{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ENV / ATM 415: Climate Laboratory\n",
    "\n",
    "# Radiative- and Radiative-Convective Equilibrium with `climlab`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thursday March 31, 2016"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import netCDF4 as nc\n",
    "import climlab"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "____________\n",
    "\n",
    "## Using `climlab` to implement the two-layer leaky greenhouse model\n",
    "____________\n",
    "\n",
    "One of the things that ``climlab`` is set up to do is the grey-radiation modeling we have already been discussing.\n",
    "\n",
    "Since we already derived a complete analytical solution to the two-layer leaky greenhouse model, we will use this to validate the `climlab` code.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Validation\n",
    "\n",
    "We want to verify that the model reproduces the observed OLR given observed temperatures, and the absorptivity that we tuned in the analytical model. The target numbers are:\n",
    "\n",
    "\\begin{align}\n",
    "T_s &= 288 \\text{ K} \\\\\n",
    "T_0 &= 275 \\text{ K} \\\\\n",
    "T_1 &= 230 \\text{ K} \\\\\n",
    "\\end{align}\n",
    "\n",
    "$$ \\epsilon = 0.58377  $$\n",
    "\n",
    "$$ OLR = 239 \\text{ W m}^{-2} $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initialize a model in `climlab`\n",
    "The first thing we do is create a new model.\n",
    "\n",
    "The following example code is sparsely commented but will hopefully orient you on the basics of defining and working with a `climlab Process` object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "climlab Process of type <class 'climlab.model.column.GreyRadiationModel'>. \n",
      "State variables and domain shapes: \n",
      "  Tatm: (2,) \n",
      "  Ts: (1,) \n",
      "The subprocess tree: \n",
      "top: <class 'climlab.model.column.GreyRadiationModel'>\n",
      "   LW: <class 'climlab.radiation.greygas.GreyGas'>\n",
      "   SW: <class 'climlab.radiation.greygas.GreyGasSW'>\n",
      "   insolation: <class 'climlab.radiation.insolation.FixedInsolation'>\n",
      "\n"
     ]
    }
   ],
   "source": [
    "#  Test in a 2-layer atmosphere\n",
    "col = climlab.GreyRadiationModel(num_lev=2)\n",
    "print col"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Tatm': Field([ 200.,  278.]), 'Ts': Field([ 288.])}"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "col.state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Field([ 288.])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "col.Ts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Tatm': Field([ 230.,  275.]), 'Ts': Field([ 288.])}"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  Set the temperatures to our observed values\n",
    "col.Ts[:] = 288.\n",
    "col.Tatm[:] = np.array([230., 275.])\n",
    "col.state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "climlab Process of type <class 'climlab.radiation.greygas.GreyGas'>. \n",
      "State variables and domain shapes: \n",
      "  Tatm: (2,) \n",
      "  Ts: (1,) \n",
      "The subprocess tree: \n",
      "top: <class 'climlab.radiation.greygas.GreyGas'>\n",
      "\n"
     ]
    }
   ],
   "source": [
    "LW = col.subprocess['LW']\n",
    "print LW"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Field([ 0.47737425,  0.47737425])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LW.absorptivity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Field([ 0.58377,  0.58377])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  Set the absorptivity to our tuned value\n",
    "LW.absorptivity = 0.58377\n",
    "LW.absorptivity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'ASR': array([ 239.2513]),\n",
       " 'LW_absorbed_atm': array([ 20.03935568, -96.82138041]),\n",
       " 'LW_absorbed_sfc': 0.0,\n",
       " 'LW_down_sfc': array([ 227.87116061]),\n",
       " 'LW_emission': Field([  92.63278385,  189.31461699]),\n",
       " 'LW_up_sfc': 0.0,\n",
       " 'OLR': array([ 239.01589408]),\n",
       " 'SW_absorbed_atm': array([ 0.,  0.]),\n",
       " 'SW_absorbed_sfc': 0.0,\n",
       " 'SW_down_TOA': array([ 341.3]),\n",
       " 'SW_up_TOA': array([ 102.0487]),\n",
       " 'SW_up_sfc': Field([ 102.0487]),\n",
       " 'absorbed': array([ 0.,  0.]),\n",
       " 'absorbed_total': 0.0,\n",
       " 'emission': Field([ 0.,  0.]),\n",
       " 'emission_sfc': Field([ 0.]),\n",
       " 'flux_from_sfc': Field([ 102.0487]),\n",
       " 'flux_reflected_up': array([   0.    ,    0.    ,  102.0487]),\n",
       " 'flux_to_sfc': array([ 341.3]),\n",
