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<!DOCTYPE html>
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<title>Tutorial and Recipes — PRMS-Python v1.0.0</title>
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<ul class="current">
<li class="toctree-l1 current"><a class="current reference internal" href="#">Tutorial and Recipes</a><ul>
<li class="toctree-l2"><a class="reference internal" href="#data"><code class="docutils literal notranslate"><span class="pre">Data</span></code></a></li>
<li class="toctree-l2"><a class="reference internal" href="#parameters"><code class="docutils literal notranslate"><span class="pre">Parameters</span></code></a></li>
<li class="toctree-l2"><a class="reference internal" href="#simulation-simulationseries"><code class="docutils literal notranslate"><span class="pre">Simulation</span> <span class="pre">&</span> <span class="pre">SimulationSeries</span></code></a></li>
<li class="toctree-l2"><a class="reference internal" href="#scenario-scenarioseries"><code class="docutils literal notranslate"><span class="pre">Scenario</span> <span class="pre">&</span> <span class="pre">ScenarioSeries</span></code></a></li>
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<div class="section" id="tutorial-and-recipes">
<h1>Tutorial and Recipes<a class="headerlink" href="#tutorial-and-recipes" title="Permalink to this headline">¶</a></h1>
<p>In this tutorial we walk through each important class and function, and explain
each one’s purpose and use with an example. At the end of the tutorial in
<a class="reference internal" href="#example"><span class="std std-ref">Example: Parameter sensitivity</span></a> we show a more advanced workflow involving parameter sensitivity
over dual parameter space that uses several of the previously described classes
and functions.</p>
<div class="section" id="data">
<h2><code class="docutils literal notranslate"><span class="pre">Data</span></code><a class="headerlink" href="#data" title="Permalink to this headline">¶</a></h2>
<p>The <a class="reference internal" href="api.html#id1"><span class="std std-ref">Data Class</span></a> class loads a PRMS data file into a Pandas DataFrame and allows
for easy modification and writing of PRMS data files.</p>
<p>A PRMS data file holds time series variables that are used as input for running
PRMS, e.g. daily air temperature and precipitation. Being tabular and date-indexed
the data file is well represented and managed as a <a class="reference external" href="https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.html#pandas.DataFrame" title="(in pandas v1.1.4)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pandas.DataFrame</span></code></a>.
A common paractice in hydrologic modeling is to evaluate hydrologic response
to multiple climate change scenarios. The <code class="docutils literal notranslate"><span class="pre">Data</span></code> class offers function-based
modification of time series variable/s so that the user can quickly create new
climate inputs for PRMS. The user can visualize the data file variables from
easily using Pandas, matplotlib or other plotting libraries. After modification
of climatic variables the <code class="docutils literal notranslate"><span class="pre">Data.write</span></code> method will save the data
to disk in the PRMS ascii format.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">prms_python</span> <span class="kn">import</span> <span class="n">Data</span>
<span class="n">d</span> <span class="o">=</span> <span class="n">Data</span><span class="p">(</span><span class="s1">'test/data/data'</span><span class="p">)</span>
<span class="c1"># modify daily temperature by adding 2 degrees to each input</span>
<span class="k">def</span> <span class="nf">f</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="k">return</span> <span class="p">(</span><span class="n">x</span> <span class="o">+</span> <span class="mi">2</span><span class="p">)</span>
<span class="c1"># apply function to daily temperature input</span>
<span class="n">d</span><span class="o">.</span><span class="n">modify</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="p">[</span><span class="s1">'tmax'</span><span class="p">,</span><span class="s1">'tmin'</span><span class="p">])</span>
<span class="c1"># write new modified data file to disk</span>
<span class="n">d</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="s1">'test/data/temp_plus2_data'</span><span class="p">)</span>
</pre></div>
</div>
<p>The <code class="docutils literal notranslate"><span class="pre">Data.data_frame</span></code> property is the <a class="reference external" href="https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.html#pandas.DataFrame" title="(in pandas v1.1.4)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pandas.DataFrame</span></code></a> representation
of hydro-climatic variables found in a PRMS data file. As such it can also
be assigned within Python. However in order to create a data file from scratch
using the <code class="docutils literal notranslate"><span class="pre">Data</span></code> object one must also assign the <code class="docutils literal notranslate"><span class="pre">Data.metadata</span></code> property.
