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VM0010-starter.html
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<meta name="author" content="Seamus Murphy">
<meta name="dcterms.date" content="2024-11-04">
<meta name="keywords" content="REDD+, VCS, Verra, Carbon verification">
<title>VM0010 Starter Script</title>
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<div id="quarto-content" class="page-columns page-rows-contents page-layout-article">
<div id="quarto-margin-sidebar" class="sidebar margin-sidebar">
<nav id="TOC" role="doc-toc" class="toc-active" data-toc-expanded="4">
<h2 id="toc-title"><strong>Contents</strong></h2>
<ul>
<li><a href="#preprocess-data" id="toc-preprocess-data" class="nav-link active" data-scroll-target="#preprocess-data">1. Preprocess data</a>
<ul>
<li><a href="#sec-1.1" id="toc-sec-1.1" class="nav-link" data-scroll-target="#sec-1.1">Import dummy data</a></li>
<li><a href="#sec-1.2" id="toc-sec-1.2" class="nav-link" data-scroll-target="#sec-1.2">Review dummy data</a></li>
<li><a href="#sec-1.3" id="toc-sec-1.3" class="nav-link" data-scroll-target="#sec-1.3">Tidy dummy data</a></li>
</ul></li>
<li><a href="#compute-equations" id="toc-compute-equations" class="nav-link" data-scroll-target="#compute-equations">2. Compute Equations</a>
<ul>
<li><a href="#eq1-plot-biomass" id="toc-eq1-plot-biomass" class="nav-link" data-scroll-target="#eq1-plot-biomass">EQ1: Plot biomass</a></li>
<li><a href="#eq2-strata-biomass" id="toc-eq2-strata-biomass" class="nav-link" data-scroll-target="#eq2-strata-biomass">EQ2: Strata biomass</a></li>
<li><a href="#eq3-harvest-carbon" id="toc-eq3-harvest-carbon" class="nav-link" data-scroll-target="#eq3-harvest-carbon">EQ3: Harvest carbon</a></li>
<li><a href="#eq4-extracted-carbon" id="toc-eq4-extracted-carbon" class="nav-link" data-scroll-target="#eq4-extracted-carbon">EQ4: Extracted carbon</a></li>
<li><a href="#eq5-slash-carbon" id="toc-eq5-slash-carbon" class="nav-link" data-scroll-target="#eq5-slash-carbon">EQ5: Slash carbon</a></li>
<li><a href="#eq6-damaged-carbon" id="toc-eq6-damaged-carbon" class="nav-link" data-scroll-target="#eq6-damaged-carbon">EQ6: Damaged carbon</a></li>
<li><a href="#eq7-undamaged-carbon" id="toc-eq7-undamaged-carbon" class="nav-link" data-scroll-target="#eq7-undamaged-carbon">EQ7: Undamaged carbon</a></li>
<li><a href="#eq8-wood-products" id="toc-eq8-wood-products" class="nav-link" data-scroll-target="#eq8-wood-products">EQ8: Wood products</a></li>
<li><a href="#eq9-hwp-carbon-loss-year-0" id="toc-eq9-hwp-carbon-loss-year-0" class="nav-link" data-scroll-target="#eq9-hwp-carbon-loss-year-0">EQ9: HWP carbon loss <sup>year-0</sup></a></li>
<li><a href="#eq10-hwp-carbon-store" id="toc-eq10-hwp-carbon-store" class="nav-link" data-scroll-target="#eq10-hwp-carbon-store">EQ10: HWP carbon store</a></li>
<li><a href="#eq11-hwp-carbon-loss-year-100" id="toc-eq11-hwp-carbon-loss-year-100" class="nav-link" data-scroll-target="#eq11-hwp-carbon-loss-year-100">EQ11: HWP carbon loss <sup>year-100</sup></a></li>
<li><a href="#eq12-fuel-emissions" id="toc-eq12-fuel-emissions" class="nav-link" data-scroll-target="#eq12-fuel-emissions">EQ12: Fuel emissions</a></li>
<li><a href="#eq13-harvesting-fuel-emissions" id="toc-eq13-harvesting-fuel-emissions" class="nav-link" data-scroll-target="#eq13-harvesting-fuel-emissions">EQ13: Harvesting fuel emissions</a></li>
<li><a href="#eq14-hauling-fuel-emissions" id="toc-eq14-hauling-fuel-emissions" class="nav-link" data-scroll-target="#eq14-hauling-fuel-emissions">EQ14: Hauling fuel emissions</a></li>
<li><a href="#eq15-transport-fuel-emissions" id="toc-eq15-transport-fuel-emissions" class="nav-link" data-scroll-target="#eq15-transport-fuel-emissions">EQ15: Transport fuel emissions</a></li>
</ul></li>
<li><a href="#appendix" id="toc-appendix" class="nav-link" data-scroll-target="#appendix">Appendix</a>
<ul>
<li><a href="#a.1-datamaid-audit" id="toc-a.1-datamaid-audit" class="nav-link" data-scroll-target="#a.1-datamaid-audit">A.1 DataMaid audit</a></li>
</ul></li>
</ul>
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</div>
<main class="content" id="quarto-document-content">
<header id="title-block-header" class="quarto-title-block default">
<div class="quarto-title">
<h1 class="title">VM0010 Starter Script</h1>
</div>
<div class="quarto-title-meta">
<div>
<div class="quarto-title-meta-heading">Author</div>
<div class="quarto-title-meta-contents">
<p>Seamus Murphy, PhD <a href="mailto:[email protected]" class="quarto-title-author-email"><i class="bi bi-envelope"></i></a> <a href="https://orcid.org/0000-0002-1792-0351" class="quarto-title-author-orcid"> <img src="data:image/png;base64,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"></a></p>
</div>
</div>
<div>
<div class="quarto-title-meta-heading">Published</div>
<div class="quarto-title-meta-contents">
<p class="date">November 4, 2024</p>
</div>
</div>
</div>
<div>
<div class="abstract">
<div class="block-title">Abstract</div>
<p>The following workflow provides a starter script for quantifying greenhouse gas emissions reduction of projects designed under the <a href="https://verra.org/wp-content/uploads/2024/10/VM0010_IFM_LtPF_v1.4_Clean_10282024.pdf">VM0010 VCS Methodology, V1.4</a>.</p>
</div>
</div>
<div>
<div class="keywords">
<div class="block-title">Keywords</div>
<p>REDD+, VCS, Verra, Carbon verification</p>
</div>
</div>
</header>
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height:200px;
width: 200px;
background-size: contain;
background-position: 50% 50%;
padding-top: 80px !important;
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</div>
<section id="preprocess-data" class="level1">
<h1>1. Preprocess data</h1>