       " 'flux_to_space': array([ 102.0487]),\n",
       " 'insolation': array([ 341.3]),\n",
       " 'planetary_albedo': array([ 0.299])}"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  This does all the calculations that would be performed at each time step, \n",
    "#  but doesn't actually update the temperatures\n",
    "col.compute_diagnostics()\n",
    "#  Let's see what's in the diagnostics dictionary\n",
    "col.diagnostics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 239.01589408])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  Check OLR against our analytical solution\n",
    "col.OLR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Tatm': Field([ 230.,  275.]), 'Ts': Field([ 288.])}"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "col.state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# perform a single time step\n",
    "col.step_forward()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Tatm': Field([ 230.33800245,  273.36692033]), 'Ts': Field([ 289.59144429])}"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "col.state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Integrating for 730 steps, 730.4844 days, or 2.0 years.\n",
      "Total elapsed time is 2.00141166601 years.\n"
     ]
    }
   ],
   "source": [
    "# integrate out to radiative equilibrium\n",
    "col.integrate_years(2.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -2.78206130e-07])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Check for equilibrium\n",
    "col.ASR - col.OLR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Tatm': Field([ 233.62925791,  262.08988335]), 'Ts': Field([ 296.20384534])}"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  The temperatures at radiative equilibrium\n",
    "col.state"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare these to the analytical solutions for radiative equilibrium with $\\epsilon = 0.58$:\n",
    "\n",
    "\\begin{align}\n",
    "T_1 &= 234 \\text{ K} \\\\\n",
    "T_0 &= 262 \\text{ K} \\\\\n",
    "T_s &= 296 \\text{ K} \\\\\n",
    "\\end{align}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So it looks like `climlab` agrees with our analytical results. That's good."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "____________\n",
    "\n",
    "## The observed annual, global mean temperature profile\n",
    "____________\n",
    "\n",
    "We want to model the OLR in a column whose temperatures match observations. We'll calculate the global, annual mean air temperature from the NCEP Reanalysis data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# This will try to read the data over the internet.\n",
    "ncep_filename = 'air.mon.1981-2010.ltm.nc'\n",
    "#ncep_url = \"http://www.esrl.noaa.gov/psd/thredds/dodsC/Datasets/ncep.reanalysis.derived/\"\n",
    "#ncep_air = nc.Dataset( ncep_url + 'pressure/' + ncep_filename )\n",
    "# Or to read from local disk\n",
    "ncep_air = nc.Dataset( ncep_filename )\n",
    "\n",
    "level = ncep_air.variables['level'][:]\n",
    "lat = ncep_air.variables['lat'][:]\n",
    "# A log-pressure height coordinate\n",
    "zstar = -np.log(level/1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#  Take averages of the temperature data\n",
    "Tzon = np.mean(ncep_air.variables['air'][:],axis=(0,3))\n",
    "Tglobal = np.average( Tzon , weights=np.cos(np.deg2rad(lat)), axis=1) + climlab.constants.tempCtoK\n",
    "#  Note the useful conversion factor. climlab.constants has lots of commonly used constant pre-defined"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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u8N+iJYughLFRSldwnZJ1Q0SkuMysm5mNSy6cWjI1fR0zu4Fwv+lZVLjXtIjk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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e7f1d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#  Here we are plotting with respect to log(pressure) but labeling the axis in pressure units\n",
    "fig = plt.figure( figsize=(8,6) )\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot( Tglobal , zstar )\n",
    "yticks = np.array([1000., 750., 500., 250., 100., 50., 20., 10.])\n",
    "ax.set_yticks(-np.log(yticks/1000.))\n",
    "ax.set_yticklabels(yticks)\n",
    "ax.set_xlabel('Temperature (K)', fontsize=16)\n",
    "ax.set_ylabel('Pressure (hPa)', fontsize=16 )\n",
    "ax.set_title('Global, annual mean sounding from NCEP Reanalysis', fontsize = 24)\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "____________\n",
    "\n",
    "## A 30-layer model using the observed temperatures\n",
    "____________\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "climlab Process of type <class 'climlab.model.column.GreyRadiationModel'>. \n",