For an example of what is stored in the <code class="docutils literal notranslate"><span class="pre">metadata</span></code> attribute please refer
to the <a class="reference external" href="https://github.com/PRMS-Python/PRMS-Python/blob/master/notebooks/data_examples.ipynb">data examples Jupyter notebook</a>.</p>
<p>The <code class="docutils literal notranslate"><span class="pre">write</span></code> method of data has dual functions
depending on the status of a <code class="docutils literal notranslate"><span class="pre">Data</span></code> instance– if the method is called before
the <code class="docutils literal notranslate"><span class="pre">Data.data_frame</span></code> is accessed then the original file will be simply copied
to the path given to <code class="docutils literal notranslate"><span class="pre">write</span></code>, on the other hand if the <code class="docutils literal notranslate"><span class="pre">data_frame</span></code> has been
accessed within Python then the <code class="docutils literal notranslate"><span class="pre">write</span></code> method writes the current state of the
data in the <code class="docutils literal notranslate"><span class="pre">data_frame</span></code> from memory. The first function is useful in reducing
memory use and computational cost when using the <code class="docutils literal notranslate"><span class="pre">Data</span></code> class in more advanced
workflows.</p>
<p>The <code class="docutils literal notranslate"><span class="pre">Scenario</span></code> and <code class="docutils literal notranslate"><span class="pre">ScenarioSeries</span></code> will soon incorporate the functionality
to modify the climatic data within either a single Scenario or a
series of Scenarios.</p>
</div>
<div class="section" id="parameters">
<h2><code class="docutils literal notranslate"><span class="pre">Parameters</span></code><a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2>
<p>The <a class="reference internal" href="api.html#id2"><span class="std std-ref">Parameters Class</span></a> provides a NumPy-backed
representation of a PRMS parameters file that allows the user to select,
modify, and save PRMS parameters files. It can be used similarly to a
Pandas DataFrame.</p>
<p>The PRMS parameters file contains data arrays of varying dimensionality, which
is why we can’t simply use a DataFrame to do these manipulations. The
implementation of the <code class="docutils literal notranslate"><span class="pre">Parameters</span></code> class is loosely based on the netCDF
data structure, where metadata about each parameter is kept separately.
Parameters are read into memory only if the user selects or modifies a
particular parameter. This allows for memory-efficient processing of Parameter files.</p>
<p>Below is an example of reading a parameter file, reading a particular variable
from a parameter file, replacing that parameter data with other data (in this
case an array of all zeros), then saving the modified parameters to a new
Parameters file.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">prms_python</span> <span class="kn">import</span> <span class="n">Parameters</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">Parameters</span><span class="p">(</span><span class="s1">'test/data/parameter'</span><span class="p">)</span>
<span class="c1"># select PRMS parameter by name, raising KeyError if DNE</span>
<span class="n">snow_adj</span> <span class="o">=</span> <span class="n">p</span><span class="p">[</span><span class="s1">'snow_adj'</span><span class="p">]</span>
<span class="k">assert</span> <span class="n">snow_adj</span><span class="o">.</span><span class="n">shape</span> <span class="o">==</span> <span class="p">(</span><span class="mi">12</span><span class="p">,</span> <span class="mi">16</span><span class="p">)</span>
<span class="c1"># assign values to PRMS parameter</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="n">z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">snow_adj</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="n">p</span><span class="p">[</span><span class="s1">'snow_adj'</span><span class="p">]</span> <span class="o">=</span> <span class="n">z</span> <span class="c1"># now p['snow_adj'] is 12x16 matrix of zeros</span>
<span class="c1"># write modified parameters to file</span>
<span class="n">p</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="s1">'newparameters'</span><span class="p">)</span>
</pre></div>
</div>
<p>The <code class="docutils literal notranslate"><span class="pre">Scenario</span></code> and <code class="docutils literal notranslate"><span class="pre">ScenarioSeries</span></code> use this functionality (via the
<cite>prms_python.modify_params</cite> function) to implement either a single Scenario or a
series of Scenarios.</p>
</div>
<div class="section" id="simulation-simulationseries">
<h2><code class="docutils literal notranslate"><span class="pre">Simulation</span> <span class="pre">&</span> <span class="pre">SimulationSeries</span></code><a class="headerlink" href="#simulation-simulationseries" title="Permalink to this headline">¶</a></h2>
<p>The <a class="reference internal" href="api.html#id3"><span class="std std-ref">Simulation class</span></a> provides a simple wrapper around running the PRMS
model. It encourages standardization of input file names by requiring the
three PRMS inputs to be named <cite>data</cite>, <cite>parameters</cite>, and <cite>control</cite>. In order to
add some natural metadata to the inputs, the user should use a memorable name
for the directory that holds these three files. The <code class="docutils literal notranslate"><span class="pre">Simulation</span></code> and
<code class="docutils literal notranslate"><span class="pre">SimulationSeries</span></code> however are more useful as building blocks for more
advanced workflows or for new PRMS-Python submodules and routines, e.g.
new optimization routines.</p>
<p>After the user prepares their input files, say into a directory called
<code class="docutils literal notranslate"><span class="pre">prms-sim-example</span></code>, they can run the following in either a Python script or a
Python REPL</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">prms_python</span> <span class="kn">import</span> <span class="n">Simulation</span>
<span class="n">sim</span> <span class="o">=</span> <span class="n">Simulation</span><span class="p">(</span><span class="s1">'prms-sim-example'</span><span class="p">)</span>
<span class="n">sim</span><span class="o">.</span><span class="n">run</span><span class="p">()</span>
</pre></div>
</div>
<p>This will run PRMS assuming the PRMS executable is on the system path and is
called <code class="docutils literal notranslate"><span class="pre">prms</span></code>. In this usage, the outputs will go to the
<code class="docutils literal notranslate"><span class="pre">prms-sim-dir</span></code> directory.
