{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Diving into code approximations\n",
    "\n",
    "Like any code, there are several approximations that go into computing intesity from various phase functions. In reflected light models, some of these approximations drastically change the output spectra. \n",
    "\n",
    "Here we go through each approximation to show what the effects are of each. Also, to show how to toggle between various inputs. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
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       "    root._bokeh_onload_callbacks = [];\n",
       "    root._bokeh_is_loading = undefined;\n",
       "  }\n",
       "\n",
       "  var JS_MIME_TYPE = 'application/javascript';\n",
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       "    node.appendChild(script);\n",
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       "\n",
       "  /**\n",
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       "\n",
       "    var id = cell.output_area._bokeh_element_id;\n",
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       "    // Clean up Bokeh references\n",
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       "      Bokeh.index[id].model.document.clear();\n",
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       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
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       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
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       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[toinsert.length - 1]);\n",
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       "      return toinsert\n",
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       "\n",
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       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
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       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
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       "\n",
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       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
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       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.debug(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(css_urls, js_urls, callback) {\n",
       "    if (css_urls == null) css_urls = [];\n",
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       "\n",
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       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
       "\n",
       "    function on_load() {\n",
       "      root._bokeh_is_loading--;\n",
       "      if (root._bokeh_is_loading === 0) {\n",
       "        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
       "        run_callbacks()\n",
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       "\n",
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       "    }\n",
       "\n",
       "    for (var i = 0; i < css_urls.length; i++) {\n",
       "      var url = css_urls[i];\n",
       "      const element = document.createElement(\"link\");\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.rel = \"stylesheet\";\n",
       "      element.type = \"text/css\";\n",
       "      element.href = url;\n",
       "      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
       "      document.body.appendChild(element);\n",
       "    }\n",
       "\n",
       "    const hashes = {\"https://cdn.bokeh.org/bokeh/release/bokeh-2.0.1.min.js\": \"JpP8FXbgAZLkfur7LiK3j9AGBhHNIvF742meBJrjO2ShJDhCG2I1uVvW+0DUtrmc\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.0.1.min.js\": \"xZlADit0Q04ISQEdKg2k3L4W9AwQBAuDs9nJL9fM/WwzL1tEU9VPNezOFX0nLEAz\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.0.1.min.js\": \"4BuPRZkdMKSnj3zoxiNrQ86XgNw0rYmBOxe7nshquXwwcauupgBF2DHLVG1WuZlV\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.0.1.min.js\": \"Dv1SQ87hmDqK6S5OhBf0bCuwAEvL5QYL0PuR/F1SPVhCS/r/abjkbpKDYL2zeM19\"};\n",
       "\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var element = document.createElement('script');\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.async = false;\n",
       "      element.src = url;\n",
       "      if (url in hashes) {\n",
       "        element.crossOrigin = \"anonymous\";\n",
       "        element.integrity = \"sha384-\" + hashes[url];\n",
       "      }\n",