      "State variables and domain shapes: \n",
      "  Tatm: (30,) \n",
      "  Ts: (1,) \n",
      "The subprocess tree: \n",
      "top: <class 'climlab.model.column.GreyRadiationModel'>\n",
      "   LW: <class 'climlab.radiation.greygas.GreyGas'>\n",
      "   SW: <class 'climlab.radiation.greygas.GreyGasSW'>\n",
      "   insolation: <class 'climlab.radiation.insolation.FixedInsolation'>\n",
      "\n"
     ]
    }
   ],
   "source": [
    "#  initialize a grey radiation model with 30 levels\n",
    "col = climlab.GreyRadiationModel()\n",
    "print col"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 224.34736633  211.66334534  206.96233453  208.29142761  212.58644104\n",
      "  217.19397481  221.78252157  226.3520813   231.30422974  236.08017476\n",
      "  240.67991638  245.279658    249.35979716  252.92033386  256.48087056\n",
      "  259.66789246  262.48139954  265.29490662  267.81303914  270.03579712\n",
      "  272.25855509  274.21642049  275.90939331  277.60236613  279.29533895\n",
      "  280.98831177  282.48550415  283.98269653  285.6810201   287.4463874 ]\n"
     ]
    }
   ],
   "source": [
    "# interpolate to 30 evenly spaced pressure levels\n",
    "lev = col.lev\n",
    "Tinterp = np.interp(lev, np.flipud(level), np.flipud(Tglobal))\n",
    "\n",
    "print Tinterp\n",
    "#  Need to 'flipud' because the interpolation routine needs the pressure data to be in increasing order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Initialize model with observed temperatures\n",
    "col.Ts[:] = Tglobal[0]\n",
    "col.Tatm[:] = Tinterp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#  A handy re-usable routine for making a plot of the temperature profiles\n",
    "#  We will plot temperatures with respect to log(pressure) to get a height-like coordinate\n",
    "def plot_sounding(collist):\n",
    "    color_cycle=['r', 'g', 'b', 'y']\n",
    "    # col is either a column model object or a list of column model objects\n",
    "    if isinstance(collist, climlab.Process):\n",
    "        # make a list with a single item\n",
    "        collist = [collist]\n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111)\n",
    "    for i, col in enumerate(collist):\n",
    "        zstar = -np.log(col.lev/climlab.constants.ps)\n",
    "        ax.plot(col.Tatm, zstar, color=color_cycle[i])\n",
    "        ax.plot(col.Ts, 0, 'o', markersize=12, color=color_cycle[i])\n",
    "    #ax.invert_yaxis()\n",
    "    yticks = np.array([1000., 750., 500., 250., 100., 50., 20., 10.])\n",
    "    ax.set_yticks(-np.log(yticks/1000.))\n",
    "    ax.set_yticklabels(yticks)\n",
    "    ax.set_xlabel('Temperature (K)')\n",
    "    ax.set_ylabel('Pressure (hPa)')\n",
    "    ax.grid()\n",
    "    return ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x10eb39f10>"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ufI2f8sKntDQUOOUFUM+eoaecSD2iNpwGJIt1tsoUzwaZytf4ueQSePRR+Phj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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10eb54410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This should look just like the observations\n",
    "plot_sounding(col)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tune absorptivity to get observed OLR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 263.15000167])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "col.compute_diagnostics()\n",
    "col.OLR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Need to tune absorptivity to get OLR = 239\n",
    "epsarray = np.linspace(0.01, 0.1, 100)\n",
    "OLRarray = np.zeros_like(epsarray)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CoEHhBLFIsajnL1JmVq6Em26CX/4SjjwSLrkENtoo6aikXKjnL5JRHTvCmWeG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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ed41b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(epsarray.size):\n",
    "    col.subprocess['LW'].absorptivity = epsarray[i]\n",
    "    col.compute_diagnostics()\n",
    "    OLRarray[i] = col.OLR\n",
    "\n",
    "plt.plot(epsarray, OLRarray)\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The necessary value seems to lie near 0.055 or so.\n",
    "\n",
    "A precise numerical search gives $\\epsilon = 0.0534$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Field([ 0.0534,  0.0534,  0.0534,  0.0534,  0.0534,  0.0534,  0.0534,\n",
       "        0.0534,  0.0534,  0.0534,  0.0534,  0.0534,  0.0534,  0.0534,\n",
       "        0.0534,  0.0534,  0.0534,  0.0534,  0.0534,  0.0534,  0.0534,\n",
