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<h1 id="chapter-1-workbook">Chapter 1 Workbook</h1>
<p>These are my solutions to the Chapter 1 problems of <a href="http://www.amazon.com/gp/product/0521865565/">Principles of
Planetary Climate</a>. I
make no claims as to their accuracy, but if you are interested in
seeing what I've done go right ahead.</p>
<p>First we have some imports and useful constants. Python doesn't have a
built-in sign function, so we have a simple implementation here
also. I've imported seaborn, which is an interesting graphing library
built on top of matplotlib. It does a lot of fancy things we don't
need, but importing it also makes all matplotlib graphs look nicer.</p>
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<div class="highlight"><pre><span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">e</span><span class="p">,</span> <span class="n">log2</span><span class="p">,</span> <span class="n">pi</span><span class="p">,</span> <span class="n">log</span>
<span class="kn">from</span> <span class="nn">functools</span> <span class="kn">import</span> <span class="n">partial</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="kn">as</span> <span class="nn">pd</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">seaborn</span> <span class="kn">as</span> <span class="nn">sns</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">scipy.integrate</span> <span class="kn">import</span> <span class="n">romb</span><span class="p">,</span> <span class="n">quad</span><span class="p">,</span> <span class="n">odeint</span>
<span class="kn">from</span> <span class="nn">scipy.interpolate</span> <span class="kn">import</span> <span class="n">InterpolatedUnivariateSpline</span>
<span class="kn">from</span> <span class="nn">scipy.misc</span> <span class="kn">import</span> <span class="n">derivative</span>
<span class="c"># gravitational constant</span>
<span class="n">G</span> <span class="o">=</span> <span class="mf">6.67e-11</span>
<span class="c"># mass of the earth</span>
<span class="n">M_e</span> <span class="o">=</span> <span class="mf">6e24</span>
<span class="c"># radius of earth, in m</span>
<span class="n">r_earth</span> <span class="o">=</span> <span class="mi">6378100</span>
<span class="c"># surface area of earth</span>
<span class="n">sa_e</span> <span class="o">=</span> <span class="mi">4</span><span class="o">*</span><span class="n">pi</span><span class="o">*</span><span class="n">r_earth</span><span class="o">**</span><span class="mi">2</span>
<span class="n">seconds_per_year</span> <span class="o">=</span> <span class="mi">60</span> <span class="o">*</span> <span class="mi">60</span> <span class="o">*</span> <span class="mi">24</span> <span class="o">*</span> <span class="mi">365</span>
<span class="c">#VSMOW</span>
<span class="n">O18_p_O16</span> <span class="o">=</span> <span class="mi">1</span><span class="o">/</span><span class="mf">498.7</span>
<span class="n">D_p_H</span> <span class="o">=</span> <span class="mi">1</span><span class="o">/</span><span class="mi">6420</span>
<span class="k">def</span> <span class="nf">sign</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="k">try</span><span class="p">:</span>
<span class="k">return</span> <span class="n">x</span><span class="o">/</span><span class="nb">abs</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="k">except</span> <span class="ne">ZeroDivisionError</span><span class="p">:</span>
<span class="k">return</span> <span class="mi">0</span>
<span class="o">%</span><span class="k">matplotlib</span> <span class="n">inline</span>
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<h3 id="problem-1-">Problem 1.</h3>
<p>This is pretty simple. We just need to plot a function. You can do
basic math on NumPy arrays, which is pretty sweet.</p>
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<div class="highlight"><pre><span class="c"># problem 1.1 -</span>
<span class="k">def</span> <span class="nf">luminosity</span><span class="p">(</span><span class="n">ages</span><span class="p">,</span> <span class="n">t0</span><span class="o">=</span><span class="mf">4.6e9</span><span class="p">):</span>
<span class="k">return</span> <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="mf">0.4</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">ages</span><span class="o">/</span><span class="n">t0</span><span class="p">)))</span>
<span class="k">def</span> <span class="nf">problem1</span><span class="p">():</span>
<span class="n">ages</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">5e9</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
<span class="n">luminosities</span> <span class="o">=</span> <span class="n">luminosity</span><span class="p">(</span><span class="n">ages</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">9</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s">"Luminosity vs. age of the Sun"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">ages</span><span class="p">,</span> <span class="n">luminosities</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s">"Age (billions of years)"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s">"Luminosity as a fraction of current day"</span><span class="p">)</span>
<span class="n">problem1</span><span class="p">()</span>
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<h3 id="problem-2-">Problem 2.</h3>
<p>What was initially just a simple file IO example was complicated by
some interesting encoding issues. The Vostok ice core data was
unreadable with UTF-8. So I opened the file in Firefox - some of the
scientists' names were rendered improperly. I played with the encoding
until it worked - unfortunately it was just listed in Firefox as
"Western." I then looked up what possible encodings I could use and
used the one labeled "Western Europe."</p>
<p>Additionally the C CSV parsing engine was having issues using the
<code>delim_whitespace</code> option, so I had to specify the Python engine
instead. Fortunately this dataset was pretty small (about 3000 lines)
so the speed hit wasn't really important.</p>
<p>I thought that having a line connecting the data points hid the
decrease in data density as ice age increases, so I made it with
points instead.</p>
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In [3]:
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<div class="highlight"><pre><span class="k">def</span> <span class="nf">problem2</span><span class="p">():</span>
<span class="n">vostokT</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="s">"data/Chapter1Data/iceCores/vostokT.txt"</span><span class="p">,</span>
<span class="n">skiprows</span><span class="o">=</span><span class="mi">115</span><span class="p">,</span>
<span class="n">encoding</span><span class="o">=</span><span class="s">'iso8859_15'</span><span class="p">,</span> <span class="c"># "Western" encoding</span>
<span class="n">delimiter</span><span class="o">=</span><span class="s">'\s'</span><span class="p">,</span>
<span class="n">engine</span><span class="o">=</span><span class="s">"python"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s">"Temperature change vs. ice age"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">vostokT</span><span class="o">.</span><span class="n">corrected_Ice_age_GT4</span><span class="p">,</span> <span class="n">vostokT</span><span class="o">.</span><span class="n">deltaTS</span><span class="p">,</span>
<span class="n">marker</span><span class="o">=</span><span class="s">"."</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s">"none"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s">"Ice age (years)"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s">"Temperature difference from present (C)"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s">"Depth vs. ice age"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">vostokT</span><span class="o">.</span><span class="n">corrected_Ice_age_GT4</span><span class="p">,</span> <span class="n">vostokT</span><span class="o">.</span><span class="n">Depth</span><span class="p">,</span>
<span class="n">marker</span><span class="o">=</span><span class="s">"."</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s">"none"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s">"Ice age (years)"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s">"Ice core depth (m)"</span><span class="p">)</span>
<span class="n">problem2</span><span class="p">()</span>
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