If the user wishes to use a different executable name or provide the path to
it explicitly, they can do so by replacing</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">sim</span><span class="o">.</span><span class="n">run</span><span class="p">()</span>
</pre></div>
</div>
<p>with</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">sim</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">prms_executable</span><span class="o">=</span><span class="s1">'path/to/myPRMSExecutable'</span><span class="p">)</span>
</pre></div>
</div>
<p>Another available option is to specify a different directory to use as the
“simulation directory,” which can be useful if you want to separate
a directory with only input data from directories where both input and output
model run data will be stored. You can do this by specifying an additional
keyword argument in the <code class="docutils literal notranslate"><span class="pre">Simulation</span></code> constructor, like so</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">sim</span> <span class="o">=</span> <span class="n">Simulation</span><span class="p">(</span><span class="s1">'prms-sim-example'</span><span class="p">,</span> <span class="n">simulation_dir</span><span class="o">=</span><span class="s1">'sim-dir-1'</span><span class="p">)</span>
<span class="n">sim</span><span class="o">.</span><span class="n">run</span><span class="p">()</span>
</pre></div>
</div>
<p>Additional examples of <code class="docutils literal notranslate"><span class="pre">Simulation</span></code> including the file structure can be found in
the API <a class="reference internal" href="api.html#prms_python.Simulation.run" title="prms_python.Simulation.run"><code class="xref py py-meth docutils literal notranslate"><span class="pre">prms_python.Simulation.run()</span></code></a> and the class method <code class="docutils literal notranslate"><span class="pre">from_data</span></code> which
allows for initialization from PRMS-Python <code class="docutils literal notranslate"><span class="pre">Data</span></code> and <code class="docutils literal notranslate"><span class="pre">Parameter</span></code> objects can
be found in the API at <a class="reference internal" href="api.html#prms_python.Simulation.from_data" title="prms_python.Simulation.from_data"><code class="xref py py-meth docutils literal notranslate"><span class="pre">prms_python.Simulation.from_data()</span></code></a>.</p>
<div class="section" id="simulationseries">
<h3><code class="docutils literal notranslate"><span class="pre">SimulationSeries</span></code><a class="headerlink" href="#simulationseries" title="Permalink to this headline">¶</a></h3>
<p>The <a class="reference internal" href="api.html#id4"><span class="std std-ref">SimulationSeries class</span></a> offers the same functionality
as <code class="docutils literal notranslate"><span class="pre">Simulation</span></code> for an arbitrary number of simulations, with the added function
of running PRMS in parralel. The example below is taken from the PRMS-Python API.</p>
<p>Lets say you have already created a series of PRMS models by modifying
the input climatic forcing data, e.g. you have 100 <em>data</em> files and
you want to run each using the same <em>control</em> and <em>parameters</em> file.
For simplicity lets say there is a directory that contains all 100
<em>data</em> files e.g. data1, data2, … or whatever they are named and
nothing else. This example also assumes that you want each simulation
to be run and stored in directories named after the <em>data</em> files as
shown.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">data_dir</span> <span class="o">=</span> <span class="s1">'dir_that_contains_all_data_files'</span>
<span class="n">params</span> <span class="o">=</span> <span class="n">Parameters</span><span class="p">(</span><span class="s1">'path_to_parameter_file'</span><span class="p">)</span>
<span class="n">control_path</span> <span class="o">=</span> <span class="s1">'path_to_control'</span>
<span class="c1"># a list comprehension to make multiple simulations with</span>
<span class="c1"># different data files, alternatively you could use a for loop</span>
<span class="n">sims</span> <span class="o">=</span> <span class="p">[</span>
<span class="n">Simulation</span><span class="o">.</span><span class="n">from_data</span>
<span class="p">(</span>
<span class="n">Data</span><span class="p">(</span><span class="n">data_file</span><span class="p">),</span>
<span class="n">params</span><span class="p">,</span>
<span class="n">control_path</span><span class="p">,</span>
<span class="n">simulation_dir</span><span class="o">=</span><span class="s1">'sim_{}'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">data_file</span><span class="p">)</span>
<span class="p">)</span>
<span class="k">for</span> <span class="n">data_file</span> <span class="ow">in</span> <span class="n">os</span><span class="o">.</span><span class="n">listdir</span><span class="p">(</span><span class="n">data_dir</span><span class="p">)</span>
<span class="p">]</span>
</pre></div>
</div>
<p>Next we can use <code class="docutils literal notranslate"><span class="pre">SimulationSeries</span></code> to run all of these
simulations in parrallel. For example we may use 8 logical cores
on a common desktop computer.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">sim_series</span> <span class="o">=</span> <span class="n">SimulationSeries</span><span class="p">(</span><span class="n">sims</span><span class="p">)</span>
<span class="n">sim_series</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">nprocs</span><span class="o">=</span><span class="mi">8</span><span class="p">)</span>
</pre></div>
</div>
<p>The <code class="docutils literal notranslate"><span class="pre">SimulationSeries.run()</span></code> method will run all 100 simulations
where chunks of 8 at a time will be run in parrallel. Inputs and
outputs of each simulation will be sent to each simulation’s
<code class="docutils literal notranslate"><span class="pre">simulation_dir</span></code> following the file structure of
<code class="xref py py-func docutils literal notranslate"><span class="pre">Simulation.run()</span></code>.</p>
</div>
</div>
<div class="section" id="scenario-scenarioseries">
<span id="scenario-and-scenarioseries-tutorial"></span><h2><code class="docutils literal notranslate"><span class="pre">Scenario</span> <span class="pre">&</span> <span class="pre">ScenarioSeries</span></code><a class="headerlink" href="#scenario-scenarioseries" title="Permalink to this headline">¶</a></h2>
<p>The <a class="reference internal" href="api.html#id5"><span class="std std-ref">Scenario class</span></a> implements data management on top of the
<code class="docutils literal notranslate"><span class="pre">Simulation</span></code> class, enforcing the user to separate base input data and
simulation input and output data, plus simple, optional metadata. Let’s dive
in with an example, assuming there are properly-formed files called <code class="docutils literal notranslate"><span class="pre">data</span></code>,
<code class="docutils literal notranslate"><span class="pre">control</span></code>, and <code class="docutils literal notranslate"><span class="pre">parameters</span></code>, in a directory called <code class="docutils literal notranslate"><span class="pre">base-inputs</span></code>.