<section id="sec-1.1" class="level4">
<h4 class="anchored" data-anchor-id="sec-1.1">Import dummy data</h4>
<div class="cell">
<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">set.seed</span>(<span class="dv">333</span>)</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a>dataset_raw <span class="ot"><-</span> <span class="fu">read_excel</span>(<span class="st">"./R/assets/dataset_raw.xlsx"</span>)</span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="fu">write.csv</span>(dataset_raw, <span class="st">"./R/assets/dataset_tidy.csv"</span>, <span class="at">row.names =</span> <span class="cn">FALSE</span>)</span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a>dataset_tidy <span class="ot"><-</span> <span class="fu">read.csv</span>(<span class="st">"./R/assets/dataset_tidy.csv"</span>)</span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a>dataset_tidy <span class="sc">|></span> <span class="fu">kbl</span>() <span class="sc">|></span> <span class="fu">kable_styling</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<table class="table caption-top table-sm table-striped small" data-quarto-postprocess="true">
<thead>
<tr class="header">
<th style="text-align: right;" data-quarto-table-cell-role="th">Stratum...i.</th>
<th style="text-align: right;" data-quarto-table-cell-role="th">Plot..sp.</th>
<th style="text-align: left;" data-quarto-table-cell-role="th">Species..j.</th>
<th style="text-align: left;" data-quarto-table-cell-role="th">Tree..l.</th>
<th style="text-align: right;" data-quarto-table-cell-role="th">Volume..V_.l.j.I.sp..</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td style="text-align: right;">1</td>
<td style="text-align: right;">1</td>
<td style="text-align: left;">Sp1</td>
<td style="text-align: left;">t1</td>
<td style="text-align: right;">3.30</td>
</tr>
<tr class="even">
<td style="text-align: right;">1</td>
<td style="text-align: right;">1</td>
<td style="text-align: left;">Sp1</td>
<td style="text-align: left;">t2</td>
<td style="text-align: right;">4.80</td>
</tr>
<tr class="odd">
<td style="text-align: right;">1</td>
<td style="text-align: right;">1</td>
<td style="text-align: left;">Sp1</td>
<td style="text-align: left;">t3</td>
<td style="text-align: right;">4.08</td>
</tr>
<tr class="even">
<td style="text-align: right;">1</td>
<td style="text-align: right;">2</td>
<td style="text-align: left;">Sp4</td>
<td style="text-align: left;">t1</td>
<td style="text-align: right;">1.50</td>
</tr>
<tr class="odd">
<td style="text-align: right;">1</td>
<td style="text-align: right;">2</td>
<td style="text-align: left;">Sp4</td>
<td style="text-align: left;">t2</td>
<td style="text-align: right;">1.68</td>
</tr>
<tr class="even">
<td style="text-align: right;">2</td>
<td style="text-align: right;">1</td>
<td style="text-align: left;">Sp1</td>
<td style="text-align: left;">t1</td>
<td style="text-align: right;">1.38</td>
</tr>
<tr class="odd">
<td style="text-align: right;">2</td>
<td style="text-align: right;">1</td>
<td style="text-align: left;">Sp2</td>
<td style="text-align: left;">t2</td>
<td style="text-align: right;">3.24</td>
</tr>
<tr class="even">
<td style="text-align: right;">2</td>
<td style="text-align: right;">1</td>
<td style="text-align: left;">Sp3</td>
<td style="text-align: left;">t3</td>
<td style="text-align: right;">3.72</td>
</tr>
<tr class="odd">
<td style="text-align: right;">2</td>
<td style="text-align: right;">1</td>
<td style="text-align: left;">sp4</td>
<td style="text-align: left;">t4</td>
<td style="text-align: right;">2.94</td>
</tr>
<tr class="even">
<td style="text-align: right;">2</td>
<td style="text-align: right;">1</td>
<td style="text-align: left;">Sp5</td>
<td style="text-align: left;">t5</td>
<td style="text-align: right;">3.36</td>
</tr>
</tbody>
</table>
</div>
</div>
</section>
<section id="sec-1.2" class="level4">
<h4 class="anchored" data-anchor-id="sec-1.2">Review dummy data</h4>
<div class="cell">
<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="fu">str</span>(dataset_tidy)</span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a>dplyr<span class="sc">::</span><span class="fu">count</span>(dataset_tidy, Species..j.)</span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a><span class="fu">saveHTML</span>(dataMaid<span class="sc">::</span><span class="fu">makeDataReport</span>(</span>
<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a> dataset_tidy,</span>
<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a> <span class="at">output =</span> <span class="st">"html"</span>,</span>
<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a> <span class="at">codebook =</span> <span class="cn">TRUE</span>,</span>
<span id="cb2-8"><a href="#cb2-8" aria-hidden="true" tabindex="-1"></a> <span class="at">onlyProblematic =</span> <span class="cn">TRUE</span>,</span>
<span id="cb2-9"><a href="#cb2-9" aria-hidden="true" tabindex="-1"></a> <span class="at">visuals =</span> <span class="fu">setVisuals</span>(<span class="at">all =</span> <span class="st">"basicVisual"</span>),</span>
<span id="cb2-10"><a href="#cb2-10" aria-hidden="true" tabindex="-1"></a> <span class="at">replace =</span> <span class="cn">TRUE</span></span>
<span id="cb2-11"><a href="#cb2-11" aria-hidden="true" tabindex="-1"></a> )</span>
<span id="cb2-12"><a href="#cb2-12" aria-hidden="true" tabindex="-1"></a>) <span class="co"># output "dataMaid_dataset_tidy.html" shown in Appendix A.1</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div class="cell">
<div class="cell-output cell-output-stdout">
<pre><code>'data.frame': 10 obs. of 5 variables:
$ Stratum...i. : int 1 1 1 1 1 2 2 2 2 2
$ Plot..sp. : int 1 1 1 2 2 1 1 1 1 1
$ Species..j. : chr "Sp1" "Sp1" "Sp1" "Sp4" ...
