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<h1>Guidelines for Construction of CF Standard Names</h1>
<div class="plain">
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1"><title>Guidelines for Construction of CF Standard Names</title><meta name="generator" content="DocBook XSL Stylesheets V1.73.2">
<div class="article" lang="en">
<div class="titlepage">
<div>
<div> </div>
<div>
<h3 class="subtitle"><em>Version 1, 3 December 2008</em></h3>
</div>
</div>
<hr></div>
<div class="toc">
<p><strong>Table of Contents</strong></p>
<dl><dt><span class="section"></span><br></dt><dt><span class="section"><a href="#id2797697">Characters</a></span></dt><dt><span class="section"><a href="#id2797709">Spelling</a></span></dt><dt><span class="section"><a href="#id2797725">Qualifications</a></span></dt><dd>
<dl><dt><span class="section"><a href="#surface">Surface</a></span></dt><dt><span class="section"><a href="#component">Component</a></span></dt><dt><span class="section"><a href="#medium">Medium</a></span></dt><dt><span class="section"><a href="#process">Process</a></span></dt><dt><span class="section"><a href="#condition">Condition</a></span></dt></dl>
</dd><dt><span class="section"><a href="#id2798144">Transformations</a></span></dt><dt><span class="section"><a href="#id2798851">Special Phrases</a></span></dt><dt><span class="section"><a href="#id2799094">Chemical Species</a></span></dt><dt><span class="section"><a href="#id2799225">Generic Names</a></span></dt></dl>
</div>
<div class="section" lang="en">
<div class="titlepage">
<div>
<div>
<h2 class="title"><a name="id2740549"></a></h2>
</div>
</div>
</div>
<p>
Most of the CF standard names in the Standard Name Table have been constructed following
the guidelines described here, which have themselves drawn on the
<a class="ulink" href="ecmwf-grib-mapping" target="_top">ECMWF</a>
and
<a class="ulink" href="ncep-grib-code-cf-standard-name-mapping" target="_top">NCEP</a>
GRIB tables, the
<a class="ulink" href="pcmdi-name-cf-standard-name-mapping" target="_top">PCMDI</a>
standard variable names, and the
<span class="link-external"><a class="ulink" href="http://gcmd.nasa.gov/Resources/valids" target="_top">NASA Global Change Master Directory</a></span>
. The guidelines may help to interpret the names and to suggest how new names could be derived.
Please send requests and questions concerning standard names to the
<span class="link-external"><a class="ulink" href="http://mailman.cgd.ucar.edu/mailman/listinfo/cf-metadata" target="_top">CF metadata mailing list</a></span>.</p>
</div>
<div class="section" lang="en">
<div class="titlepage">
<div>
<div>
<h2 class="title"><a name="id2797697"></a>Characters</h2>
</div>
</div>
</div>
<p>
Standard names consist of lower-letters, digits and underscores, and begin with a letter. Upper case is not used.</p>
</div>
<div class="section" lang="en">
<div class="titlepage">
<div>
<div>
<h2 class="title"><a name="id2797709"></a>Spelling</h2>
</div>
</div>
</div>
<p>
US spelling is used e.g. <code class="varname">vapor</code>, <code class="varname">sulfur</code>.</p>
</div>
<div class="section" lang="en">
<div class="titlepage">
<div>
<div>
<h2 class="title"><a name="id2797725"></a>Qualifications</h2>
</div>
</div>
</div>
<p>
Standard names may be qualified by the addition of phrases in certain standard forms and order. These qualifications do not change the units of the quantity. All of the following phrases in [] are optional. The words in <code class="varname">typewriter type</code> appear explicitly as stated, while the words in italic indicate other words or phrases to be substituted. The new standard name is constructed by joining the base standard name to the qualifiers using underscores.</p>
<p>
[<a title="Surface" class="link" href="#surface">surface</a>] [<a title="Component" class="link" href="#component">component</a>] standard_name [<code class="varname">at</code> <a title="Surface" class="link" href="#surface">surface</a>] [<code class="varname">in</code> <a title="Medium" class="link" href="#medium">medium</a>] [<code class="varname">due to</code> <a title="Process" class="link" href="#process">process</a>] [<code class="varname">assuming</code> <a title="Condition" class="link" href="#condition">condition</a>]</p>