We’ll use a simulation directory called <code class="docutils literal notranslate"><span class="pre">sim-dir</span></code> and further provide a title
and description for the Scenario. If <code class="docutils literal notranslate"><span class="pre">sim-dir</span></code> exists it will be overwritten
and if it does not exist it will be created. It’s up to the user to make sure
data doesn’t get overwritten.</p>
<p>Both Scenarios and ScenarioSeries have a three-step process for set-up and run.
First the Scenario or ScenarioSeries must be initialized with the base and
simulation paths, plus, optionally, a title and description. Next, the
Scenario(Series) must be “built”. This means defining which/how parameters
should be modified.</p>
<div class="section" id="scenario">
<span id="scenario-tutorial"></span><h3><code class="docutils literal notranslate"><span class="pre">Scenario</span></code><a class="headerlink" href="#scenario" title="Permalink to this headline">¶</a></h3>
<p>First, let’s see how we implement these three steps for
a single Scenario. We’ll just increase one parameter, <code class="docutils literal notranslate"><span class="pre">jh_coef</span></code>, by 10%, or
multiply by a scaling factor of 1.10.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">sc</span> <span class="o">=</span> <span class="n">Scenario</span><span class="p">(</span><span class="s1">'base-inputs'</span><span class="p">,</span> <span class="s1">'sim-dir'</span><span class="p">,</span>
<span class="n">title</span><span class="o">=</span><span class="s1">'Example Scenario'</span><span class="p">,</span>
<span class="n">description</span><span class="o">=</span><span class="s1">'''</span>
<span class="s1">For the case of documentation we are including some example code.</span>
<span class="s1">Unless you actually have some inputs in the base-inputs directory used above</span>
<span class="s1">this will fail in an interpreter.</span>
<span class="s1">'''</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">scale_1p1</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="k">return</span> <span class="n">x</span> <span class="o">*</span> <span class="mf">1.1</span>
<span class="n">sc</span><span class="o">.</span><span class="n">build</span><span class="p">({</span><span class="s1">'jh_coeff'</span><span class="p">:</span> <span class="n">scale_1p1</span><span class="p">})</span>
<span class="n">sc</span><span class="o">.</span><span class="n">run</span><span class="p">()</span>
</pre></div>
</div>
</div>
<div class="section" id="scenarioseries">
<span id="scenarioseries-tutorial"></span><h3><code class="docutils literal notranslate"><span class="pre">ScenarioSeries</span></code><a class="headerlink" href="#scenarioseries" title="Permalink to this headline">¶</a></h3>
<p>Now let’s build and run a series of scenarios. Each Scenario in the series is
specified by a dictionary that needs to have the title of the scenario and
a key-value pair of parameter-function for every parameter that should be
modified. In this example, we’ll still just scale <code class="docutils literal notranslate"><span class="pre">jh_coef</span></code>, but now over a
range of values from 0.5 to 1.5, in increments of 0.1.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">base_dir</span> <span class="o">=</span> <span class="s1">'../models/lbcd/'</span>
<span class="n">simulation_dir</span> <span class="o">=</span> <span class="s1">'example-sim-series-dir'</span>
<span class="n">title</span> <span class="o">=</span> <span class="s1">'Jensen-Hays and Radiative Transfer Function Sensitivity Analysis'</span>
<span class="n">description</span> <span class="o">=</span> <span class="s1">'''</span>
<span class="s1">Use title of </span><span class="se">\'</span><span class="s1">"jh_coef":{jh factor value}</span><span class="se">\'</span><span class="s1"> so later</span>
<span class="s1">we can easily generate a dictionary of these param/function combinations.</span>
<span class="s1">'''</span>
<span class="n">sc_series</span> <span class="o">=</span> <span class="n">ScenarioSeries</span><span class="p">(</span><span class="n">base_dir</span><span class="p">,</span> <span class="n">simulation_dir</span><span class="p">,</span> <span class="n">title</span><span class="p">,</span> <span class="n">description</span><span class="p">)</span>
<span class="c1"># define the scenario_list used to build the ScenarioSeries;</span>
<span class="c1"># build series in three steps:</span>
<span class="c1"># 1) define fun to return a function that scales a value by an amount</span>
<span class="k">def</span> <span class="nf">_scale_fun</span><span class="p">(</span><span class="n">scale_val</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">scale</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="k">return</span> <span class="n">x</span> <span class="o">*</span> <span class="n">scale_val</span>
<span class="k">return</span> <span class="n">scale</span>
<span class="c1"># 2) use the function generator `_scale_fun` in scenario_list comprehension</span>
<span class="n">scenario_list</span> <span class="o">=</span> <span class="p">[</span>
<span class="p">{</span>
