</cite>, <cite>{time}</cite>, <cite>{time,latitude,longitude}</cite>,
or no dimensions at all.</p>
<div class="math notranslate nohighlight">
\[\bar{\nu}_{x} = \bar{q}_{x}\frac{M_{dry\_air}}{M_{x}}\]</div>
</li>
<li><p class="first">tropospheric column volume mixing ratio dry air from tropospheric column mass mixing ratio dry air</p>
<table border="1" class="docutils">
<colgroup>
<col width="15%" />
<col width="27%" />
<col width="15%" />
<col width="44%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">symbol</th>
<th class="head">description</th>
<th class="head">unit</th>
<th class="head">variable name</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td><span class="math notranslate nohighlight">\(M_{dry\_air}\)</span></td>
<td>molar mass for dry air</td>
<td><span class="math notranslate nohighlight">\(\frac{g}{mol}\)</span></td>
<td> </td>
</tr>
<tr class="row-odd"><td><span class="math notranslate nohighlight">\(M_{x}\)</span></td>
<td>molar mass for air component x</td>
<td><span class="math notranslate nohighlight">\(\frac{g}{mol}\)</span></td>
<td> </td>
</tr>
<tr class="row-even"><td><span class="math notranslate nohighlight">\(\bar{q}_{x}\)</span></td>
<td>tropospheric column mass mixing ratio
of quantity x with regard to dry air</td>
<td><span class="math notranslate nohighlight">\(\frac{kg}{kg}\)</span></td>
<td><cite>tropospheric_<species>_column_mass_mixing_ratio_dry_air {:}</cite></td>
</tr>
<tr class="row-odd"><td><span class="math notranslate nohighlight">\(\bar{\nu}_{x}\)</span></td>
<td>tropospheric column volume mixing ratio
of quantity x with regard to dry air</td>
<td><span class="math notranslate nohighlight">\(ppv\)</span></td>
<td><cite>tropospheric_<species>_column_volume_mixing_ratio_dry_air {:}</cite></td>
</tr>
</tbody>
</table>
<p>The pattern <cite>:</cite> for the dimensions can represent <cite>{latitude,longitude}</cite>, <cite>{time}</cite>, <cite>{time,latitude,longitude}</cite>,
or no dimensions at all.</p>
<div class="math notranslate nohighlight">
\[\bar{\nu}_{x} = \bar{q}_{x}\frac{M_{dry\_air}}{M_{x}}\]</div>
</li>
</ol>
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