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<li><a href="#introduction" id="toc-introduction" class="nav-link" data-scroll-target="#introduction"><span class="header-section-number">10.1</span> Introduction</a></li>
<li><a href="#methods" id="toc-methods" class="nav-link" data-scroll-target="#methods"><span class="header-section-number">10.2</span> Methods</a></li>
<li><a href="#example" id="toc-example" class="nav-link" data-scroll-target="#example"><span class="header-section-number">10.3</span> Example</a></li>
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<span class="chapter-number">10</span> <span class="chapter-title">Temporal reduction operations</span>
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<section id="configurations-to-run-this-chapter" class="level3 unnumbered"><h3 class="unnumbered anchored" data-anchor-id="configurations-to-run-this-chapter">Configurations to run this chapter</h3>
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<div class="code-copy-outer-scaffold"><div class="sourceCode" id="cb1"><pre class="downlit sourceCode r code-with-copy"><code class="sourceCode R"><span><span class="co"># load package "tibble"</span></span>
<span><span class="kw"><a href="https://rdrr.io/r/base/library.html">library</a></span><span class="op">(</span><span class="va"><a href="https://tibble.tidyverse.org/">tibble</a></span><span class="op">)</span></span>
<span><span class="co"># load packages "sits" and "sitsdata"</span></span>
<span><span class="kw"><a href="https://rdrr.io/r/base/library.html">library</a></span><span class="op">(</span><span class="va"><a href="https://github.com/e-sensing/sits/">sits</a></span><span class="op">)</span></span>
<span><span class="kw"><a href="https://rdrr.io/r/base/library.html">library</a></span><span class="op">(</span><span class="va"><a href="https://github.com/e-sensing/sitsdata/">sitsdata</a></span><span class="op">)</span></span>
<span><span class="co"># set tempdir if it does not exist </span></span>
<span><span class="va">tempdir_r</span> <span class="op"><-</span> <span class="st">"~/sitsbook/tempdir/R/dc_reduce"</span></span>
<span><span class="fu"><a href="https://rdrr.io/r/base/files2.html">dir.create</a></span><span class="op">(</span><span class="va">tempdir_r</span>, showWarnings <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></div>
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb2"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="co"># load "pysits" library</span></span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="im">from</span> pysits <span class="im">import</span> <span class="op">*</span></span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a><span class="im">from</span> pathlib <span class="im">import</span> Path</span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a><span class="co"># set tempdir if it does not exist </span></span>
<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a>tempdir_py <span class="op">=</span> Path.home() <span class="op">/</span> <span class="st">"sitsbook/tempdir/Python/dc_reduce"</span></span>
<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a>tempdir_py.mkdir(parents<span class="op">=</span><span class="va">True</span>, exist_ok<span class="op">=</span><span class="va">True</span>)</span></code></pre></div><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></div>
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</section><section id="introduction" class="level2" data-number="10.1"><h2 data-number="10.1" class="anchored" data-anchor-id="introduction">
<span class="header-section-number">10.1</span> Introduction</h2>
<p>There are cases when users want to combine the values of a time series associated to each pixel of a data cube using reduction operators. In time series analysis, a reduction operator is a function that combines a sequence of data points into a single value. This process involves summarizing or aggregating the information from the time series in a meaningful way. Reduction operators are often used to extract key statistics or features from the data, making it easier to analyze and interpret.</p>
</section><section id="methods" class="level2" data-number="10.2"><h2 data-number="10.2" class="anchored" data-anchor-id="methods">
<span class="header-section-number">10.2</span> Methods</h2>
<p>To produce temporal combinations, <code>sits</code> provides <code>sits_reduce</code>, with associated functions:</p>
<ul>
<li>
<code>t_max()</code>: maximum value of the series.</li>
<li>
<code>t_min()</code>: minimum value of the series</li>
<li>
<code>t_mean()</code>: mean of the series.</li>
<li>
<code>t_median()</code>: median of the series.</li>
<li>
<code>t_std()</code>: standard deviation of the series.</li>
<li>
<code>t_skewness()</code>: skewness of the series.</li>
<li>
<code>t_kurtosis()</code>: kurtosis of the series.</li>
<li>
<code>t_amplitude()</code>: difference between maximum and minimum values of the cycle. A small amplitude means a stable cycle.</li>
<li>
<code>t_fslope()</code>: maximum value of the first slope of the cycle. Indicates when the cycle presents an abrupt change in the curve. The slope between two values relates the speed of the growth or senescence phases</li>
<li>
<code>t_mse()</code>: average spectral energy density. The energy of the time series is distributed by frequency.</li>
<li>
<code>t_fqr()</code>: value of the first quartile of the series (0.25).</li>
<li>
<code>t_tqr()</code>: value of the third quartile of the series (0.75).</li>
<li>
<code>t_iqr()</code>: interquartile range (difference between the third and first quartiles).</li>