<span class="s1">'title'</span><span class="p">:</span> <span class="s1">'"jh_coef":{0:.1f}'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">jh_val</span><span class="p">),</span>
<span class="s1">'jh_coef'</span><span class="p">:</span> <span class="n">_scale_fun</span><span class="p">(</span><span class="n">jh_val</span><span class="p">),</span>
<span class="p">}</span>
<span class="k">for</span> <span class="n">jh_val</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">1.5</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">)</span>
<span class="p">]</span>
<span class="c1"># 3) "build" the series, meaning create scenario inputs and scenario dirs</span>
<span class="n">sc_series</span><span class="o">.</span><span class="n">build</span><span class="p">(</span><span class="n">scenario_list</span><span class="p">)</span>
<span class="n">sc_series</span><span class="o">.</span><span class="n">run</span><span class="p">()</span> <span class="c1"># could provide nproc, ex: sc_series.run(nproc=10)</span>
</pre></div>
</div>
<p>If, for example, we wanted to co-vary <code class="docutils literal notranslate"><span class="pre">jh_coef</span></code> with scalings of <code class="docutils literal notranslate"><span class="pre">rad_trncf</span></code>
(or any other parameter) we can use the following as a recipe. Just add one
more key/value pair to the dictionaries generated in the list comprehension
that build the <code class="docutils literal notranslate"><span class="pre">scenario_list</span></code>.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">scenario_list</span> <span class="o">=</span> <span class="p">[</span>
<span class="p">{</span>
<span class="s1">'title'</span><span class="p">:</span> <span class="s1">'"jh_coef":{0:.1f}|"rad_trncf":{1:.1f}'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">jh_val</span><span class="p">,</span> <span class="n">rad_val</span><span class="p">),</span>
<span class="s1">'jh_coef'</span><span class="p">:</span> <span class="n">_scale_fun</span><span class="p">(</span><span class="n">jh_val</span><span class="p">),</span>
<span class="s1">'rad_trncf'</span><span class="p">:</span> <span class="n">_scale_fun</span><span class="p">(</span><span class="n">rad_val</span><span class="p">)</span>
<span class="p">}</span>
<span class="k">for</span> <span class="n">jh_val</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">1.5</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">)</span>
<span class="k">for</span> <span class="n">rad_val</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">1.5</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">)</span>
<span class="p">]</span>
</pre></div>
</div>
<p>Note that this will square the number of scenarios to be done.</p>
<p>The <code class="docutils literal notranslate"><span class="pre">title</span></code> might look strange, but it is useful as part of the metadata to recover information
about the individual Scenarios in the data analysis steps shown below in
<a class="reference internal" href="#example"><span class="std std-ref">Example: Parameter sensitivity</span></a>. Alternatively, if the title is omitted the subdirectory names of
each scenario will not be intuitively matched to the unique universal identifiers
that are assigned automatically by <code class="docutils literal notranslate"><span class="pre">ScenarioSeries.build</span></code>. However metadata for
each scenario’s simulation will be stored in its respective directory and could
later be used to refer which parameter(s) were modified and how because the metadata
file contains a text representation of the Python functions that were used to modify the
parameter(s).</p>
<p>Additional explanations and examples including the file structures and metadata created
by the <code class="docutils literal notranslate"><span class="pre">Scenario</span></code> and <code class="docutils literal notranslate"><span class="pre">ScenarioSeries</span></code> are found in the API <a class="reference internal" href="api.html#prms_python.Scenario" title="prms_python.Scenario"><code class="xref py py-class docutils literal notranslate"><span class="pre">prms_python.Scenario</span></code></a> and <a class="reference internal" href="api.html#prms_python.ScenarioSeries" title="prms_python.ScenarioSeries"><code class="xref py py-class docutils literal notranslate"><span class="pre">prms_python.ScenarioSeries</span></code></a>.</p>
</div>
</div>
<div class="section" id="optimizer-optimizationresult">
<h2><code class="docutils literal notranslate"><span class="pre">Optimizer</span> <span class="pre">&</span> <span class="pre">OptimizationResult</span></code><a class="headerlink" href="#optimizer-optimizationresult" title="Permalink to this headline">¶</a></h2>
<p>The <a class="reference internal" href="api.html#id9"><span class="std std-ref">Optimizer class</span></a> holds routines for PRMS parameter
optimization or calibration, and sensitivity.uncertainty analysis. Currently
the <code class="docutils literal notranslate"><span class="pre">Optimizer.monte_carlo</span></code> method offers a parameter resampling routine that
can automate the resampling or an arbitrary number of PRMS parameters, conduct
simulations for each set of resampled parameters, and self-generate metadata for