       "      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.head.appendChild(element);\n",
       "    }\n",
       "  };var element = document.getElementById(\"1001\");\n",
       "  if (element == null) {\n",
       "    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '1001' but no matching script tag was found. \")\n",
       "    return false;\n",
       "  }\n",
       "\n",
       "  function inject_raw_css(css) {\n",
       "    const element = document.createElement(\"style\");\n",
       "    element.appendChild(document.createTextNode(css));\n",
       "    document.body.appendChild(element);\n",
       "  }\n",
       "\n",
       "  \n",
       "  var js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.0.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.0.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.0.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.0.1.min.js\"];\n",
       "  var css_urls = [];\n",
       "  \n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    function(Bokeh) {\n",
       "    \n",
       "    \n",
       "    }\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if (root.Bokeh !== undefined || force === true) {\n",
       "      \n",
       "    for (var i = 0; i < inline_js.length; i++) {\n",
       "      inline_js[i].call(root, root.Bokeh);\n",
       "    }\n",
       "    if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"1001\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(css_urls, js_urls, function() {\n",
       "      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"1001\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error() {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (var i = 0; i < css_urls.length; i++) {\n      var url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    const hashes = {\"https://cdn.bokeh.org/bokeh/release/bokeh-2.0.1.min.js\": \"JpP8FXbgAZLkfur7LiK3j9AGBhHNIvF742meBJrjO2ShJDhCG2I1uVvW+0DUtrmc\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.0.1.min.js\": \"xZlADit0Q04ISQEdKg2k3L4W9AwQBAuDs9nJL9fM/WwzL1tEU9VPNezOFX0nLEAz\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.0.1.min.js\": \"4BuPRZkdMKSnj3zoxiNrQ86XgNw0rYmBOxe7nshquXwwcauupgBF2DHLVG1WuZlV\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.0.1.min.js\": \"Dv1SQ87hmDqK6S5OhBf0bCuwAEvL5QYL0PuR/F1SPVhCS/r/abjkbpKDYL2zeM19\"};\n\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      if (url in hashes) {\n        element.crossOrigin = \"anonymous\";\n        element.integrity = \"sha384-\" + hashes[url];\n      }\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };var element = document.getElementById(\"1001\");\n  if (element == null) {\n    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '1001' but no matching script tag was found. \")\n    return false;\n  }\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  \n  var js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.0.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.0.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.0.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.0.1.min.js\"];\n  var css_urls = [];\n  \n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    function(Bokeh) {\n    \n    \n    }\n  ];\n\n  function run_inline_js() {\n    \n    if (root.Bokeh !== undefined || force === true) {\n      \n    for (var i = 0; i < inline_js.length; i++) {\n      inline_js[i].call(root, root.Bokeh);\n    }\n    if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"1001\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "#picaso\n",
    "from picaso import justdoit as jdi \n",
    "from picaso import justplotit as jpi \n",
    "from bokeh.plotting import show, figure\n",
    "from bokeh.layouts import column\n",
    "from bokeh.palettes import Colorblind8\n",
    "from bokeh.io import output_notebook \n",
    "import astropy.units as u\n",
    "output_notebook()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using the `approx` key"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "opa = jdi.opannection(wave_range=[0.3,1])\n",
    "cloud_free = jdi.inputs()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that all the `approx` keys have predefined inputs. These are our recommendations for how to run the code. But, users should always be weary of these and test their sensitivity to your results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What approximations exist?\n",
    "\n",