$ Tree..l. : chr "t1" "t2" "t3" "t1" ...
$ Volume..V_.l.j.I.sp..: num 3.3 4.8 4.08 1.5 1.68 1.38 3.24 3.72 2.94 3.36</code></pre>
</div>
<div class="cell-output-display">
<div class="kable-table">
<table class="caption-top table table-sm table-striped small">
<thead>
<tr class="header">
<th style="text-align: left;">Species..j.</th>
<th style="text-align: right;">n</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td style="text-align: left;">Sp1</td>
<td style="text-align: right;">4</td>
</tr>
<tr class="even">
<td style="text-align: left;">Sp2</td>
<td style="text-align: right;">1</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Sp3</td>
<td style="text-align: right;">1</td>
</tr>
<tr class="even">
<td style="text-align: left;">Sp4</td>
<td style="text-align: right;">2</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Sp5</td>
<td style="text-align: right;">1</td>
</tr>
<tr class="even">
<td style="text-align: left;">sp4</td>
<td style="text-align: right;">1</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</section>
<section id="sec-1.3" class="level4">
<h4 class="anchored" data-anchor-id="sec-1.3">Tidy dummy data</h4>
<p>Clean dataset and relabel to match <a href="https://verra.org/wp-content/uploads/2018/03/VM0010-Methodology-for-IMF-LtPF-v1.3_0.pdf">VM0010 Verra Methodology</a> and <a href="https://style.tidyverse.org/">Tidyverse style guide</a></p>
<div class="cell">
<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>data.table<span class="sc">::</span><span class="fu">setnames</span>(dataset_tidy, <span class="at">old =</span> <span class="st">"Stratum...i."</span>, <span class="at">new =</span> <span class="st">"stratum_i"</span>, <span class="at">skip_absent =</span> <span class="cn">TRUE</span>)</span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a>data.table<span class="sc">::</span><span class="fu">setnames</span>(dataset_tidy, <span class="at">old =</span> <span class="st">"Species..j."</span>, <span class="at">new =</span> <span class="st">"species_j"</span>, <span class="at">skip_absent =</span> <span class="cn">TRUE</span>)</span>
<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a>data.table<span class="sc">::</span><span class="fu">setnames</span>(dataset_tidy, <span class="at">old =</span> <span class="st">"Plot..sp."</span>, <span class="at">new =</span> <span class="st">"plot_sp"</span>, <span class="at">skip_absent =</span> <span class="cn">TRUE</span>)</span>
<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a>data.table<span class="sc">::</span><span class="fu">setnames</span>(dataset_tidy, <span class="at">old =</span> <span class="st">"Tree..l."</span>, <span class="at">new =</span> <span class="st">"tree_l"</span>, <span class="at">skip_absent =</span> <span class="cn">TRUE</span>)</span>
<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a>data.table<span class="sc">::</span><span class="fu">setnames</span>(dataset_tidy, <span class="at">old =</span> <span class="st">"Volume..V_.l.j.I.sp.."</span>, <span class="at">new =</span> <span class="st">"volume"</span>, <span class="at">skip_absent =</span> <span class="cn">TRUE</span>)</span>
<span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a>dataset_tidy<span class="sc">$</span>species_j[dataset_tidy<span class="sc">$</span>species_j <span class="sc">==</span> <span class="st">"sp4"</span>] <span class="ot"><-</span> <span class="st">"Sp4"</span></span>
<span id="cb4-7"><a href="#cb4-7" aria-hidden="true" tabindex="-1"></a>dataset_tidy<span class="sc">$</span>species_j <span class="ot">=</span> <span class="fu">as.factor</span>(dataset_tidy<span class="sc">$</span>species_j)</span>
<span id="cb4-8"><a href="#cb4-8" aria-hidden="true" tabindex="-1"></a>dataset_tidy<span class="sc">$</span>stratum_i <span class="ot">=</span> <span class="fu">as.factor</span>(dataset_tidy<span class="sc">$</span>stratum_i)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>Compute new variables & save copy of cleaned <code>dataset_tidy.csv</code></p>
<div class="cell">
<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>dataset_tidy<span class="sc">$</span>bcef_r <span class="ot">=</span> <span class="fl">0.7</span></span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>dataset_tidy<span class="sc">$</span>cf <span class="ot">=</span> <span class="fl">0.5</span></span>
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a>dataset_tidy<span class="sc">$</span>d <span class="ot">=</span> <span class="fl">0.5</span></span>
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a>dataset_tidy<span class="sc">$</span>a_sp <span class="ot">=</span> <span class="fl">0.1</span></span>
<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a>dataset_tidy<span class="sc">$</span>a_sp_m2 <span class="ot">=</span> dataset_tidy<span class="sc">$</span>a_sp <span class="sc">*</span> <span class="dv">10000</span></span>
<span id="cb5-6"><a href="#cb5-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb5-7"><a href="#cb5-7" aria-hidden="true" tabindex="-1"></a>dataset_tidy <span class="ot">=</span> dataset_tidy <span class="sc">%>%</span></span>
<span id="cb5-8"><a href="#cb5-8" aria-hidden="true" tabindex="-1"></a> <span class="fu">group_by</span>(stratum_i) <span class="sc">%>%</span></span>
<span id="cb5-9"><a href="#cb5-9" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">a_I_m2 =</span> <span class="fu">sum</span>(a_sp_m2), <span class="at">a_I_ha =</span> <span class="fu">sum</span>(a_sp)) </span>
<span id="cb5-10"><a href="#cb5-10" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb5-11"><a href="#cb5-11" aria-hidden="true" tabindex="-1"></a><span class="fu">write.csv</span>(dataset_tidy, <span class="st">"./R/assets/dataset_tidy.csv"</span>, <span class="at">row.names =</span> <span class="cn">FALSE</span>)</span>