each. The routine uses the stand-alone function <a class="reference internal" href="api.html#prms_python.optimizer.resample_param" title="prms_python.optimizer.resample_param"><code class="xref any py py-func docutils literal notranslate"><span class="pre">prms_python.optimizer.resample_param</span></code></a>
which utilizes the uniform and normal distributions with added functionalities for
parameters of varying dimensions. In other words there are different rules for
parameter resampling for spatial parameters or parameters of large dimension than
those of single value or monthly dimensions.</p>
<p>The <a class="reference internal" href="api.html#id10"><span class="std std-ref">OptimizationResult class</span></a> is designed to aid
management and analysis of output from a single optimization stage.</p>
<p>Note, this section is currently under development, please refer to the
example Jupyter notebook <a class="reference external" href="https://github.com/PRMS-Python/PRMS-Python/blob/master/notebooks/monte_carlo_param_resampling.ipynb">here</a> for detailed documentation of the <code class="docutils literal notranslate"><span class="pre">monte_carlo</span></code>
parameter resampling routine. And the notebook <a class="reference external" href="https://github.com/PRMS-Python/PRMS-Python/blob/master/notebooks/monte_carlo_optimization_result.ipynb">here</a> for explanations and
examples for <code class="docutils literal notranslate"><span class="pre">OptimizationResult</span></code>.</p>
</div>
<div class="section" id="load-data-load-statvar">
<h2><code class="docutils literal notranslate"><span class="pre">load_data</span> <span class="pre">&</span> <span class="pre">load_statvar</span></code><a class="headerlink" href="#load-data-load-statvar" title="Permalink to this headline">¶</a></h2>
<p>Among other uses, if we want to compare the performance of our model to
historical data for the purposes of parameterization or analyzing climate change
scenarios, we will have to load the input and output hydrographs. The two
functions <a class="reference internal" href="api.html#prms_python.load_data" title="prms_python.load_data"><code class="xref any py py-func docutils literal notranslate"><span class="pre">prms_python.load_data</span></code></a> and <a class="reference internal" href="api.html#prms_python.load_statvar" title="prms_python.load_statvar"><code class="xref any py py-func docutils literal notranslate"><span class="pre">prms_python.load_statvar</span></code></a>
read the data and statvar files into a Pandas DataFrame, which allows for
streamlined plotting and analysis.</p>
<p>Here is a simple example of how to use these functions to generate a plot
like (not identical to) the one shown in <a class="reference internal" href="#obs-mod-fig"><span class="std std-ref">Comparison of observed and modeled flow</span></a>.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></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">prms_python</span> <span class="kn">import</span> <span class="n">load_data</span><span class="p">,</span> <span class="n">load_statvar</span>
<span class="n">data_df</span> <span class="o">=</span> <span class="n">load_data</span><span class="p">(</span><span class="s1">'path/to/data'</span><span class="p">)</span>
<span class="n">data_df</span><span class="o">.</span><span class="n">runoff_1</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">label</span><span class="o">=</span><span class="s1">'observed'</span><span class="p">)</span>
<span class="n">statvar_df</span> <span class="o">=</span> <span class="n">load_statvar</span><span class="p">(</span><span class="s1">'path/to/statvar.dat'</span><span class="p">)</span>
<span class="n">statvar_df</span><span class="o">.</span><span class="n">basin_cfs_1</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">label</span><span class="o">=</span><span class="s1">'modeled'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
</div>
</div>
<div class="section" id="example-parameter-sensitivity">
<span id="example"></span><h1>Example: Parameter sensitivity<a class="headerlink" href="#example-parameter-sensitivity" title="Permalink to this headline">¶</a></h1>
<p>This is a full example of how the tools outlined above can be used together to
build a parameter sensitivity analysis and goodness-of-fit. We’ll be modifying two parameters,
the monthly <em>jh_coef</em> and the HRU scale <em>rad_trncf</em>. We will
create a list of scenario definitions to “build” the <a class="reference internal" href="api.html#prms_python.ScenarioSeries" title="prms_python.ScenarioSeries"><code class="xref py py-class docutils literal notranslate"><span class="pre">prms_python.ScenarioSeries</span></code></a>. We’ll
then use the parallelized <a class="reference internal" href="api.html#prms_python.ScenarioSeries.run" title="prms_python.ScenarioSeries.run"><code class="xref py py-meth docutils literal notranslate"><span class="pre">prms_python.ScenarioSeries.run()</span></code></a> method to execute all
requested scenarios.</p>
<p>This is adapted from the <a class="reference external" href="https://github.com/PRMS-Python/PRMS-Python/blob/master/notebooks/scenario_series.ipynb">scenario_series.ipynb, viewable on GitHub</a>.
