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<h1>Calculate Percentage of Radiation in Spectral Bands</h1>
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<h1>Calculate Percentage of Radiation in Spectral Bands<a class="headerlink" href="#calculate-percentage-of-radiation-in-spectral-bands" title="Permalink to this headline">#</a></h1>
<p><i>© Von P. Walden, Washington State University</i></p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">xarray</span> <span class="k">as</span> <span class="nn">xr</span>
</pre></div>
</div>
</div>
</div>
<section id="for-a-given-temperature-t-calculate-the-proportion-of-radiation-emitted-in-various-spectral-bands-uv-visible-near-infrared-and-infrared">
<h2>For a given temperature T, calculate the proportion of radiation emitted in various spectral bands (UV, visible, near-infrared, and infrared).<a class="headerlink" href="#for-a-given-temperature-t-calculate-the-proportion-of-radiation-emitted-in-various-spectral-bands-uv-visible-near-infrared-and-infrared" title="Permalink to this headline">#</a></h2>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Temperature of the object</span>
<span class="c1">#T = 5700. # K</span>
<span class="n">T</span> <span class="o">=</span> <span class="mf">3300.</span> <span class="c1"># K</span>
<span class="c1">#T = 300. # K</span>
</pre></div>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Calculate the Planck radiation distribution between 0 and 50 microns</span>
<span class="n">c</span> <span class="o">=</span> <span class="mf">2.998e8</span> <span class="c1"># m s-1</span>
<span class="n">h</span> <span class="o">=</span> <span class="mf">6.626e-34</span> <span class="c1"># m2 kg s-1</span>
<span class="n">kB</span> <span class="o">=</span> <span class="mf">1.381e-23</span> <span class="c1"># m2 kg s-2 K-1</span>
<span class="n">dl</span> <span class="o">=</span> <span class="mf">0.01</span> <span class="c1"># meters</span>
<span class="n">l</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">dl</span><span class="p">,</span><span class="mi">50</span><span class="p">,</span><span class="n">dl</span><span class="p">)</span> <span class="o">*</span> <span class="mf">1e-6</span> <span class="c1"># meters</span>
<span class="n">B</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">h</span><span class="o">*</span><span class="n">c</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="n">l</span><span class="o">**</span><span class="mi">5</span> <span class="o">*</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">((</span><span class="n">h</span><span class="o">*</span><span class="n">c</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">l</span> <span class="o">*</span><span class="n">kB</span> <span class="o">*</span> <span class="n">T</span><span class="p">))</span> <span class="o">-</span> <span class="mf">1.</span><span class="p">))</span> <span class="o">*</span> <span class="mf">1e-6</span> <span class="c1"># W m-2 um-1</span>
<span class="n">spectralFlux</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">B</span> <span class="c1"># W m-2 um-1</span>
<span class="c1"># Convert spectralFlux to an Xarray data array</span>
<span class="n">spectralFlux</span> <span class="o">=</span> <span class="n">xr</span><span class="o">.</span><span class="n">DataArray</span><span class="p">(</span><span class="n">spectralFlux</span><span class="p">,</span> <span class="n">coords</span><span class="o">=</span><span class="p">{</span><span class="s1">'wavelength'</span><span class="p">:</span> <span class="n">l</span><span class="o">*</span><span class="mf">1e6</span><span class="p">},</span> <span class="n">dims</span><span class="o">=</span><span class="p">[</span><span class="s1">'wavelength'</span><span class="p">])</span>
<span class="c1"># Sum the radiation in uv, vis, nir and ir spectral bands:</span>
<span class="c1"># UV = 0 to 0.3 microns</span>
<span class="c1"># visible = 0.3 to 0.7 microns</span>
<span class="c1"># near infrared = 0.7 to 4 microns</span>
<span class="c1"># infrared = 4 to 50 microns</span>
<span class="n">uv</span> <span class="o">=</span> <span class="n">spectralFlux</span><span class="o">.</span><span class="n">sel</span><span class="p">(</span><span class="n">wavelength</span><span class="o">=</span><span class="nb">slice</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mf">0.3</span><span class="p">))</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span><span class="o">*</span><span class="n">dl</span>
<span class="n">vis</span> <span class="o">=</span> <span class="n">spectralFlux</span><span class="o">.</span><span class="n">sel</span><span class="p">(</span><span class="n">wavelength</span><span class="o">=</span><span class="nb">slice</span><span class="p">(</span><span class="mf">0.3</span><span class="p">,</span><span class="mf">0.7</span><span class="p">))</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span><span class="o">*</span><span class="n">dl</span>
<span class="n">nir</span> <span class="o">=</span> <span class="n">spectralFlux</span><span class="o">.</span><span class="n">sel</span><span class="p">(</span><span class="n">wavelength</span><span class="o">=</span><span class="nb">slice</span><span class="p">(</span><span class="mf">0.7</span><span class="p">,</span><span class="mi">4</span><span class="p">))</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span><span class="o">*</span><span class="n">dl</span>
<span class="n">ir</span> <span class="o">=</span> <span class="n">spectralFlux</span><span class="o">.</span><span class="n">sel</span><span class="p">(</span><span class="n">wavelength</span><span class="o">=</span><span class="nb">slice</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span><span class="mi">50</span><span class="p">))</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span><span class="o">*</span><span class="n">dl</span>
<span class="c1"># Calculate the percent contribution in each band</span>
<span class="n">Flux</span> <span class="o">=</span> <span class="n">spectralFlux</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span><span class="o">*</span><span class="n">dl</span> <span class="c1"># Total flux in W m-2; Should be nearly equal to sigma * T^4 !!</span>
<span class="n">p_uv</span> <span class="o">=</span> <span class="n">uv</span> <span class="o">/</span> <span class="n">Flux</span> <span class="o">*</span> <span class="mi">100</span>
<span class="n">p_vis</span> <span class="o">=</span> <span class="n">vis</span> <span class="o">/</span> <span class="n">Flux</span> <span class="o">*</span> <span class="mi">100</span>
<span class="n">p_nir</span> <span class="o">=</span> <span class="n">nir</span> <span class="o">/</span> <span class="n">Flux</span> <span class="o">*</span> <span class="mi">100</span>
<span class="n">p_ir</span> <span class="o">=</span> <span class="n">ir</span> <span class="o">/</span> <span class="n">Flux</span> <span class="o">*</span> <span class="mi">100</span>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1">#%% Sum all the spectral bands; should be close to 100% !!</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'Percent UV: '</span><span class="p">,</span> <span class="n">p_uv</span><span class="o">.</span><span class="n">values</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'Percent visible: '</span><span class="p">,</span> <span class="n">p_vis</span><span class="o">.</span><span class="n">values</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'Percent near infrared: '</span><span class="p">,</span> <span class="n">p_nir</span><span class="o">.</span><span class="n">values</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'Percent infrared: '</span><span class="p">,</span> <span class="n">p_ir</span><span class="o">.</span><span class="n">values</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'Total percent: '</span><span class="p">,</span> <span class="n">p_uv</span><span class="o">.</span><span class="n">values</span> <span class="o">+</span> <span class="n">p_vis</span><span class="o">.</span><span class="n">values</span> <span class="o">+</span> <span class="n">p_nir</span><span class="o">.</span><span class="n">values</span> <span class="o">+</span> <span class="n">p_ir</span><span class="o">.</span><span class="n">values</span><span class="p">)</span>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Percent UV: 0.034502797207032025
Percent visible: 11.862449236428064
Percent near infrared: 83.81426836992065
Percent infrared: 4.327490415712202
Total percent: 100.03871081926796
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