       "        0.0534,  0.0534,  0.0534,  0.0534,  0.0534,  0.0534,  0.0534,\n",
       "        0.0534,  0.0534])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eps = 0.0534\n",
    "\n",
    "col.subprocess.LW.absorptivity = eps\n",
    "col.subprocess.LW.absorptivity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 239.00554514])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  Double check to make sure this gives the right OLR\n",
    "\n",
    "col.compute_diagnostics()\n",
    "col.OLR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.24575486])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "col.ASR - col.OLR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "____________\n",
    "\n",
    "## Radiative equilibrium in the 30-layer model\n",
    "____________\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#  Make a clone of our first model\n",
    "re = climlab.process_like(col)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Integrating for 730 steps, 730.4844 days, or 2.0 years.\n",
      "Total elapsed time is 1.99867375676 years.\n"
     ]
    }
   ],
   "source": [
    "#  To get to equilibrium, we just time-step the model forward long enough\n",
    "re.integrate_years(2.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -4.63536253e-07])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  Check for energy balance\n",
    "re.ASR - re.OLR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make a plot that compares the **observed temperatures** to the **radiative equilibrium** temperature profile."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x10e3c3090>"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Jx5gYFelBA/uz3qhqfMyPb0JTrx588AFpDz4IY8e67TFj8jxjQX4USSrCe9e8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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ecc2250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_sounding([col, re])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some properties of the **radiative equilibrium** temperature profile:\n",
    "\n",
    "- The surface is warmer than observed.\n",
    "- The lower troposphere is colder than observed.\n",
    "- Very cold air is sitting immediately above the warm surface.\n",
    "- There is no tropopause, no stratosphere."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "____________\n",
    "\n",
    "## Radiative-Convective Equilibrium in the 30-layer model\n",
    "____________\n",
    "\n",
    "We recognize that the large drop in temperature just above the surface is unphysical. Parcels of air in direct contact with the ground will be warmed by mechansisms other than radiative transfer.\n",
    "\n",
    "These warm air parcels will then become buoyant, and will convect upward, mixing their heat content with the environment.\n",
    "\n",
    "We **parameterize** the statistical effects of this mixing through a **convective adjustment**. \n",
    "\n",
    "At each timestep, our model checks for any locations at which the **lapse rate** exceeds some threshold. Unstable layers are removed through an energy-conserving mixing formula.\n",
    "\n",
    "This process is assumed to be fast relative to radiative heating. In the model, it is instantaneous."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "climlab Process of type <class 'climlab.model.column.RadiativeConvectiveModel'>. \n",
      "State variables and domain shapes: \n",
      "  Tatm: (30,) \n",
      "  Ts: (1,) \n",
      "The subprocess tree: \n",
      "top: <class 'climlab.model.column.RadiativeConvectiveModel'>\n",
      "   convective adjustment: <class 'climlab.convection.convadj.ConvectiveAdjustment'>\n",
      "   LW: <class 'climlab.radiation.greygas.GreyGas'>\n",
      "   SW: <class 'climlab.radiation.greygas.GreyGasSW'>\n",
      "   insolation: <class 'climlab.radiation.insolation.FixedInsolation'>\n",
      "\n"
     ]
    }
   ],
   "source": [
    "rce = climlab.RadiativeConvectiveModel(adj_lapse_rate=6.)\n",
    "print rce"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This model is exactly like our previous models, except for one additional subprocess called ``convective adjustment``. \n",
    "\n",
    "We passed a parameter ``adj_lapse_rate`` (in K / km) that sets the neutrally stable lapse rate -- in this case, 6 K / km.\n",
    "\n",
    "This number is chosed to very loosely represent the net effect of **moist convection**. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Set our tuned absorptivity value\n",
    "rce.subprocess.LW.absorptivity = eps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Integrating for 730 steps, 730.4844 days, or 2.0 years.\n",