There are some details on customizing the plots that can be viewed there.</p>
<p>See inline comments for more details.</p>
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115</pre></div></td><td class="code"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">itertools</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">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">prms_python</span> <span class="kn">import</span> <span class="p">(</span>
<span class="n">ScenarioSeries</span><span class="p">,</span> <span class="n">load_data</span><span class="p">,</span> <span class="n">load_statvar</span><span class="p">,</span> <span class="n">nash_sutcliffe</span>
<span class="p">)</span>
<span class="c1"># define some ScenarioSeries metadata and initialize the series</span>
<span class="n">base_dir</span> <span class="o">=</span> <span class="s1">'../models/lbcd/'</span>
<span class="n">simulation_dir</span> <span class="o">=</span> <span class="s1">'example-sim-series-dir'</span>
<span class="n">title</span> <span class="o">=</span> <span class="s1">'Jensen-Hays and Radiative Transfer Function Sensitivity Analysis'</span>
<span class="n">description</span> <span class="o">=</span> <span class="s1">'''</span>
<span class="s1">Use title of </span><span class="se">\'</span><span class="s1">"jh_coef":{jh factor value}|"rad_trncf":{rad factor value}</span><span class="se">\'</span><span class="s1"> so later</span>
<span class="s1">we can easily generate a dictionary of these factor value combinations.</span>
<span class="s1">'''</span>
<span class="n">sc_series</span> <span class="o">=</span> <span class="n">ScenarioSeries</span><span class="p">(</span><span class="n">base_dir</span><span class="p">,</span> <span class="n">simulation_dir</span><span class="p">,</span> <span class="n">title</span><span class="p">,</span> <span class="n">description</span><span class="p">)</span>
<span class="c1"># define the scenario_list used to build the ScenarioSeries;</span>
<span class="c1"># build series in three steps:</span>
<span class="c1"># 1) define fun to return a function that scales a value by an amount</span>
<span class="k">def</span> <span class="nf">_scale_fun</span><span class="p">(</span><span class="n">scale_val</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">scale</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="k">return</span> <span class="n">x</span> <span class="o">*</span> <span class="n">scale_val</span>
<span class="k">return</span> <span class="n">scale</span>
<span class="c1"># 2) use the function generator `_scale_fun` in scenario_list comprehension</span>
<span class="n">scenario_list</span> <span class="o">=</span> <span class="p">[</span>
<span class="p">{</span>
<span class="s1">'title'</span><span class="p">:</span> <span class="s1">'"jh_coef":{0:.1f}|"rad_trncf":{1:.1f}'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">jh_val</span><span class="p">,</span> <span class="n">rad_val</span><span class="p">),</span>
<span class="s1">'jh_coef'</span><span class="p">:</span> <span class="n">_scale_fun</span><span class="p">(</span><span class="n">jh_val</span><span class="p">),</span>
<span class="s1">'rad_trncf'</span><span class="p">:</span> <span class="n">_scale_fun</span><span class="p">(</span><span class="n">rad_val</span><span class="p">)</span>
<span class="p">}</span>
<span class="k">for</span> <span class="n">jh_val</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">0.7</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">)</span>
<span class="k">for</span> <span class="n">rad_val</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">0.7</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">)</span>
<span class="p">]</span>
<span class="c1"># 3) "build" the series, meaning create scenario inputs and scenario dirs</span>
<span class="n">sc_series</span><span class="o">.</span><span class="n">build</span><span class="p">(</span><span class="n">scenario_list</span><span class="p">)</span>
<span class="n">sc_series</span><span class="o">.</span><span class="n">run</span><span class="p">()</span> <span class="c1"># could provide nproc, ex: sc_series.run(nproc=10)</span>
<span class="c1"># now we want to analyze the results by plotting the model efficiency matrix</span>
<span class="c1"># for the two parameters we varied, in three steps:</span>
<span class="c1"># 1) Load basin_cfs_1 streamflow timeseries for every scenario</span>
<span class="n">metadata</span> <span class="o">=</span> <span class="n">json</span><span class="o">.</span><span class="n">loads</span><span class="p">(</span>
<span class="nb">open</span><span class="p">(</span><span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">simulation_dir</span><span class="p">,</span> <span class="s1">'series_metadata.json'</span><span class="p">))</span><span class="o">.</span><span class="n">read</span><span class="p">()</span>
<span class="p">)</span>
<span class="k">def</span> <span class="nf">_build_statvar_path</span><span class="p">(</span><span class="n">uu</span><span class="p">):</span>
<span class="s1">'Given a scenario UUID, build the path to the statvar file'</span>
<span class="k">return</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">simulation_dir</span><span class="p">,</span> <span class="n">uu</span><span class="p">,</span> <span class="s1">'outputs'</span><span class="p">,</span> <span class="s1">'statvar.dat'</span><span class="p">)</span>
<span class="n">modeled_flows</span> <span class="o">=</span> <span class="p">{</span>
<span class="n">title</span><span class="p">:</span> <span class="n">load_statvar</span><span class="p">(</span><span class="n">_build_statvar_path</span><span class="p">(</span><span class="n">uu</span><span class="p">))</span><span class="o">.</span><span class="n">basin_cfs_1</span>
<span class="k">for</span> <span class="n">uu</span> <span class="ow">in</span> <span class="n">metadata</span><span class="p">[</span><span class="s1">'uuid_title_map'</span><span class="p">]</span><span class="o">.</span><span class="n">iteritems</span><span class="p">()</span>
<span class="p">}</span>
<span class="c1"># 2) load the data file which contains the original streamflow</span>
<span class="n">data_path</span> <span class="o">=</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">base_dir</span><span class="p">,</span> <span class="s1">'data'</span><span class="p">)</span>
<span class="n">data_df</span> <span class="o">=</span> <span class="n">load_data_file</span><span class="p">(</span><span class="n">data_path</span><span class="p">)</span>
<span class="n">observed</span> <span class="o">=</span> <span class="n">data_df</span><span class="o">.</span><span class="n">runoff_1</span>
<span class="c1"># 3) check model sensitivity via the Nash-Sutcliffe goodness of fit</span>
<span class="c1"># define index lookup for scaling labels</span>
<span class="n">idx_lookup</span> <span class="o">=</span> <span class="p">{</span>