<span id="cb5-12"><a href="#cb5-12" aria-hidden="true" tabindex="-1"></a>dataset_tidy <span class="sc">|></span> <span class="fu">kbl</span>() <span class="sc">|></span> <span class="fu">kable_styling</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<table class="table caption-top table-sm table-striped small" data-quarto-postprocess="true">
<thead>
<tr class="header">
<th style="text-align: left;" data-quarto-table-cell-role="th">stratum_i</th>
<th style="text-align: right;" data-quarto-table-cell-role="th">plot_sp</th>
<th style="text-align: left;" data-quarto-table-cell-role="th">species_j</th>
<th style="text-align: left;" data-quarto-table-cell-role="th">tree_l</th>
<th style="text-align: right;" data-quarto-table-cell-role="th">volume</th>
<th style="text-align: right;" data-quarto-table-cell-role="th">bcef_r</th>
<th style="text-align: right;" data-quarto-table-cell-role="th">cf</th>
<th style="text-align: right;" data-quarto-table-cell-role="th">d</th>
<th style="text-align: right;" data-quarto-table-cell-role="th">a_sp</th>
<th style="text-align: right;" data-quarto-table-cell-role="th">a_sp_m2</th>
<th style="text-align: right;" data-quarto-table-cell-role="th">a_I_m2</th>
<th style="text-align: right;" data-quarto-table-cell-role="th">a_I_ha</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td style="text-align: left;">1</td>
<td style="text-align: right;">1</td>
<td style="text-align: left;">Sp1</td>
<td style="text-align: left;">t1</td>
<td style="text-align: right;">3.30</td>
<td style="text-align: right;">0.7</td>
<td style="text-align: right;">0.5</td>
<td style="text-align: right;">0.5</td>
<td style="text-align: right;">0.1</td>
<td style="text-align: right;">1000</td>
<td style="text-align: right;">5000</td>
<td style="text-align: right;">0.5</td>
</tr>
<tr class="even">
<td style="text-align: left;">1</td>
<td style="text-align: right;">1</td>
<td style="text-align: left;">Sp1</td>
<td style="text-align: left;">t2</td>
<td style="text-align: right;">4.80</td>
<td style="text-align: right;">0.7</td>
<td style="text-align: right;">0.5</td>
<td style="text-align: right;">0.5</td>
<td style="text-align: right;">0.1</td>
<td style="text-align: right;">1000</td>
<td style="text-align: right;">5000</td>
<td style="text-align: right;">0.5</td>
</tr>
<tr class="odd">
<td style="text-align: left;">1</td>
<td style="text-align: right;">1</td>
<td style="text-align: left;">Sp1</td>
<td style="text-align: left;">t3</td>
<td style="text-align: right;">4.08</td>
<td style="text-align: right;">0.7</td>
<td style="text-align: right;">0.5</td>
<td style="text-align: right;">0.5</td>
<td style="text-align: right;">0.1</td>
<td style="text-align: right;">1000</td>
<td style="text-align: right;">5000</td>
<td style="text-align: right;">0.5</td>
</tr>
<tr class="even">
<td style="text-align: left;">1</td>
<td style="text-align: right;">2</td>
<td style="text-align: left;">Sp4</td>
<td style="text-align: left;">t1</td>
<td style="text-align: right;">1.50</td>
<td style="text-align: right;">0.7</td>
<td style="text-align: right;">0.5</td>
<td style="text-align: right;">0.5</td>
<td style="text-align: right;">0.1</td>
<td style="text-align: right;">1000</td>
<td style="text-align: right;">5000</td>
<td style="text-align: right;">0.5</td>
</tr>
<tr class="odd">
<td style="text-align: left;">1</td>
<td style="text-align: right;">2</td>
<td style="text-align: left;">Sp4</td>
<td style="text-align: left;">t2</td>
<td style="text-align: right;">1.68</td>
<td style="text-align: right;">0.7</td>
<td style="text-align: right;">0.5</td>
<td style="text-align: right;">0.5</td>
<td style="text-align: right;">0.1</td>
<td style="text-align: right;">1000</td>
<td style="text-align: right;">5000</td>
<td style="text-align: right;">0.5</td>
</tr>
<tr class="even">
<td style="text-align: left;">2</td>
<td style="text-align: right;">1</td>
<td style="text-align: left;">Sp1</td>
<td style="text-align: left;">t1</td>
<td style="text-align: right;">1.38</td>
<td style="text-align: right;">0.7</td>
<td style="text-align: right;">0.5</td>
<td style="text-align: right;">0.5</td>
<td style="text-align: right;">0.1</td>
<td style="text-align: right;">1000</td>
<td style="text-align: right;">5000</td>
<td style="text-align: right;">0.5</td>
</tr>
<tr class="odd">
<td style="text-align: left;">2</td>
<td style="text-align: right;">1</td>
<td style="text-align: left;">Sp2</td>
<td style="text-align: left;">t2</td>
<td style="text-align: right;">3.24</td>
<td style="text-align: right;">0.7</td>
<td style="text-align: right;">0.5</td>
<td style="text-align: right;">0.5</td>
<td style="text-align: right;">0.1</td>
<td style="text-align: right;">1000</td>
<td style="text-align: right;">5000</td>
<td style="text-align: right;">0.5</td>
</tr>
<tr class="even">
<td style="text-align: left;">2</td>
<td style="text-align: right;">1</td>
<td style="text-align: left;">Sp3</td>
<td style="text-align: left;">t3</td>
<td style="text-align: right;">3.72</td>
<td style="text-align: right;">0.7</td>
<td style="text-align: right;">0.5</td>
<td style="text-align: right;">0.5</td>
<td style="text-align: right;">0.1</td>
<td style="text-align: right;">1000</td>
<td style="text-align: right;">5000</td>
<td style="text-align: right;">0.5</td>
</tr>
<tr class="odd">
<td style="text-align: left;">2</td>
<td style="text-align: right;">1</td>
<td style="text-align: left;">Sp4</td>
<td style="text-align: left;">t4</td>
<td style="text-align: right;">2.94</td>
<td style="text-align: right;">0.7</td>
<td style="text-align: right;">0.5</td>
<td style="text-align: right;">0.5</td>
<td style="text-align: right;">0.1</td>
<td style="text-align: right;">1000</td>