    "We can easily print out all our options for what approximations exist in the code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Can also set functional form of forward/back scattering in approx['TTHG_params']\n",
      "Options for Direct Scattring Phase:  ['cahoy', 'OTHG', 'TTHG', 'TTHG_ray']\n",
      "Can also set delta_eddington=True/False in approx['delta_eddington']\n",
      "Options for Multiple Scattring Phase:  ['N=2', 'N=1']\n",
      "Options for Raman Scattring:  ['oklopcic', 'pollack', 'none']\n"
     ]
    }
   ],
   "source": [
    "print('Options for Direct Scattring Phase: ', jdi.single_phase_options())\n",
    "\n",
    "print('Options for Multiple Scattring Phase: ', jdi.multi_phase_options())\n",
    "\n",
    "print('Options for Raman Scattring: ', jdi.raman_options())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Set inputs normally"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "cloud_free.phase_angle(0) #phase in radians\n",
    "\n",
    "cloud_free.gravity(gravity=25, gravity_unit=u.Unit('m/(s**2)' ))\n",
    "\n",
    "#set star \n",
    "cloud_free.star(opa, 6000, 0.0122, 4.437)\n",
    "\n",
    "#set atmosphere comp and temp \n",
    "cloud_free.atmosphere(filename=jdi.jupiter_pt(),delim_whitespace=True)\n",
    "\n",
    "#make a copy to have a separate cloud input dict\n",
    "from copy import deepcopy\n",
    "cloudy=deepcopy(cloud_free)\n",
    "cloudy.clouds( filename=jdi.jupiter_cld(),delim_whitespace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Direct Scattering Approximation\n",
    "\n",
    "The [derivation documentation](https://natashabatalha.github.io/picaso_dev#slide02) has a full description of these direct scattering approximations. Briefly I'll describe them here: \n",
    "\n",
    "At the center of each is the [One Term Henyey-Greenstein Phase Function (OTHG)](http://adsabs.harvard.edu/abs/1941ApJ....93...70H) and the [Two Term HG Phase Function (TTHG)](http://adsabs.harvard.edu/abs/1965ApJ...142.1563I). \n",
    "\n",
    "We also know that planet atmospheres have high degrees of Rayleigh scattering. [Cahoy+2010](http://adsabs.harvard.edu/abs/2010ApJ...724..189C) developed a methodology for incorporating Rayleigh into the direct scattering component. \n",
    "\n",
    "A more rrobust way of dealing with Rayleigh is to directly fold it's phase function into the TTHG phase function (TTHG_Ray). \n",
    "\n",
    "We'll run each case with and without a cloud so you can see what happens in both regimes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Can also set functional form of forward/back scattering in approx['TTHG_params']\n"
     ]
    },
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   "source": [
    "#let's make two different figures for this\n",
    "fig_cloudy = figure(x_range=[0.3,1],y_range=[0,1.2], width=500, height=300\n",
    "                    ,x_axis_label='Wavelength [μm]', y_axis_label='Geometric Albedo',)\n",
    "fig_no_cloud = figure(x_range=[0.3,1],y_range=[0,1.2], width=500, height=300\n",
    "                      ,x_axis_label='Wavelength [μm]', y_axis_label='Geometric Albedo',)\n",
    "\n",
    "#define our options\n",
    "options = jdi.single_phase_options()\n",
    "colors = Colorblind8[0:len(options)]\n",
    "\n",
    "#loop through all approximations \n",
    "for approx, c in zip(options, colors):\n",
    "    #set approximations\n",
    "    cloud_free.approx(single_phase = approx)    \n",
    "    cloudy.approx(single_phase = approx)  \n",
    "    df = cloud_free.spectrum(opa)\n",
    "    wno_nc, alb_nc = jdi.mean_regrid(df['wavenumber'] , df['albedo'],R=150)\n",
    "    df = cloudy.spectrum(opa)\n",
    "    wno_c, alb_c = jdi.mean_regrid(df['wavenumber'] , df['albedo'],R=150)\n",
    "    fig_no_cloud.line(1e4/wno_nc, alb_nc, legend_label=approx, color=c, line_width=3)\n",
    "    fig_cloudy.line(1e4/wno_c, alb_c,  color=c, line_width=3)\n",
    "jpi.plot_format(fig_cloudy)\n",
    "jpi.plot_format(fig_no_cloud)\n",
    "show(column(fig_no_cloud,fig_cloudy ))"
   ]
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   "source": [
    "## Multiple Scattering Approximations\n",
    "\n",
    "Again, [derivation documentation](https://natashabatalha.github.io/picaso_dev#slide03) has a full description of these multiple scattering approximations. \n",
    "\n",