</ul>
<p>The functions <code>t_std()</code>, <code>t_skewness()</code>, <code>t_kurtosis()</code>, and <code>t_mse()</code> produce values greater than the limit of a two-byte integer. Therefore, we save the images generated by them in floating point format.</p>
</section><section id="example" class="level2" data-number="10.3"><h2 data-number="10.3" class="anchored" data-anchor-id="example">
<span class="header-section-number">10.3</span> Example</h2>
<p>The following example shows how to execute a temporal reduction operation.</p>
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<div class="code-copy-outer-scaffold"><div class="sourceCode" id="cb3"><pre class="downlit sourceCode r code-with-copy"><code class="sourceCode R"><span><span class="co"># Define a region of interest to be enclosed in the data cube</span></span>
<span><span class="va">roi</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span></span>
<span> <span class="st">"lon_min"</span> <span class="op">=</span> <span class="op">-</span><span class="fl">55.80259</span>, </span>
<span> <span class="st">"lon_max"</span> <span class="op">=</span> <span class="op">-</span><span class="fl">55.199</span>, </span>
<span> <span class="st">"lat_min"</span> <span class="op">=</span> <span class="op">-</span><span class="fl">11.80208</span>, </span>
<span> <span class="st">"lat_max"</span> <span class="op">=</span> <span class="op">-</span><span class="fl">11.49583</span></span>
<span><span class="op">)</span></span>
<span></span>
<span><span class="co"># Define a data cube in the MPC repository using NDVI MODIS data</span></span>
<span><span class="va">ndvi_cube</span> <span class="op"><-</span> <span class="fu"><a href="https://e-sensing.github.io/sits/reference/sits_cube.html">sits_cube</a></span><span class="op">(</span></span>
<span> source <span class="op">=</span> <span class="st">"MPC"</span>,</span>
<span> collection <span class="op">=</span> <span class="st">"MOD13Q1-6.1"</span>,</span>
<span> bands <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="st">"NDVI"</span><span class="op">)</span>,</span>
<span> roi <span class="op">=</span> <span class="va">roi</span>,</span>
<span> start_date <span class="op">=</span> <span class="st">"2018-05-01"</span>,</span>
<span> end_date <span class="op">=</span> <span class="st">"2018-09-30"</span></span>
<span><span class="op">)</span></span>
<span></span>
<span><span class="co"># Copy the cube to a local file system</span></span>
<span><span class="va">ndvi_cube_local</span> <span class="op"><-</span> <span class="fu"><a href="https://e-sensing.github.io/sits/reference/sits_cube_copy.html">sits_cube_copy</a></span><span class="op">(</span></span>
<span> cube <span class="op">=</span> <span class="va">ndvi_cube</span>,</span>
<span> output_dir <span class="op">=</span> <span class="va">tempdir_r</span>,</span>
<span> multicores <span class="op">=</span> <span class="fl">4</span></span>
<span><span class="op">)</span></span></code></pre></div><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></div>
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb4"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Define a region of interest to be enclosed in the data cube</span></span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a>roi <span class="op">=</span> <span class="bu">dict</span>(</span>
<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a> lon_min <span class="op">=</span> <span class="op">-</span><span class="fl">55.80259</span>, </span>
<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a> lon_max <span class="op">=</span> <span class="op">-</span><span class="fl">55.199</span>, </span>
<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a> lat_min <span class="op">=</span> <span class="op">-</span><span class="fl">11.80208</span>, </span>
<span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a> lat_max <span class="op">=</span> <span class="op">-</span><span class="fl">11.49583</span></span>
<span id="cb4-7"><a href="#cb4-7" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb4-8"><a href="#cb4-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb4-9"><a href="#cb4-9" aria-hidden="true" tabindex="-1"></a><span class="co"># Define a data cube in the MPC repository using NDVI MODIS data</span></span>
<span id="cb4-10"><a href="#cb4-10" aria-hidden="true" tabindex="-1"></a>ndvi_cube <span class="op">=</span> sits_cube(</span>
<span id="cb4-11"><a href="#cb4-11" aria-hidden="true" tabindex="-1"></a> source <span class="op">=</span> <span class="st">"MPC"</span>,</span>
<span id="cb4-12"><a href="#cb4-12" aria-hidden="true" tabindex="-1"></a> collection <span class="op">=</span> <span class="st">"MOD13Q1-6.1"</span>,</span>
<span id="cb4-13"><a href="#cb4-13" aria-hidden="true" tabindex="-1"></a> bands <span class="op">=</span> <span class="st">"NDVI"</span>,</span>
<span id="cb4-14"><a href="#cb4-14" aria-hidden="true" tabindex="-1"></a> roi <span class="op">=</span> roi,</span>
<span id="cb4-15"><a href="#cb4-15" aria-hidden="true" tabindex="-1"></a> start_date <span class="op">=</span> <span class="st">"2018-05-01"</span>,</span>
<span id="cb4-16"><a href="#cb4-16" aria-hidden="true" tabindex="-1"></a> end_date <span class="op">=</span> <span class="st">"2018-09-30"</span></span>
<span id="cb4-17"><a href="#cb4-17" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb4-18"><a href="#cb4-18" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb4-19"><a href="#cb4-19" aria-hidden="true" tabindex="-1"></a><span class="co"># Copy the cube to a local file system</span></span>