<td style="text-align: right;">5000</td>
<td style="text-align: right;">0.5</td>
</tr>
<tr class="even">
<td style="text-align: left;">2</td>
<td style="text-align: right;">1</td>
<td style="text-align: left;">Sp5</td>
<td style="text-align: left;">t5</td>
<td style="text-align: right;">3.36</td>
<td style="text-align: right;">0.7</td>
<td style="text-align: right;">0.5</td>
<td style="text-align: right;">0.5</td>
<td style="text-align: right;">0.1</td>
<td style="text-align: right;">1000</td>
<td style="text-align: right;">5000</td>
<td style="text-align: right;">0.5</td>
</tr>
</tbody>
</table>
</div>
</div>
</section>
</section>
<section id="compute-equations" class="level1">
<h1>2. Compute Equations</h1>
<p>Note all four equations that follow derive estimates according to specific species, whether measured at the plot level, stratum or globally. Hence, caution is advised when computing initial, absolute estimates and when deriving or applying hectare expansion factors.</p>
<p>On page 19 of <a href="https://verra.org/wp-content/uploads/2024/10/VM0010_IFM_LtPF_v1.4_Clean_10282024.pdf">VM0010 Methodology</a>, ‘equation 1’ calculates merchantable timber volume in cubic meters using the following:</p>
<section id="eq1-plot-biomass" class="level4">
<h4 class="anchored" data-anchor-id="eq1-plot-biomass">EQ1: Plot biomass</h4>
<p><span class="math display">\[V_{j,i|sp} = \sum_{l = 1}^{L} V_{l,j,i,sp}\]</span></p>
<p>where <span class="math inline">\(V_{j,i|sp}\)</span> refers to the sum of merchantable volume of species <em>j</em> from plot <em>sp</em> in stratum <em>i,</em> as computed in the following.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>dataset_tidy <span class="ot">=</span> dataset_tidy <span class="sc">|></span></span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">group_by</span>(species_j, stratum_i, plot_sp) <span class="sc">|></span></span>
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">vji_sp_m3 =</span> <span class="fu">sum</span>(volume))</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"># compute new variable 'vji_sp_m3'</span></span>
<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a>data.table<span class="sc">::</span><span class="fu">setDT</span>(dataset_tidy)[, .(</span>
<span id="cb6-7"><a href="#cb6-7" aria-hidden="true" tabindex="-1"></a> <span class="at">vji_sp_m3 =</span> <span class="fu">sum</span>(volume)</span>
<span id="cb6-8"><a href="#cb6-8" aria-hidden="true" tabindex="-1"></a> ),</span>
<span id="cb6-9"><a href="#cb6-9" aria-hidden="true" tabindex="-1"></a> by <span class="ot">=</span> .(stratum_i, plot_sp, species_j)</span>
<span id="cb6-10"><a href="#cb6-10" aria-hidden="true" tabindex="-1"></a>] <span class="sc">|></span> <span class="fu">kbl</span>() <span class="sc">|></span> <span class="fu">kable_styling</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<table class="table caption-top table-sm table-striped small" data-quarto-postprocess="true">
<thead>
<tr class="header">
<th style="text-align: left;" data-quarto-table-cell-role="th">stratum_i</th>
<th style="text-align: right;" data-quarto-table-cell-role="th">plot_sp</th>
<th style="text-align: left;" data-quarto-table-cell-role="th">species_j</th>
<th style="text-align: right;" data-quarto-table-cell-role="th">vji_sp_m3</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td style="text-align: left;">1</td>
<td style="text-align: right;">1</td>
<td style="text-align: left;">Sp1</td>
<td style="text-align: right;">12.18</td>
</tr>
<tr class="even">
<td style="text-align: left;">1</td>
<td style="text-align: right;">2</td>
<td style="text-align: left;">Sp4</td>
<td style="text-align: right;">3.18</td>
</tr>
<tr class="odd">
<td style="text-align: left;">2</td>
<td style="text-align: right;">1</td>
<td style="text-align: left;">Sp1</td>
<td style="text-align: right;">1.38</td>
</tr>
<tr class="even">
<td style="text-align: left;">2</td>
<td style="text-align: right;">1</td>
<td style="text-align: left;">Sp2</td>
<td style="text-align: right;">3.24</td>
</tr>
<tr class="odd">
<td style="text-align: left;">2</td>
<td style="text-align: right;">1</td>
<td style="text-align: left;">Sp3</td>
<td style="text-align: right;">3.72</td>
</tr>
<tr class="even">
<td style="text-align: left;">2</td>
<td style="text-align: right;">1</td>
<td style="text-align: left;">Sp4</td>
<td style="text-align: right;">2.94</td>
</tr>
<tr class="odd">
<td style="text-align: left;">2</td>
<td style="text-align: right;">1</td>
<td style="text-align: left;">Sp5</td>
<td style="text-align: right;">3.36</td>
</tr>
</tbody>
</table>
</div>
</div>
</section>
<section id="eq2-strata-biomass" class="level4">
<h4 class="anchored" data-anchor-id="eq2-strata-biomass">EQ2: Strata biomass</h4>
<p>On page 19 of the VM0010 Methodology, ‘equation 2’ provides calculation of merchantable timber volume of a species at the stratum level:</p>
<p><span class="math display">\[V_{j,i|BSL} = \displaystyle \frac{1}{SP} \sum_{sp=1}^{sp} \displaystyle \frac{V_{j,i,sp}}{A_{sp}}\]</span></p>
<p>where <span class="math inline">\(V_{j,i|BSL}\)</span> refers to the <u><strong><em>mean</em></strong></u> merchantable timber volume of species <em>j</em> measured across all plots within stratum <em>i</em> in the baseline scenario. Volume estimates are derived in terms of m<sup>3</sup>/ha<sup>-1</sup> using an expansion factor derived as the ratio of plot area 1,000m<sup>2</sup> to 10,000m<sup>2</sup>, as follows.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>dataset_tidy <span class="ot">=</span> dataset_tidy <span class="sc">|></span></span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">group_by</span>(stratum_i, species_j) <span class="sc">|></span></span>