<div class="section" lang="en">
<div class="titlepage">
<div>
<div>
<h3 class="title"><a name="surface"></a>Surface</h3>
</div>
</div>
</div>
<p>
A surface is defined as a function of horizontal position. Surfaces which are defined using a coordinate value (e.g. height of 1.5 m) are indicated by a single-valued coordinate variable, not by the standard name. In the standard name, some surfaces are named by single words which are placed at the start: <code class="varname">toa</code> (top of atmosphere), <code class="varname">tropopause</code>, <code class="varname">surface</code>. Other surfaces are named by multi-word phrases put after <code class="varname">at</code>:
<code class="varname">at_adiabatic_condensation_level</code>,
<code class="varname">at_cloud_top</code>,
<code class="varname">at_convective_cloud_top</code>,
<code class="varname">at_cloud_base</code>,
<code class="varname">at_convective_cloud_base</code>,
<code class="varname">at_freezing_level</code>,
<code class="varname">at_ground_level</code>,
<code class="varname">at_maximum_wind_speed_level</code>,
<code class="varname">at_sea_floor</code>,
<code class="varname">at_sea_ice_base</code>,
<code class="varname">at_sea_level</code>,
<code class="varname">at_top_of_atmosphere_boundary_layer</code>,
<code class="varname">at_top_of_atmosphere_model</code>,
<code class="varname">at_top_of_dry_convection</code>.
The surface called "<code class="varname">surface</code>" means the lower boundary of the atmosphere. <code class="varname">sea_level</code> means mean sea level, which is close to the geoid in sea areas. <code class="varname">ground_level</code> means the land surface (beneath the snow and surface water, if any). <code class="varname">cloud_base</code> refers to the base of the lowest cloud. <code class="varname">cloud_top</code> refers to the top of the highest cloud. Fluxes at the <code class="varname">top_of_atmosphere_model</code> differ from TOA fluxes only if the model TOA fluxes make some allowance for the atmosphere above the top of the model; if not, it is usual to give standard names with <code class="varname">toa</code> to the fluxes at the top of the model atmosphere.</p>
</div>
<div class="section" lang="en">
<div class="titlepage">
<div>
<div>
<h3 class="title"><a name="component"></a>Component</h3>
</div>
</div>
</div>
<p>
The direction of the spatial component of a vector is indicated by one of the words
<code class="varname">upward</code>,
<code class="varname">downward</code>,
<code class="varname">northward</code>,
<code class="varname">southward</code>,
<code class="varname">eastward</code>,
<code class="varname">westward</code>,
<code class="varname">x</code>,
<code class="varname">y</code>.
The last two indicate directions along the horizontal grid being used when they are not true longitude and latitude (if there is a rotated pole, for instance).
If the standard name indicates a tensor quantity, two of these direction words may be included, applying to two of the spatial dimensions Z Y X, in that order. If only one component is indicated for a tensor, it means the flux in the indicated direction of the magnitude of the vector quantity in the plane of the other two spatial dimensions.</p>
<p>
The names of vertical components of radiative fluxes are prefixed with <code class="varname">net_</code>, thus: <code class="varname">net_downward</code> and <code class="varname">net_upward</code>. This treatment is not applied for any kinds of flux other than radiative. Radiative fluxes from above and below are often measured and calculated separately, the "net" being the difference. Within the atmosphere, radiation from below (not net) is indicated by a prefix of <code class="varname">upwelling</code>, and from above with <code class="varname">downwelling</code>. For the top of the atmosphere, the prefixes <code class="varname">incoming</code> and <code class="varname">outgoing</code> are used instead.</p>
