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<li class="toctree-l2 current"><a class="current reference internal" href="#">Axis variables</a><ul>
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<section id="axis-variables">
<h1>Axis variables</h1>
<p>HARP does not impose a fixed link between dimensions and its axis variables.
A product can contain multiple variables that can function as an axis variable for a dimension.
For instance, for the vertical dimension, a product can contain both a <code class="docutils literal notranslate"><span class="pre">pressure</span></code> and an <code class="docutils literal notranslate"><span class="pre">altitude</span></code> variable
where either can function as an axis variable.
The same applies for e.g. <code class="docutils literal notranslate"><span class="pre">wavelength</span></code> and <code class="docutils literal notranslate"><span class="pre">wavenumber</span></code> for the spectral axis.</p>
<p>In order for a variable to function as an axis variable it should have either strict ascending or strict descending values.</p>
<section id="intervals">
<h2>Intervals</h2>
<p>HARP has strict rules when it comes to dealing with the specification of an applicable interval along a dimension.</p>
<p>Especially for the vertical dimension there is often some degree of confusion about the concept of layers vs. levels
and whether levels are the centers of layers or the edges of layers.</p>
<p>Values in HARP are always provided at the <em>center</em> of an interval.
In HARP, levels are <em>always</em> the center point of layers and values are <em>always</em> provided at levels (never at layer edges).
If you have data that is provided at the edges of layers then you will have to redefine the layer grid when bringing
the data into HARP such that edges become centers (and centers become edges).</p>
<p>When using intervals, the axis variables should always indicate the center of these intervals.
A separate <code class="docutils literal notranslate"><span class="pre"><axis_variable>_bounds</span></code> variable can be used to define the edges of the intervals.
This bounds variable has one extra dimension, which is an independent dimension of length 2.
This independent dimension should contain the edge values of the interval.
The ordering of these values needs to be exactly the same as the ordering of the axis itself
(i.e. if the values of the axis are ascending, then the values defining the interval edges should also be ascending).</p>
<p>Intervals are usually connected. So, if for instance we have an altitude grid of center points <code class="docutils literal notranslate"><span class="pre">latitude</span> <span class="pre">=</span> <span class="pre">[5,</span> <span class="pre">10,</span> <span class="pre">15,</span> <span class="pre">20]</span></code>
then the corresponding intervals could be <code class="docutils literal notranslate"><span class="pre">latitude_bounds</span> <span class="pre">=</span> <span class="pre">[[2.5,</span> <span class="pre">7.5],</span> <span class="pre">[7.5,</span> <span class="pre">12.5],</span> <span class="pre">[12.5,</span> <span class="pre">17.5],</span> <span class="pre">[17.5,</span> <span class="pre">22.5]]</span></code>.</p>
<p>There are two special cases for intervals, which are described below.</p>
<section id="time-intervals">
<h3>Time intervals</h3>
<p>One special case is the time dimension.
In addition to a <code class="docutils literal notranslate"><span class="pre">datetime_bounds</span></code> variable, HARP supports separate <code class="docutils literal notranslate"><span class="pre">datetime_start</span></code> and <code class="docutils literal notranslate"><span class="pre">datetime_stop</span></code> variables
to define the edges of a time interval.
Be aware that in HARP the <code class="docutils literal notranslate"><span class="pre">datetime</span></code> variable always needs to represent the center of a time interval.</p>
<p>If you provide two out of <code class="docutils literal notranslate"><span class="pre">datetime</span></code>, <code class="docutils literal notranslate"><span class="pre">datetime_start</span></code>, <code class="docutils literal notranslate"><span class="pre">datetime_stop</span></code>, <code class="docutils literal notranslate"><span class="pre">datetime_length</span></code> then you can use
the HARP derivation operations to automatically have the other two variables calculated.
In addition any of these two can be converted into a <code class="docutils literal notranslate"><span class="pre">datetime_bounds</span></code> variable and vice-versa.</p>
</section>
<section id="spatial-extent">
<h3>Spatial extent</h3>
<p>The other special case is the spatial dimensions.</p>
<p>When data is gridded spatially using a <code class="docutils literal notranslate"><span class="pre">latitude</span></code> and <code class="docutils literal notranslate"><span class="pre">longitude</span></code> dimension then the normal rules apply and you
would have a <code class="docutils literal notranslate"><span class="pre">latitude_bounds</span> <span class="pre">{latitude,2}</span></code> and <code class="docutils literal notranslate"><span class="pre">longitude_bounds</span> <span class="pre">{longitude,2}</span></code> to define the edges of the grid cells.</p>
<p>However, when <code class="docutils literal notranslate"><span class="pre">latitude</span></code> and <code class="docutils literal notranslate"><span class="pre">longitude</span></code> are not explicit dimensions, which is the case when e.g. you have a time
series of areas, then <code class="docutils literal notranslate"><span class="pre">latitude_bounds</span></code> and <code class="docutils literal notranslate"><span class="pre">longitude_bounds</span></code> can still be used, but with a different convention.</p>
<ul class="simple">
<li><p>if the independent dimension in <code class="docutils literal notranslate"><span class="pre">latitude_bounds</span> <span class="pre">{time,independent}</span></code> and <code class="docutils literal notranslate"><span class="pre">longitude_bounds</span> <span class="pre">{time,independent}</span></code>
has a length of 2 then the two values define the corner of a bounding rectangle of a spatial area.</p></li>
<li><p>if the independent dimension has length 3 or higher, then the points define the vertices of a polygon that defines the spatial area.</p></li>
</ul>
<p>A bounding rectangle can always be represented by a 4 point polygon with the exact same meaning.
For instance, <code class="docutils literal notranslate"><span class="pre">latitude_bounds</span> <span class="pre">=</span> <span class="pre">[[3.3,</span> <span class="pre">7.1]]</span></code> and <code class="docutils literal notranslate"><span class="pre">longitude_bounds</span> <span class="pre">=</span> <span class="pre">[[50.8,</span> <span class="pre">53.6]]</span></code> as a bounding rectangle definition
is the same as <code class="docutils literal notranslate"><span class="pre">latitude_bounds</span> <span class="pre">=</span> <span class="pre">[[3.3,</span> <span class="pre">3.3,</span> <span class="pre">7.1,</span> <span class="pre">7.1]]</span></code> and <code class="docutils literal notranslate"><span class="pre">longitude_bounds</span> <span class="pre">=</span> <span class="pre">[[50.8,</span> <span class="pre">53.6,</span> <span class="pre">53.6,</span> <span class="pre">50.8]]</span></code>
in terms of a polygon definition (mind the counter clockwise ordering of the polygon points).</p>
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