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">vji_ha_m3 =</span> <span class="fu">mean</span>(vji_sp_m3) <span class="sc">*</span> <span class="dv">10</span>)</span>
<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a>data.table<span class="sc">::</span><span class="fu">setDT</span>(dataset_tidy)[, .(</span>
<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a> vji_sp_m3,</span>
<span id="cb7-7"><a href="#cb7-7" aria-hidden="true" tabindex="-1"></a> vji_ha_m3</span>
<span id="cb7-8"><a href="#cb7-8" aria-hidden="true" tabindex="-1"></a> ),</span>
<span id="cb7-9"><a href="#cb7-9" aria-hidden="true" tabindex="-1"></a> by <span class="ot">=</span> .(stratum_i, species_j)</span>
<span id="cb7-10"><a href="#cb7-10" aria-hidden="true" tabindex="-1"></a>] <span class="sc">|></span> <span class="fu">kbl</span>() <span class="sc">|></span> <span class="fu">kable_styling</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<table class="table caption-top table-sm table-striped small" data-quarto-postprocess="true">
<thead>
<tr class="header">
<th style="text-align: left;" data-quarto-table-cell-role="th">stratum_i</th>
<th style="text-align: left;" data-quarto-table-cell-role="th">species_j</th>
<th style="text-align: right;" data-quarto-table-cell-role="th">vji_sp_m3</th>
<th style="text-align: right;" data-quarto-table-cell-role="th">vji_ha_m3</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td style="text-align: left;">1</td>
<td style="text-align: left;">Sp1</td>
<td style="text-align: right;">12.18</td>
<td style="text-align: right;">121.8</td>
</tr>
<tr class="even">
<td style="text-align: left;">1</td>
<td style="text-align: left;">Sp1</td>
<td style="text-align: right;">12.18</td>
<td style="text-align: right;">121.8</td>
</tr>
<tr class="odd">
<td style="text-align: left;">1</td>
<td style="text-align: left;">Sp1</td>
<td style="text-align: right;">12.18</td>
<td style="text-align: right;">121.8</td>
</tr>
<tr class="even">
<td style="text-align: left;">1</td>
<td style="text-align: left;">Sp4</td>
<td style="text-align: right;">3.18</td>
<td style="text-align: right;">31.8</td>
</tr>
<tr class="odd">
<td style="text-align: left;">1</td>
<td style="text-align: left;">Sp4</td>
<td style="text-align: right;">3.18</td>
<td style="text-align: right;">31.8</td>
</tr>
<tr class="even">
<td style="text-align: left;">2</td>
<td style="text-align: left;">Sp1</td>
<td style="text-align: right;">1.38</td>
<td style="text-align: right;">13.8</td>
</tr>
<tr class="odd">
<td style="text-align: left;">2</td>
<td style="text-align: left;">Sp2</td>
<td style="text-align: right;">3.24</td>
<td style="text-align: right;">32.4</td>
</tr>
<tr class="even">
<td style="text-align: left;">2</td>
<td style="text-align: left;">Sp3</td>
<td style="text-align: right;">3.72</td>
<td style="text-align: right;">37.2</td>
</tr>
<tr class="odd">
<td style="text-align: left;">2</td>
<td style="text-align: left;">Sp4</td>
<td style="text-align: right;">2.94</td>
<td style="text-align: right;">29.4</td>
</tr>
<tr class="even">
<td style="text-align: left;">2</td>
<td style="text-align: left;">Sp5</td>
<td style="text-align: right;">3.36</td>
<td style="text-align: right;">33.6</td>
</tr>
</tbody>
</table>
</div>
</div>
</section>
<section id="eq3-harvest-carbon" class="level4">
<h4 class="anchored" data-anchor-id="eq3-harvest-carbon">EQ3: Harvest carbon</h4>
<p>On page 20 of the VM0010 Methodology, ‘equation 3’ provides calculation of carbon stock of harvested timber volumes for species <em>i</em> in stratum <em>i</em>.</p>
<p>In the absence of harvest plan data, carbon stocks of commercial timber will be derived from the full inventory <code>dataset_tidy</code>.</p>
<p>This differs to ‘equation 3’ below, which measures mean carbon stock from volumes of ‘harvested biomass’ <span class="math inline">\(C_{HB,j,i|BSL}\)</span> comprised of volumes estimates from extracted timber that is destined off-site for market sales, in addition to volume estimates from extracted timber that is remaining on-site due to damage or use during site operations and road construction. The difference in destinations of these carbon stocks means that alternative carbon factors must be applied in their calculation, as indicated in following two equations</p>
<p><span class="math display">\[C_{HB,j,i|BSL} = (V_{EX,j,i|BSL} + V_{EX,INF,j,i|BSL} ) * BCEF_{R} * CF_{j}\]</span></p>
<p>Carbon estimates are calculated in units of metric tons per hectare (tC/ha<sup>-1</sup>) by multiplying mean volume per hectare of extracted timber of species <em>i</em> from stratum <em>j</em> by the carbon fraction <span class="math inline">\(CF\)</span> (default = 0.5) and biomass conversion and expansion factor <span class="math inline">\(BCEF_{R}\)</span> of that species. If needed, VM0010 methoodology provides guidance on approriate literature source for defining CF with prioritiy of local forest types over national and regional forest types, over forest types from neighboring countries. However, if defaulting to global forest type values, recommendations point to chapter four of <span class="citation" data-cites="krey1Chapter4">(<a href="#ref-krey1Chapter4" role="doc-biblioref">Krey et al., n.d.</a>)</span> that cite value of 1.11. We rely on the provided value of 0.7.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a>dataset_tidy <span class="ot"><-</span> dataset_tidy <span class="sc">%>%</span></span>
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">chb_ha_tC =</span> vji_ha_m3 <span class="sc">*</span> bcef_r <span class="sc">*</span> cf)</span>
<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a>data.table<span class="sc">::</span><span class="fu">setDT</span>(dataset_tidy)[, .(</span>