</div>
<div class="section" lang="en">
<div class="titlepage">
<div>
<div>
<h3 class="title"><a name="medium"></a>Medium</h3>
</div>
</div>
</div>
<p>
A medium indicates the local medium or layer within which an intensive quantity applies:
<code class="varname">in_air</code>,
<code class="varname">in_atmosphere_boundary_layer</code>,
<code class="varname">in_mesosphere</code>,
<code class="varname">in_sea_ice</code>,
<code class="varname">in_sea_water</code>,
<code class="varname">in_soil</code>,
<code class="varname">in_soil_water</code>,
<code class="varname">in_stratosphere</code>,
<code class="varname">in_thermosphere</code>,
<code class="varname">in_troposphere</code>.</p>
</div>
<div class="section" lang="en">
<div class="titlepage">
<div>
<div>
<h3 class="title"><a name="process"></a>Process</h3>
</div>
</div>
</div>
<p>
The specification of a physical process by the phrase <code class="varname">due_to_</code><span class="emphasis"><em>process</em></span> means that the quantity named is a single term in a sum of terms which together compose the general quantity named by omitting the phrase. Possibilites are:
<code class="varname">due_to_advection</code>,
<code class="varname">due_to_convection</code>,
<code class="varname">due_to_deep_convection</code>,
<code class="varname">due_to_diabatic_processes</code>,
<code class="varname">due_to_diffusion</code>,
<code class="varname">due_to_dry_convection</code>,
<code class="varname">due_to_gravity_wave_drag</code>,
<code class="varname">due_to_gyre</code>,
<code class="varname">due_to_isostatic_adjustment</code>,
<code class="varname">due_to_large_scale_precipitation</code>,
<code class="varname">due_to_longwave_heating</code>,
<code class="varname">due_to_moist_convection</code>,
<code class="varname">due_to_overturning</code>,
<code class="varname">due_to_shallow_convection</code>,
<code class="varname">due_to_shortwave_heating</code>,
<code class="varname">due_to_thermodynamics</code> (referring to sea ice freezing and melting).</p>
</div>
<div class="section" lang="en">
<div class="titlepage">
<div>
<div>
<h3 class="title"><a name="condition"></a>Condition</h3>
</div>
</div>
</div>
<p>
A phrase <code class="varname">assuming_</code><span class="emphasis"><em>condition</em></span> indicates that the named quantity is the value which would obtain if all aspects of the system were unaltered except for the assumption of the circumstances specified by the condition. Possibilities are
<code class="varname">assuming_clear_sky</code>,
<code class="varname">assuming_deep_snow</code>,
<code class="varname">assuming_no_snow</code>.</p>
</div>
</div>
<div class="section" lang="en">
<div class="titlepage">
<div>
<div>
<h2 class="title"><a name="id2798144"></a>Transformations</h2>
</div>
</div>
</div>
<p>
Standard names may be derived from other standard names (represented here by X, Y and Z) by the following rules. Successive transformations may be applied. Transformations may alter the units as shown.</p>
<div class="table"><a name="id2798156"></a>
<p class="title"><strong></strong></p>
<div class="table-contents">
<table border="1"><colgroup><col align="left"><col align="left"><col align="left"></colgroup>
<thead>
<tr>
<th align="left">Rule</th>
<th align="left">Units</th>
<th align="left">Meaning</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left"><code class="varname">change_over_time_in_</code>X</td>
<td align="left">[X]</td>
<td align="left">change in a quantity X over a time-interval, which should be defined by the bounds of the time coordinate.</td>
</tr>
<tr>
<td align="left">[<code class="varname">horizontal_</code>]<code class="varname">convergence_of_</code>X</td>
<td align="left">[X] <code class="varname">m-1</code></td>
<td align="left">[horizontal] convergence of a vector X (i.e. the divergence multiplied by -1); if X does not have a vertical component then "horizontal" should be omitted.</td>
</tr>
<tr>
<td align="left"><code class="varname">correlation_of_</code>X<code class="varname">_and_</code>Y[<code class="varname">_over_</code>Z]</td>