<span class="s1">'{:.1f}'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">val</span><span class="p">):</span> <span class="n">idx</span>
<span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">val</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">0.7</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">))</span>
<span class="p">}</span>
<span class="c1"># initialize the Nash-Sutcliffe matrix with all zeros</span>
<span class="n">nash_sutcliffe_mat</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<span class="c1"># build nash_sutcliffe_mat</span>
<span class="k">for</span> <span class="n">title</span><span class="p">,</span> <span class="n">hydrograph</span> <span class="ow">in</span> <span class="n">modeled_flows</span><span class="o">.</span><span class="n">iteritems</span><span class="p">():</span>
<span class="n">param_scalings</span> <span class="o">=</span> <span class="nb">eval</span><span class="p">(</span><span class="s1">'{'</span> <span class="o">+</span> <span class="n">title</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="s1">'|'</span><span class="p">,</span> <span class="s1">','</span><span class="p">)</span> <span class="o">+</span> <span class="s1">'}'</span><span class="p">)</span>
<span class="n">coord</span> <span class="o">=</span> <span class="p">(</span>
<span class="n">idx_lookup</span><span class="p">[</span><span class="nb">str</span><span class="p">(</span><span class="n">param_scalings</span><span class="p">[</span><span class="s1">'jh_coef'</span><span class="p">])],</span>
<span class="n">idx_lookup</span><span class="p">[</span><span class="nb">str</span><span class="p">(</span><span class="n">param_scalings</span><span class="p">[</span><span class="s1">'rad_trncf'</span><span class="p">])]</span>
<span class="p">)</span>
<span class="n">nash_sutcliffe_mat</span><span class="p">[</span><span class="n">coord</span><span class="p">]</span> <span class="o">=</span> <span class="n">nash_sutcliffe</span><span class="p">(</span><span class="n">observed</span><span class="p">,</span> <span class="n">hydrograph</span><span class="p">)</span>
<span class="c1"># Finally let's visualize these results. First just a comparison of</span>
<span class="c1"># one of the modeled flows and the observed streamflow; Figure 1 below.</span>
<span class="n">observed</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">label</span><span class="o">=</span><span class="s1">'observed'</span><span class="p">)</span>
<span class="n">ex_uuid</span><span class="p">,</span> <span class="n">ex_title</span> <span class="o">=</span> <span class="n">metadata</span><span class="p">[</span><span class="s1">'uuid_title_map'</span><span class="p">]</span><span class="o">.</span><span class="n">iteritems</span><span class="p">()</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
<span class="n">ex_modeled_flow</span> <span class="o">=</span> <span class="n">load_statvar</span><span class="p">(</span><span class="n">_build_statvar_path</span><span class="p">(</span><span class="n">ex_uuid</span><span class="p">))</span><span class="o">.</span><span class="n">basin_cfs_1</span>
<span class="n">ex_modeled_flow</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">label</span><span class="o">=</span><span class="n">ex_title</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="s1">'"'</span><span class="p">,</span> <span class="s1">''</span><span class="p">)</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="s1">'|'</span><span class="p">,</span> <span class="s1">', '</span><span class="p">))</span>
<span class="c1"># now let's plot the Nash-Sutcliffe Matrix, Figure 2 below</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">'Streamflow (cfs)'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
<span class="n">cax</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">matshow</span><span class="p">(</span><span class="n">nash_sutcliffe_mat</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'viridis'</span><span class="p">)</span>
<span class="n">tix</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.7</span><span class="p">,</span> <span class="mf">0.8</span><span class="p">,</span> <span class="mf">0.9</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xticks</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">4</span><span class="p">),</span> <span class="n">tix</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">yticks</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">4</span><span class="p">),</span> <span class="n">tix</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">xaxis</span><span class="o">.</span><span class="n">set_ticks_position</span><span class="p">(</span><span class="s1">'bottom'</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="s1">'jh_coef factor'</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="s1">'rad_trncf factor'</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="ow">in</span> <span class="n">itertools</span><span class="o">.</span><span class="n">product</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">4</span><span class="p">),</span> <span class="nb">range</span><span class="p">(</span><span class="mi">4</span><span class="p">)):</span>
<span class="n">plt</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="n">j</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="s2">"</span><span class="si">%.2f</span><span class="s2">"</span> <span class="o">%</span> <span class="n">nash_sutcliffe_mat</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">],</span>
<span class="n">horizontalalignment</span><span class="o">=</span><span class="s2">"center"</span><span class="p">,</span>
<span class="n">color</span><span class="o">=</span><span class="s2">"w"</span> <span class="k">if</span> <span class="n">nash_sutcliffe_mat</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o"><</span> <span class="o">.</span><span class="mi">61</span> <span class="k">else</span> <span class="s2">"k"</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="s1">'Nash-Sutcliffe Matrix'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="n">b</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span>
<span class="n">cbar</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">cax</span><span class="p">)</span>
</pre></div>
</td></tr></table></div>
<p>The resulting plots from the end of the example script are shown below</p>
<div class="figure align-default" id="id2">
<span id="obs-mod-fig"></span><img alt="comparison of observed and modeled flow" src="_images/obs-mod-flow.png" />
<p class="caption"><span class="caption-text">Comparison of observed and modeled flow</span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p>
</div>
<div class="figure align-default" id="id3">
<img alt="nash-sutcliffe matrix" src="_images/nash-sutcliffe-ex.png" />
<p class="caption"><span class="caption-text">Nash-Sutcliffe Matrix of model efficiencies</span><a class="headerlink" href="#id3" title="Permalink to this image">¶</a></p>
</div>
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