<span id="cb4-20"><a href="#cb4-20" aria-hidden="true" tabindex="-1"></a>ndvi_cube_local <span class="op">=</span> sits_cube_copy(</span>
<span id="cb4-21"><a href="#cb4-21" aria-hidden="true" tabindex="-1"></a> cube <span class="op">=</span> ndvi_cube,</span>
<span id="cb4-22"><a href="#cb4-22" aria-hidden="true" tabindex="-1"></a> output_dir <span class="op">=</span> tempdir_py,</span>
<span id="cb4-23"><a href="#cb4-23" aria-hidden="true" tabindex="-1"></a> multicores <span class="op">=</span> <span class="dv">4</span></span>
<span id="cb4-24"><a href="#cb4-24" aria-hidden="true" tabindex="-1"></a>)</span></code></pre></div><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></div>
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<p>After creating a local data cube based on the contents of the MPC MODIS cube with the NDVI band, we can now compute the maximum NDVI values for each pixel for the images during the period from 2018-05-01 to 2018-09-30.</p>
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<div class="code-copy-outer-scaffold"><div class="sourceCode" id="cb5"><pre class="downlit sourceCode r code-with-copy"><code class="sourceCode R"><span><span class="co"># create a local directory to store the result of the operation</span></span>
<span><span class="va">tempdir_r_ndvi_max</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html">file.path</a></span><span class="op">(</span><span class="va">tempdir_r</span>, <span class="st">"ndvi_max"</span><span class="op">)</span></span>
<span><span class="fu"><a href="https://rdrr.io/r/base/files2.html">dir.create</a></span><span class="op">(</span><span class="va">tempdir_r_ndvi_max</span>, showWarnings <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span>
<span></span>
<span><span class="co"># Calculate the NBR index</span></span>
<span><span class="va">max_ndvi_cube</span> <span class="op"><-</span> <span class="fu"><a href="https://e-sensing.github.io/sits/reference/sits_reduce.html">sits_reduce</a></span><span class="op">(</span><span class="va">ndvi_cube_local</span>,</span>
<span> NDVIMAX <span class="op">=</span> <span class="fu">t_max</span><span class="op">(</span><span class="va">NDVI</span><span class="op">)</span>,</span>
<span> output_dir <span class="op">=</span> <span class="va">tempdir_r_ndvi_max</span>,</span>
<span> multicores <span class="op">=</span> <span class="fl">4</span>,</span>
<span> progress <span class="op">=</span> <span class="cn">TRUE</span></span>
<span><span class="op">)</span></span>
<span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">max_ndvi_cube</span>, band <span class="op">=</span> <span class="st">"NDVIMAX"</span><span class="op">)</span></span></code></pre></div><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></div>
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb6"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="co"># create a local directory to store the result of the operation</span></span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a>tempdir_py_ndvi_max <span class="op">=</span> tempdir_py <span class="op">/</span> <span class="st">"ndvi_max"</span></span>
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a>tempdir_py_ndvi_max.mkdir(parents<span class="op">=</span><span class="va">True</span>, exist_ok<span class="op">=</span><span class="va">True</span>)</span>
<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a><span class="co"># Calculate the NBR index</span></span>
<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a>max_ndvi_cube <span class="op">=</span> sits_reduce(ndvi_cube_local,</span>
<span id="cb6-7"><a href="#cb6-7" aria-hidden="true" tabindex="-1"></a> NDVIMAX <span class="op">=</span> <span class="st">"t_max(NDVI)"</span>,</span>
<span id="cb6-8"><a href="#cb6-8" aria-hidden="true" tabindex="-1"></a> output_dir <span class="op">=</span> tempdir_py_ndvi_max,</span>
<span id="cb6-9"><a href="#cb6-9" aria-hidden="true" tabindex="-1"></a> multicores <span class="op">=</span> <span class="dv">4</span>,</span>
<span id="cb6-10"><a href="#cb6-10" aria-hidden="true" tabindex="-1"></a> progress <span class="op">=</span> <span class="va">True</span></span>
<span id="cb6-11"><a href="#cb6-11" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb6-12"><a href="#cb6-12" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb6-13"><a href="#cb6-13" aria-hidden="true" tabindex="-1"></a>plot(max_ndvi_cube, band <span class="op">=</span> <span class="st">"NDVIMAX"</span>)</span></code></pre></div><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></div>
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<figcaption class="quarto-float-caption-bottom quarto-float-caption quarto-float-fig" id="fig-dc-reduce-ndvimax-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
Figure 10.1: Maximum NDVI for MPC MODIS cube for period 2018-05-01 to 2018-09-30.
</figcaption></figure>
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</section><section id="summary" class="level2" data-number="10.4"><h2 data-number="10.4" class="anchored" data-anchor-id="summary">
<span class="header-section-number">10.4</span> Summary</h2>
<p>Temporal reducing operations in Earth Observation (EO) data cubes are aggregations or summaries performed along the time dimension. These operations compress temporal information—typically multiple observations of the same location over time—into a single value or summary per pixel or area. They are useful for generating cloud-free composites, trend analyses, and preparing data for classification or modeling.</p>
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