<td align="left"><code class="varname">1</code></td>
<td align="left">correlation coefficient for variations (over Z e.g. time, longitude) of X and Y. X and Y are ordered alphabetically.</td>
</tr>
<tr>
<td align="left"><code class="varname">covariance_of_</code>X<code class="varname">_and_</code>Y[_over_<code class="varname">Z</code>]</td>
<td align="left">[X]*[Y]</td>
<td align="left">covariance for variations (over Z e.g. time, longitude) of X and Y. X and Y are ordered alphabetically.</td>
</tr>
<tr>
<td align="left"><span class="emphasis"><em>component</em></span><code class="varname">_derivative_of_</code>X</td>
<td align="left">[X] <code class="varname">m-1</code></td>
<td align="left">derivative of X with respect to distance in the component direction, which may be <code class="varname">northward</code>, <code class="varname">southward</code>, <code class="varname">eastward</code>, <code class="varname">westward</code>, <code class="varname">x</code> or <code class="varname">y</code>. The last two indicate derivatives along the axes of the grid, in the case where they are not true longitude and latitude.</td>
</tr>
<tr>
<td align="left"><code class="varname">derivative_of_</code>X<code class="varname">_wrt_</code>Y</td>
<td align="left">[X]/[Y]</td>
<td align="left">dX/dY (keeping any other independent variables constant, i.e. the partial derivative if appropriate).</td>
</tr>
<tr>
<td align="left"><code class="varname">direction_of_</code>X</td>
<td align="left"><code class="varname">degree</code></td>
<td align="left">direction of a vector, a bearing.</td>
</tr>
<tr>
<td align="left">[<code class="varname">horizontal_</code>]<code class="varname">divergence_of_</code>X</td>
<td align="left">[X] <code class="varname">m-1</code></td>
<td align="left">[horizontal] divergence of a vector X; if X does not have a vertical component then "horizontal" should be omitted.</td>
</tr>
<tr>
<td align="left"><code class="varname">histogram_of_</code>X[<code class="varname">_over_</code>Z]</td>
<td align="left"><code class="varname">1</code></td>
<td align="left">histogram (i.e. number of counts for each range of X) of variations (over Z) of X. The data variable should have an axis for X.</td>
</tr>
<tr>
<td align="left"><code class="varname">integral_of_</code>Y<code class="varname">_wrt_</code>X</td>
<td align="left">[X]*[Y]</td>
<td align="left">int Y dX. The data variable should have an axis for X specifying the limits of the integral as bounds.</td>
</tr>
<tr>
<td align="left"><code class="varname">ln_</code>X</td>
<td align="left"><code class="varname">1</code></td>
<td align="left">natural logarithm of X. X must be dimensionless.</td>
</tr>
<tr>
<td align="left"><code class="varname">log10_</code>X</td>
<td align="left"><code class="varname">1</code></td>
<td align="left">common logarithm (i.e. base 10) of X. X must be dimensionless.</td>
</tr>
<tr>
<td align="left"><code class="varname">magnitude_of_</code>X</td>
<td align="left">[X]</td>
<td align="left">magnitude of a vector X.</td>
</tr>
<tr>
<td align="left"><code class="varname">probability_distribution_of_</code>X[<code class="varname">_over_</code>Z]</td>
<td align="left"><code class="varname">1</code></td>
<td align="left">probability distribution (i.e. a number in the range 0.0-1.0 for each range of X) of variations (over Z) of X. The data variable should have an axis for X.</td>
</tr>
<tr>
<td align="left"><code class="varname">probability_density_function_of_</code>X[<code class="varname">_over_</code>Z]</td>
<td align="left"><code class="varname">1</code>/[X]</td>
<td align="left">PDF for variations (over Z) of X. The data variable should have an axis for X.</td>
</tr>
<tr>
<td align="left"><code class="varname">product_of_</code>X<code class="varname">_and_</code>Y</td>
<td align="left">[X]*[Y]</td>
<td align="left">X*Y. If X and Y are both scalars or both components of vectors, they are put in alphabetical order. If one of them is the component of a vector, it is put first i.e. the vector component is X, the scalar is Y.</td>
</tr>
<tr>
<td align="left"><code class="varname">ratio_of_</code>X<code class="varname">_to_</code>Y</td>