<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a> vji_sp_m3,</span>
<span id="cb8-6"><a href="#cb8-6" aria-hidden="true" tabindex="-1"></a> vji_ha_m3,</span>
<span id="cb8-7"><a href="#cb8-7" aria-hidden="true" tabindex="-1"></a> chb_ha_tC</span>
<span id="cb8-8"><a href="#cb8-8" aria-hidden="true" tabindex="-1"></a> ),</span>
<span id="cb8-9"><a href="#cb8-9" aria-hidden="true" tabindex="-1"></a> by <span class="ot">=</span> .(stratum_i, species_j)</span>
<span id="cb8-10"><a href="#cb8-10" aria-hidden="true" tabindex="-1"></a>] <span class="sc">|></span> <span class="fu">kbl</span>() <span class="sc">|></span> <span class="fu">kable_styling</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<table class="table caption-top table-sm table-striped small" data-quarto-postprocess="true">
<thead>
<tr class="header">
<th style="text-align: left;" data-quarto-table-cell-role="th">stratum_i</th>
<th style="text-align: left;" data-quarto-table-cell-role="th">species_j</th>
<th style="text-align: right;" data-quarto-table-cell-role="th">vji_sp_m3</th>
<th style="text-align: right;" data-quarto-table-cell-role="th">vji_ha_m3</th>
<th style="text-align: right;" data-quarto-table-cell-role="th">chb_ha_tC</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td style="text-align: left;">1</td>
<td style="text-align: left;">Sp1</td>
<td style="text-align: right;">12.18</td>
<td style="text-align: right;">121.8</td>
<td style="text-align: right;">42.63</td>
</tr>
<tr class="even">
<td style="text-align: left;">1</td>
<td style="text-align: left;">Sp1</td>
<td style="text-align: right;">12.18</td>
<td style="text-align: right;">121.8</td>
<td style="text-align: right;">42.63</td>
</tr>
<tr class="odd">
<td style="text-align: left;">1</td>
<td style="text-align: left;">Sp1</td>
<td style="text-align: right;">12.18</td>
<td style="text-align: right;">121.8</td>
<td style="text-align: right;">42.63</td>
</tr>
<tr class="even">
<td style="text-align: left;">1</td>
<td style="text-align: left;">Sp4</td>
<td style="text-align: right;">3.18</td>
<td style="text-align: right;">31.8</td>
<td style="text-align: right;">11.13</td>
</tr>
<tr class="odd">
<td style="text-align: left;">1</td>
<td style="text-align: left;">Sp4</td>
<td style="text-align: right;">3.18</td>
<td style="text-align: right;">31.8</td>
<td style="text-align: right;">11.13</td>
</tr>
<tr class="even">
<td style="text-align: left;">2</td>
<td style="text-align: left;">Sp1</td>
<td style="text-align: right;">1.38</td>
<td style="text-align: right;">13.8</td>
<td style="text-align: right;">4.83</td>
</tr>
<tr class="odd">
<td style="text-align: left;">2</td>
<td style="text-align: left;">Sp2</td>
<td style="text-align: right;">3.24</td>
<td style="text-align: right;">32.4</td>
<td style="text-align: right;">11.34</td>
</tr>
<tr class="even">
<td style="text-align: left;">2</td>
<td style="text-align: left;">Sp3</td>
<td style="text-align: right;">3.72</td>
<td style="text-align: right;">37.2</td>
<td style="text-align: right;">13.02</td>
</tr>
<tr class="odd">
<td style="text-align: left;">2</td>
<td style="text-align: left;">Sp4</td>
<td style="text-align: right;">2.94</td>
<td style="text-align: right;">29.4</td>
<td style="text-align: right;">10.29</td>
</tr>
<tr class="even">
<td style="text-align: left;">2</td>
<td style="text-align: left;">Sp5</td>
<td style="text-align: right;">3.36</td>
<td style="text-align: right;">33.6</td>
<td style="text-align: right;">11.76</td>
</tr>
</tbody>
</table>
</div>
</div>
</section>
<section id="eq4-extracted-carbon" class="level4">
<h4 class="anchored" data-anchor-id="eq4-extracted-carbon">EQ4: Extracted carbon</h4>
<p>“Not all of the harvested biomass leaves the forest because the timber harvested has two components: 1) wood removed to market (extracted timber) and 2) wood remaining in the forest as a result of harvest” (VM0010, 2024:21).</p>
<p>To account for all harvest removals, ‘equation 4’ computes mean carbon of species <em>i</em> in stratum <em>j</em> by adding mean timber to market (<span class="math inline">\(V_{EX,j,i|BSL}\)</span>) and mean timber used in harvest infrastructure (<span class="math inline">\(V_{EX,INF,j,i|BSL}\)</span>). This sum is then multiplied by the wood density <span class="math inline">\(D\)</span> and carbon fraction <span class="math inline">\(CF\)</span> of that species and reported in units of tC.ha<sup>-1</sup> using the following formula:</p>
<p><span class="math display">\[C_{EX,j,i|BSL} = (V_{EX,j,i|BSL} + V_{EX,INF,j,i|BSL} ) * D_{j} * CF_{j}\]</span></p>
<div class="cell">
<div class="sourceCode cell-code" id="cb9"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>dataset_tidy <span class="ot"><-</span> dataset_tidy <span class="sc">%>%</span></span>
<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">cex_ha_tC =</span> vji_ha_m3 <span class="sc">*</span> d <span class="sc">*</span> cf)</span>
<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a>data.table<span class="sc">::</span><span class="fu">setDT</span>(dataset_tidy)[, .(</span>
<span id="cb9-5"><a href="#cb9-5" aria-hidden="true" tabindex="-1"></a> vji_sp_m3,</span>
<span id="cb9-6"><a href="#cb9-6" aria-hidden="true" tabindex="-1"></a> vji_ha_m3,</span>
<span id="cb9-7"><a href="#cb9-7" aria-hidden="true" tabindex="-1"></a> chb_ha_tC,</span>
<span id="cb9-8"><a href="#cb9-8" aria-hidden="true" tabindex="-1"></a> cex_ha_tC</span>
<span id="cb9-9"><a href="#cb9-9" aria-hidden="true" tabindex="-1"></a> ),</span>
<span id="cb9-10"><a href="#cb9-10" aria-hidden="true" tabindex="-1"></a> by <span class="ot">=</span> .(stratum_i, species_j)</span>