      "Total elapsed time is 1.99867375676 years.\n"
     ]
    }
   ],
   "source": [
    "#  Run out to equilibrium\n",
    "rce.integrate_years(2.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1.96076689e-06])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  Check for energy balance\n",
    "rce.ASR - rce.OLR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x10ed4a310>"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Fixzn7JY/2WqhxuQBWbbhiMinuMGes4H2wHpVvT9EZQuamG/DycratfDMM/DV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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ecc2350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#  Make a plot to compare observations, Radiative Equilibrium, and Radiative-Convective Equilibrium\n",
    "plot_sounding([col, re, rce])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Introducing convective adjustment into the model cools the surface quite a bit (compared to Radiative Equilibrium, in green here) -- and warms the lower troposphere. It gives us a MUCH better fit to observations.\n",
    "\n",
    "But of course we still have no stratosphere.\n",
    "\n",
    "The missing ingredient is **absorption of shortwave UV radiation by ozone**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The heating rates due to radiation and convection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#  Here we plotting the heating rates in K / day\n",
    "degrees_per_day_atm = {'LW': (rce.subprocess['LW'].heating_rate['Tatm'] /\n",
    "                                 rce.Tatm.domain.heat_capacity * \n",
    "                                 climlab.constants.seconds_per_day),\n",
    "                       'SW': (rce.subprocess['SW'].heating_rate['Tatm'] /\n",
    "                                 rce.Tatm.domain.heat_capacity * \n",
    "                                 climlab.constants.seconds_per_day),\n",
    "                   'Convection': (rce.subprocess['convective adjustment'].adjustment['Tatm'] /\n",
    "                                  rce.timestep * \n",
    "                                  climlab.constants.seconds_per_day)}\n",
    "degrees_per_day_sfc = {'LW': (rce.subprocess['LW'].heating_rate['Ts'] / \n",
    "                                      rce.Ts.domain.heat_capacity *\n",
    "                                      climlab.constants.seconds_per_day),\n",
    "                        'SW': (rce.subprocess['SW'].heating_rate['Ts'] / \n",
    "                                      rce.Ts.domain.heat_capacity *\n",
    "                                      climlab.constants.seconds_per_day),\n",
    "                        'Convection': (rce.subprocess['convective adjustment'].adjustment['Ts'] /\n",
    "                                       rce.timestep * \n",
    "                                       climlab.constants.seconds_per_day)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Ro0bx8ccfA7B8+XIeeughunfvDkTFwvTp01m+fDmdOnUCoisLqVSK119/XcVCNVQsBCaU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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e663590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "color_cycle=['r', 'g', 'b', 'y']\n",
    "\n",
    "fig = plt.figure( figsize=(8,6) )\n",
    "ax = fig.add_subplot(111)\n",
    "zstar = -np.log(rce.lev/climlab.constants.ps)\n",
    "for i, item in enumerate(degrees_per_day_atm):\n",
    "    ax.plot(degrees_per_day_atm[item], zstar, color=color_cycle[i], label=item)\n",
    "for i, item in enumerate(degrees_per_day_sfc):\n",
    "    ax.plot(degrees_per_day_sfc[item], 0, 'o', markersize=12, color=color_cycle[i])\n",
    "yticks = np.array([1000., 750., 500., 250., 100., 50., 20., 10.])\n",
    "ax.set_yticks(-np.log(yticks/1000.))\n",
    "ax.set_yticklabels(yticks)\n",
    "ax.set_xlabel('Heating rates (degrees per day)', fontsize=16)\n",
    "ax.set_ylabel('Pressure (hPa)', fontsize=16 )\n",
    "ax.legend()\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What do we see here?\n",
    "\n",
    "- SW radiation is acting to heat the surface strongly\n",
    "- No SW heating in the atmosphere (assumed to be transparent)\n",
    "- At the surface, there is a **balance** between **heat gain from SW radiation** and **heat loss from both LW radiation and convection**\n",
    "- LW radiation is acting to **cool the troposphere**\n",
    "- Convection is acting to **warm the troposphere**\n",
    "\n",
    "Collectively the LW and SW radiation are trying to push the temperatures towards **radiative equilibrium** while the convection is moving heat from the surface to the troposphere."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}