<td align="left">[X]/[Y]</td>
<td align="left">X/Y.</td>
</tr>
<tr>
<td align="left"><code class="varname">square_of_</code>X</td>
<td align="left">[X]*[X]</td>
<td align="left">X*X.</td>
</tr>
<tr>
<td align="left"><code class="varname">tendency_of_</code>X</td>
<td align="left">[X] <code class="varname">s-1</code></td>
<td align="left">derivative of X with respect to time.</td>
</tr>
</tbody>
</table>
</div>
</div>
<p><br class="table-break"></p>
</div>
<div class="section" lang="en">
<div class="titlepage">
<div>
<div>
<h2 class="title"><a name="id2798851"></a>Special Phrases</h2>
</div>
</div>
</div>
<p>
Some words and phrases have meanings which should be noted.</p>
<div class="table"><a name="id2798860"></a>
<p class="title"><strong></strong></p>
<div class="table-contents">
<table border="1"><colgroup><col align="left"><col align="left"></colgroup>
<thead>
<tr>
<th align="left">Phrase</th>
<th align="left">Meaning</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left"><code class="varname">anomaly</code></td>
<td align="left">difference from climatology</td>
</tr>
<tr>
<td align="left"><code class="varname">area</code></td>
<td align="left">horizontal area unless otherwise stated</td>
</tr>
<tr>
<td align="left"><code class="varname">atmosphere</code></td>
<td align="left">used instead of <code class="varname">in_air</code> for quantities which are large-scale rather than local</td>
</tr>
<tr>
<td align="left"><code class="varname">condensed_water</code></td>
<td align="left">liquid and ice</td>
</tr>
<tr>
<td align="left"><code class="varname">frozen_water</code></td>
<td align="left">ice</td>
</tr>
<tr>
<td align="left"><code class="varname">longwave</code></td>
<td align="left">longwave radiation</td>
</tr>
<tr>
<td align="left"><code class="varname">lwe</code></td>
<td align="left">liquid water equivalent</td>
</tr>
<tr>
<td align="left"><code class="varname">moisture</code></td>
<td align="left">water in all phases contained in soil</td>
</tr>
<tr>
<td align="left"><code class="varname">ocean</code></td>
<td align="left">used instead of <code class="varname">in_sea_water</code> for quantities which are large-scale rather than local</td>
</tr>
<tr>
<td align="left"><code class="varname">shortwave</code></td>
<td align="left">shortwave radiation</td>
</tr>
<tr>
<td align="left"><code class="varname">specific</code></td>
<td align="left">per unit mass unless otherwise stated</td>
</tr>
<tr>
<td align="left"><code class="varname">stp</code></td>
<td align="left">standard temperature (0 degC) and pressure (101325 Pa)</td>
</tr>
<tr>
<td align="left"><code class="varname">toa</code></td>
<td align="left">top of atmosphere</td>
</tr>
<tr>
<td align="left"><code class="varname">unfrozen_water</code></td>
<td align="left">liquid and vapour</td>
</tr>
<tr>
<td align="left"><code class="varname">water</code></td>
<td align="left">water in all phases if not otherwise qualified</td>
</tr>
<tr>
<td align="left"><code class="varname">wrt</code></td>
<td align="left">with respect to</td>
</tr>
</tbody>
</table>
</div>
</div>
<p><br class="table-break"></p>
</div>
<div class="section" lang="en">
<div class="titlepage">
<div>
<div>
<h2 class="title"><a name="id2799094"></a>Chemical Species</h2>
</div>
</div>
</div>
<p>
The following names are used to identify chemical species in standard names.</p>
<div class="table"><a name="id2799104"></a>
<p class="title"><strong></strong></p>
<div class="table-contents">
<table border="1"><colgroup><col align="left"></colgroup>
<thead>
<tr>
<th align="left">Species</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left"><code class="varname">carbon_dioxide</code></td>
</tr>
<tr>
<td align="left"><code class="varname">dimethyl_sulfide</code></td>
</tr>
<tr>
<td align="left"><code class="varname">nitrate</code></td>
</tr>
<tr>
<td align="left"><code class="varname">nitrate_and_nitrite</code></td>
</tr>
<tr>
<td align="left"><code class="varname">nitrite</code></td>
</tr>
<tr>
<td align="left"><code class="varname">oxygen</code></td>
</tr>
<tr>