    "To complete the multiple scattering integration over all _diffuse angles_, we have to use some mathematical tricks. [Legendre Polynomials](http://mathworld.wolfram.com/LegendrePolynomial.html) are often used to complete this integration to varying degrees. For Solar System/Exoplanet papers, we often stop the expansion at either `N=1` or `N=2`. Our standard will be to run with `N=2`, but below we show how to run each."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Can also set delta_eddington=True/False in approx['delta_eddington']\n"
     ]
    },
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":\"1392\",\"type\":\"Line\"},{\"attributes\":{\"data_source\":{\"id\":\"1396\"},\"glyph\":{\"id\":\"1397\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"1398\"},\"selection_glyph\":null,\"view\":{\"id\":\"1400\"}},\"id\":\"1399\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"axis\":{\"id\":\"1369\"},\"ticker\":null},\"id\":\"1372\",\"type\":\"Grid\"},{\"attributes\":{\"data\":{\"x\":{\"__ndarray__\":\"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\",\"dtype\":\"float64\",\"shape\":[181]},\"y\":{\"__ndarray__\":\"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\",\"dtype\":\"float64\",\"shape\":[181]}},\"selected\":{\"id\":\"1447\"},\"selection_policy\":{\"id\":\"1448\"}},\"id\":\"1391\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"source\":{\"id\":\"1401\"}},\"id\":\"1405\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1451\",\"type\":\"Selection\"},{\"attributes\":{\"source\":{\"id\":\"1406\"}},\"id\":\"1410\",\"type\":\"CDSView\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#009E73\",\"line_width\":3,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1408\",\"type\":\"Line\"},{\"attributes\":{\"data_source\":{\"id\":\"1401\"},\"glyph\":{\"id\":\"1402\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"1403\"},\"selection_glyph\":null,\"view\":{\"id\":\"1405\"}},\"id\":\"1404\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"overlay\":{\"id\":\"1383\"}},\"id\":\"1379\",\"type\":\"BoxZoomTool\"},{\"attributes\":{},\"id\":\"1370\",\"type\":\"BasicTicker\"}],\"root_ids\":[\"1360\"]},\"title\":\"Bokeh Application\",\"version\":\"2.0.1\"}};\n",
       "  var render_items = [{\"docid\":\"add2fa2b-bd3d-4f84-8715-dcf2469ee07d\",\"root_ids\":[\"1360\"],\"roots\":{\"1360\":\"d8d25f39-51c8-4b5a-ab67-002795cbcadd\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1360"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = figure(x_range=[0.3,1],y_range=[0,1.2], width=500, height=300,\n",
    "             x_axis_label='Wavelength [μm]', y_axis_label='Geometric Albedo',)\n",
    "\n",
    "options = jdi.multi_phase_options()\n",
    "colors = Colorblind8[0:len(options)*2]\n",
    "\n",
    "for approx, c1,c2 in zip(options, colors[0:2], colors[2:]):\n",
    "    cloud_free.approx(multi_phase= approx)\n",
    "    cloudy.approx(multi_phase = approx)\n",
    "    df = cloud_free.spectrum(opa)\n",
    "    wno_nc, alb_nc =jdi.mean_regrid( df['wavenumber'] , df['albedo'],R=150)\n",
    "    df = cloudy.spectrum(opa)\n",
    "    wno_c, alb_c =jdi.mean_regrid( df['wavenumber'] , df['albedo'],R=150)\n",
    "    fig.line(1e4/wno_nc, alb_nc, color=c1, line_width=3)\n",
    "    fig.line(1e4/wno_c, alb_c,  color=c2, line_width=3)\n",
    "jpi.plot_format(fig)\n",
    "show(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
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    "## Raman Scattering Approximations\n",
    "\n",
    "We all know the importance of Rayleigh scattering in planetary atmospheres. Raman scattering also has important implications for our spectra (these features have been observed in Solar System planets). In particular, at short wavelengths, Raman scattering imprints molecular features from the star on the planetary spectrum. \n",
    "\n",
    "The most complete analysis of all Raman approximations is in [Sromosvky+2005](http://adsabs.harvard.edu/abs/2005Icar..173..254S). From these, we use the _Pollack Approximation_ that was used in [Cahoy+2010](http://adsabs.harvard.edu/abs/2010ApJ...724..189C) and others. \n",
    "\n",
    "We include the original Pollack methodology, but also include a modified version with [Oklopcic et al 2018](http://iopscience.iop.org/article/10.3847/0004-637X/832/1/30/meta) cross sections and updated methodology to include effects of stellar spectrum.  "
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       "  var render_items = [{\"docid\":\"9e233371-00c7-4def-bb78-8198c19a743a\",\"root_ids\":[\"1669\"],\"roots\":{\"1669\":\"af24c9d2-98be-4570-b746-383a1c0b75dc\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
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       "        attempts++;\n",