<span id="cb9-11"><a href="#cb9-11" aria-hidden="true" tabindex="-1"></a>] <span class="sc">|></span> <span class="fu">kbl</span>() <span class="sc">|></span> <span class="fu">kable_styling</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<table class="table caption-top table-sm table-striped small" data-quarto-postprocess="true">
<thead>
<tr class="header">
<th style="text-align: left;" data-quarto-table-cell-role="th">stratum_i</th>
<th style="text-align: left;" data-quarto-table-cell-role="th">species_j</th>
<th style="text-align: right;" data-quarto-table-cell-role="th">vji_sp_m3</th>
<th style="text-align: right;" data-quarto-table-cell-role="th">vji_ha_m3</th>
<th style="text-align: right;" data-quarto-table-cell-role="th">chb_ha_tC</th>
<th style="text-align: right;" data-quarto-table-cell-role="th">cex_ha_tC</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td style="text-align: left;">1</td>
<td style="text-align: left;">Sp1</td>
<td style="text-align: right;">12.18</td>
<td style="text-align: right;">121.8</td>
<td style="text-align: right;">42.63</td>
<td style="text-align: right;">30.45</td>
</tr>
<tr class="even">
<td style="text-align: left;">1</td>
<td style="text-align: left;">Sp1</td>
<td style="text-align: right;">12.18</td>
<td style="text-align: right;">121.8</td>
<td style="text-align: right;">42.63</td>
<td style="text-align: right;">30.45</td>
</tr>
<tr class="odd">
<td style="text-align: left;">1</td>
<td style="text-align: left;">Sp1</td>
<td style="text-align: right;">12.18</td>
<td style="text-align: right;">121.8</td>
<td style="text-align: right;">42.63</td>
<td style="text-align: right;">30.45</td>
</tr>
<tr class="even">
<td style="text-align: left;">1</td>
<td style="text-align: left;">Sp4</td>
<td style="text-align: right;">3.18</td>
<td style="text-align: right;">31.8</td>
<td style="text-align: right;">11.13</td>
<td style="text-align: right;">7.95</td>
</tr>
<tr class="odd">
<td style="text-align: left;">1</td>
<td style="text-align: left;">Sp4</td>
<td style="text-align: right;">3.18</td>
<td style="text-align: right;">31.8</td>
<td style="text-align: right;">11.13</td>
<td style="text-align: right;">7.95</td>
</tr>
<tr class="even">
<td style="text-align: left;">2</td>
<td style="text-align: left;">Sp1</td>
<td style="text-align: right;">1.38</td>
<td style="text-align: right;">13.8</td>
<td style="text-align: right;">4.83</td>
<td style="text-align: right;">3.45</td>
</tr>
<tr class="odd">
<td style="text-align: left;">2</td>
<td style="text-align: left;">Sp2</td>
<td style="text-align: right;">3.24</td>
<td style="text-align: right;">32.4</td>
<td style="text-align: right;">11.34</td>
<td style="text-align: right;">8.10</td>
</tr>
<tr class="even">
<td style="text-align: left;">2</td>
<td style="text-align: left;">Sp3</td>
<td style="text-align: right;">3.72</td>
<td style="text-align: right;">37.2</td>
<td style="text-align: right;">13.02</td>
<td style="text-align: right;">9.30</td>
</tr>
<tr class="odd">
<td style="text-align: left;">2</td>
<td style="text-align: left;">Sp4</td>
<td style="text-align: right;">2.94</td>
<td style="text-align: right;">29.4</td>
<td style="text-align: right;">10.29</td>
<td style="text-align: right;">7.35</td>
</tr>
<tr class="even">
<td style="text-align: left;">2</td>
<td style="text-align: left;">Sp5</td>
<td style="text-align: right;">3.36</td>
<td style="text-align: right;">33.6</td>
<td style="text-align: right;">11.76</td>
<td style="text-align: right;">8.40</td>
</tr>
</tbody>
</table>
</div>
</div>
</section>
<section id="eq5-slash-carbon" class="level4">
<h4 class="anchored" data-anchor-id="eq5-slash-carbon">EQ5: Slash carbon</h4>
<p><span class="math display">\[∆C_{DWSLASH_,i,p|BSL} = \sum_{i=1}^{j} \space [C_{HB,j,i|BSL} - C_{EX,j,i|BSL} + C_{RSD,j,i|BSL} + C_{notHB,inf,j,i|BSL}]\]</span></p>
<p>Equation 5 computes carbon change produced by slash as “the difference between the total carbon stock of the harvested biomass and the carbon stock of the extracted timber, plus the residual stand damage and biomass of trees left to decay as a result forestry infrastructure establishment”. Specifically, values of <span class="math inline">\(C_{notHB,inf,j,i|BSL}\)</span> are computed by applying a fractional value of timber used in harvesting infrastructure development (<span class="math inline">\(F_{V,INF,HWP}\)</span>), which may be provided by project proponent, and if missing will be conservatively assumed as 0.0%.</p>
</section>
<section id="eq6-damaged-carbon" class="level4">
<h4 class="anchored" data-anchor-id="eq6-damaged-carbon">EQ6: Damaged carbon</h4>
<p><span class="math inline">\(C_{RSD,j,i\|BSL}\)</span> is defined in units of tC·ha<sup>-1</sup> as mean carbon change from residual stand damage as computed in the following:</p>
<p><span class="math display">\[C_{RSD,j,i\|BSL} = C_{EX,j,i|BSL} \times F_{RSD|BSL}\]</span> where <span class="math inline">\(F_{RSD|BSL}\)</span> represents a dimensionless value for the factor of “residual stand damage” per species in that area. On page 56 of the VM0010 document, an example reference is cited for sourcing residual stand damage values <span class="citation" data-cites="winjum1998">(<a href="#ref-winjum1998" role="doc-biblioref">Winjum, Brown, and Schlamadinger 1998</a>)</span>. We apply the reported value of Congo operations of 1.74 t compute the following:</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb10"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>dataset_tidy <span class="ot">=</span> dataset_tidy <span class="sc">%>%</span></span>
<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">f_rsd =</span> <span class="fl">1.74</span>)</span>
<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb10-4"><a href="#cb10-4" aria-hidden="true" tabindex="-1"></a>dataset_tidy <span class="ot">=</span> dataset_tidy <span class="sc">%>%</span></span>