<td align="left"><code class="varname">ozone</code></td>
</tr>
<tr>
<td align="left"><code class="varname">phosphate</code></td>
</tr>
<tr>
<td align="left"><code class="varname">silicate</code></td>
</tr>
<tr>
<td align="left"><code class="varname">sulfate</code></td>
</tr>
<tr>
<td align="left"><code class="varname">sulfur_dioxide</code></td>
</tr>
</tbody>
</table>
</div>
</div>
<p><br class="table-break"></p>
</div>
<div class="section" lang="en">
<div class="titlepage">
<div>
<div>
<h2 class="title"><a name="id2799225"></a>Generic Names</h2>
</div>
</div>
</div>
<p>
The following names are used with consistent meanings and units as elements in other standard names, although they are themselves too general to be chosen as standard names. They are recorded here for reference only. <span class="emphasis"><em>These are not standard names.</em></span></p>
<div class="table"><a name="id2799240"></a>
<p class="title"><strong></strong></p>
<div class="table-contents">
<table border="1"><colgroup><col align="left"><col align="left"></colgroup>
<thead>
<tr>
<th align="left">Units</th>
<th align="left">Generic Name</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">kg m-2</td>
<td align="left">amount</td>
</tr>
<tr>
<td align="left">m2</td>
<td align="left">area</td>
</tr>
<tr>
<td align="left">1</td>
<td align="left">area_fraction</td>
</tr>
<tr>
<td align="left">1</td>
<td align="left">binary_mask</td>
</tr>
<tr>
<td align="left">1</td>
<td align="left">data_mask</td>
</tr>
<tr>
<td align="left">kg m-3</td>
<td align="left">density</td>
</tr>
<tr>
<td align="left">J</td>
<td align="left">energy</td>
</tr>
<tr>
<td align="left">J m-2</td>
<td align="left">energy_content</td>
</tr>
<tr>
<td align="left">J m-3</td>
<td align="left">energy_density</td>
</tr>
<tr>
<td align="left">s-1</td>
<td align="left">frequency</td>
</tr>
<tr>
<td align="left">s-1</td>
<td align="left">frequency_of_occurrence</td>
</tr>
<tr>
<td align="left">W m-2</td>
<td align="left">heat_flux</td>
</tr>
<tr>
<td align="left">W</td>
<td align="left">heat_transport</td>
</tr>
<tr>
<td align="left">m2 s-1</td>
<td align="left">horizontal_streamfunction</td>
</tr>
<tr>
<td align="left">m2 s-1</td>
<td align="left">horizontal_velocity_potential</td>
</tr>
<tr>
<td align="left">kg</td>
<td align="left">mass</td>
</tr>
<tr>
<td align="left">kg m-2 s-1</td>
<td align="left">mass_flux</td>
</tr>
<tr>
<td align="left">1</td>
<td align="left">mass_fraction</td>
</tr>
<tr>
<td align="left">1</td>
<td align="left">mass_mixing_ration</td>
</tr>
<tr>
<td align="left">kg s-1</td>
<td align="left">mass_transport</td>
</tr>
<tr>
<td align="left">1</td>
<td align="left">mole_fraction</td>
</tr>
<tr>
<td align="left">mol m-2 s-1</td>
<td align="left">mole_flux</td>
</tr>
<tr>
<td align="left">Pa</td>
<td align="left">momentum_flux</td>
</tr>
<tr>
<td align="left">Pa</td>
<td align="left">partial_pressure</td>
</tr>
<tr>
<td align="left">s</td>
<td align="left">period</td>
</tr>
<tr>
<td align="left">W</td>
<td align="left">power</td>
</tr>
<tr>
<td align="left">Pa</td>
<td align="left">pressure</td>
</tr>
<tr>
<td align="left">1</td>
<td align="left">probability</td>
</tr>
<tr>
<td align="left">W m-2</td>
<td align="left">radiative_flux</td>
</tr>
<tr>
<td align="left">m2 s-2</td>
<td align="left">specific_eddy_kinetic_energy</td>
</tr>
<tr>
<td align="left">m s-1</td>
<td align="left">speed</td>
</tr>
<tr>
<td align="left">Pa</td>
<td align="left">stress</td>
</tr>
<tr>
<td align="left">K</td>
<td align="left">temperature</td>
</tr>
<tr>
<td align="left">m</td>
<td align="left">thickness</td>
</tr>
<tr>
<td align="left">m s-1</td>
<td align="left">velocity</td>
</tr>
<tr>
<td align="left">m3</td>
<td align="left">volume</td>
</tr>
<tr>
<td align="left">m s-1</td>
<td align="left">volume_flux</td>
</tr>
<tr>
<td align="left">1</td>
<td align="left">volume_fraction</td>
</tr>
<tr>
<td align="left">m3 s-1</td>
<td align="left">volume_transport</td>
</tr>
<tr>
<td align="left">s-1</td>
<td align="left">vorticity</td>
</tr>
</tbody>
</table>
</div>
</div>
<p><br class="table-break"></p>
</div>
</div>
</div>