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       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
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       "    }, 10, root)\n",
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      "application/vnd.bokehjs_exec.v0+json": ""
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     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1669"
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     "output_type": "display_data"
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   ],
   "source": [
    "fig_cloudy = figure(x_range=[0.3,1],y_range=[0,1.2], width=500, height=300\n",
    "                    ,x_axis_label='Wavelength [μm]', y_axis_label='Geometric Albedo',)\n",
    "fig_no_cloud = figure(x_range=[0.3,1],y_range=[0,1.2], width=500, height=300\n",
    "                      ,x_axis_label='Wavelength [μm]', y_axis_label='Geometric Albedo',)\n",
    "\n",
    "options = jdi.raman_options()\n",
    "colors = Colorblind8[0:len(options)]\n",
    "\n",
    "for approx, c in zip(options, colors):\n",
    "    cloud_free.approx(raman = approx)\n",
    "    cloud_free.star(opa, 6000, 0.0122, 4.437)\n",
    "    cloudy.approx(raman = approx)\n",
    "    cloudy.star(opa, 6000, 0.0122, 4.437)\n",
    "    df = cloud_free.spectrum(opa)\n",
    "    wno_nc, alb_nc = jdi.mean_regrid(df['wavenumber'] , df['albedo'],R=150)\n",
    "    df = cloudy.spectrum(opa)\n",
    "    wno_c, alb_c = jdi.mean_regrid(df['wavenumber'] , df['albedo'],R=150)\n",
    "    fig_no_cloud.line(1e4/wno_nc, alb_nc, legend_label=approx, color=c, line_width=3)\n",
    "    fig_cloudy.line(1e4/wno_c, alb_c,  color=c, line_width=3)\n",
    "\n",
    "jpi.plot_format(fig_cloudy)\n",
    "jpi.plot_format(fig_no_cloud)\n",
    "show(column(fig_no_cloud,fig_cloudy ))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Effect of Stellar Spectrum\n",
    "\n",
    "With the updated Raman scattering approximation, you will notice imprints of the stellar spectrum in the planet reflected light spectrum. Take a look below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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Application\",\"version\":\"2.0.1\"}};\n",
       "  var render_items = [{\"docid\":\"bd617366-da0d-462d-8265-5f0f66adf2d5\",\"root_ids\":[\"2044\"],\"roots\":{\"2044\":\"ed760157-b96e-4bb0-9592-b74f11331dfb\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "2044"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig_cloudy = figure(x_range=[0.3,1],y_range=[0,1.2], width=500, height=300\n",
    "                    ,x_axis_label='Wavelength [μm]', y_axis_label='Geometric Albedo',)\n",
    "fig_no_cloud = figure(x_range=[0.3,1],y_range=[0,1.2], width=500, height=300\n",
    "                      ,x_axis_label='Wavelength [μm]', y_axis_label='Geometric Albedo',)\n",
    "\n",
    "#lets play around with different stellar spectra Teff\n",
    "stellar_teff = [6000,4000,3500]\n",
    "\n",
    "colors = Colorblind8[0:len(options)]\n",
    "\n",
    "cloud_free.approx(raman = 'oklopcic')\n",
    "cloudy.approx(raman = 'oklopcic')\n",
    "\n",
    "for approx, c in zip(stellar_teff, colors):\n",
    "    cloud_free.star(opa, approx, 0.0122, 4.437) \n",
    "    cloudy.star(opa, approx ,0.0122, 4.437) \n",
    "    df = cloud_free.spectrum(opa)\n",
    "    wno_nc, alb_nc = jdi.mean_regrid(df['wavenumber'] , df['albedo'],R=150)\n",
    "    df = cloudy.spectrum(opa)\n",
    "    wno_c, alb_c = jdi.mean_regrid(df['wavenumber'] , df['albedo'],R=150)\n",
    "    fig_no_cloud.line(1e4/wno_nc, alb_nc, legend_label=str(approx), color=c, line_width=3)\n",
    "    fig_cloudy.line(1e4/wno_c, alb_c,  color=c, line_width=3)\n",
    "\n",
    "cloud_free.approx(raman = 'pollack')\n",
    "cloudy.approx(raman = 'pollack')\n",
    "\n",
    "df = cloud_free.spectrum(opa)\n",
    "wno_nc, alb_nc = jdi.mean_regrid(df['wavenumber'] , df['albedo'],R=150)\n",
    "df = cloudy.spectrum(opa)\n",
    "wno_c, alb_c =jdi.mean_regrid( df['wavenumber'] , df['albedo'],R=150)\n",
    "fig_no_cloud.line(1e4/wno_nc, alb_nc, legend_label='Pollack', color='black', line_width=2, line_dash='dashed')\n",
    "fig_cloudy.line(1e4/wno_c, alb_c,  color='black', line_width=2, line_dash='dashed')\n",
    "\n",
    "\n",
    "jpi.plot_format(fig_cloudy)\n",
    "jpi.plot_format(fig_no_cloud)\n",
    "show(column(fig_no_cloud,fig_cloudy ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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