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   "source": [
    "# [ATM 623: Climate Modeling](../index.ipynb)\n",
    "\n",
    "[Brian E. J. Rose](http://www.atmos.albany.edu/facstaff/brose/index.html), University at Albany\n",
    "\n",
    "# Lecture 18: The one-dimensional energy balance model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Warning: content out of date and not maintained\n",
    "\n",
    "You really should be looking at [The Climate Laboratory book](https://brian-rose.github.io/ClimateLaboratoryBook) by Brian Rose, where all the same content (and more!) is kept up to date.\n",
    "\n",
    "***Here you are likely to find broken links and broken code.***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
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   "source": [
    "### About these notes:\n",
    "\n",
    "This document uses the interactive [`Jupyter notebook`](https://jupyter.org) format. The notes can be accessed in several different ways:\n",
    "\n",
    "- The interactive notebooks are hosted on `github` at https://github.com/brian-rose/ClimateModeling_courseware\n",
    "- The latest versions can be viewed as static web pages [rendered on nbviewer](http://nbviewer.ipython.org/github/brian-rose/ClimateModeling_courseware/blob/master/index.ipynb)\n",
    "- A complete snapshot of the notes as of May 2017 (end of spring semester) are [available on Brian's website](http://www.atmos.albany.edu/facstaff/brose/classes/ATM623_Spring2017/Notes/index.html).\n",
    "\n",
    "[Also here is a legacy version from 2015](http://www.atmos.albany.edu/facstaff/brose/classes/ATM623_Spring2015/Notes/index.html).\n",
    "\n",
    "Many of these notes make use of the `climlab` package, available at https://github.com/brian-rose/climlab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#  Ensure compatibility with Python 2 and 3\n",
    "from __future__ import print_function, division"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Contents\n",
    "\n",
    "1. [Simulation versus parameterization of heat transport](#section1)\n",
    "2. [The temperature diffusion parameterization](#section2)\n",
    "3. [Solving the temperature diffusion equation with `climlab`](#section3)\n",
    "4. [Parameterizing the radiation terms](#section4)\n",
    "5. [The one-dimensional diffusive energy balance model](#section5)\n",
    "6. [The annual-mean EBM](#section6)\n",
    "7. [Effects of diffusivity in the EBM](#section7)\n",
    "8. [Summary: parameter values in the diffusive EBM](#section8)"
   ]
  },
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   "source": [
    "____________\n",
    "<a id='section1'></a>\n",
    "\n",
    "## 1. Simulation versus parameterization of heat transport\n",
    "____________\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
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   "source": [
    "In the previous lectures we have seen how heat transport by winds and ocean currents acts to COOL the tropics and WARM the poles. The observed temperature gradient is a product of both the insolation and the heat transport!"
   ]
  },
  {
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   "source": [
    "We were able to ignore this issue in our models of the global mean temperature, because the transport just moves energy around between latitude bands – does not create or destroy energy.\n",
    "\n",
    "But if want to move beyond the global mean and create models of the equator-to-pole temperature structure, we cannot ignore heat transport. Has to be included somehow!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
    }
   },
   "source": [
    "This leads to us the old theme of **simulation versus parameterization**.\n",
    "\n",
    "Complex climate models like the CESM simulate the heat transport by solving the full equations of motion for the atmosphere (and ocean too, if coupled)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Simulation of synoptic-scale variability in CESM\n",
    "\n",
    "Let's revisit an animation of the global 6-hourly sea-level pressure field from our slab ocean simulation with CESM. (We first saw this [back in Lecture 5](./Lecture05 -- Climate system and climate models.ipynb)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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     "slide_type": "slide"
    }
   },
   "outputs": [
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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/As85L34fKYQ\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x102c38ac8>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('As85L34fKYQ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "All these traveling weather systems tend to move **warm, moist air poleward** and **cold, dry air equatorward**. There is thus a **net poleward energy transport**.\n",
    "\n",
    "A model like this needs to **simulate the weather** in order to **model the heat transport**.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### A simpler statistical approach\n",
    "\n",
    "Let’s emphasize: the most important role for heat transport by winds and ocean currents is to more energy from where it’s WARM to where it’s COLD, thereby reducing the temperature gradient (equator to pole) from what it would be if the planet were in radiative-convective equilibrium everywhere with no north-south motion.\n",
    "\n",
    "This is the basis for the parameterization of heat transport often used in simple climate models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Discuss analogy with molecular heat conduction: metal rod with one end in the fire.\n",
    "\n",
    "Define carefully temperature gradient dTs / dy\n",
    "Measures how quickly the temperature  decreases as we move northward\n",
    "(negative in NH, positive in SH)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "In any conduction or diffusion process, the flux (transport) of a quantity is always DOWN-gradient  (from WARM to COLD).\n",
    "\n",
    "So our parameterization will look like\n",
    "\n",
    "$$ \\mathcal{H} = -K ~ dT / dy $$\n",
    "\n",
    "Where $K$ is some positive number “diffusivity of the climate system”.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "____________\n",
    "<a id='section2'></a>\n",
    "\n",
    "## 2. The temperature diffusion parameterization\n",
    "____________\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Last time we wrote down an energy budget for a thin zonal band centered at latitude $\\phi$:\n",
    "\n",
    "$$ \\frac{\\partial E(\\phi)}{\\partial t} = \\text{ASR}(\\phi) - \\text{OLR}(\\phi) - \\frac{1}{2 \\pi a^2  \\cos⁡\\phi } \\frac{\\partial \\mathcal{H}}{\\partial \\phi} $$\n",
    "\n",
    "where we have written every term as an explicit function of latitude to remind ourselves that this is a **local** budget, unlike the zero-dimensional global budget we considered at the start of the course."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let’s now formally introduce a parameterization that **approximates the heat transport as a down-gradient diffusion process**:\n",
    "\n",
    "$$ \\mathcal{H}(\\phi) \\approx -2 \\pi a^2  \\cos⁡\\phi ~ D ~ \\frac{\\partial T_s}{\\partial \\phi} $$\n",
    "\n",
    "With $D$ a parameter for the **diffusivity** or **thermal conductivity** of the climate system, a number in W m$^{-2}$ ºC$^{-1}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The value of $D$ will be chosen to match observations – i.e. tuned.\n",
    "\n",
    "Notice that we have explicitly chosen to the use **surface temperature gradient** to set the heat transport. This is a convenient (and traditional) choice to make, but it is not the only possibility! We could instead tune our parameterization to some measure of the free-tropospheric temperature gradient."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The diffusive parameterization in the planetary energy budget\n",
    "\n",
    "Plug the parameterization into our energy budget to get\n",
    "\n",
    "$$ \\frac{\\partial E(\\phi)}{\\partial t} = \\text{ASR}(\\phi) - \\text{OLR}(\\phi) - \\frac{1}{2 \\pi a^2  \\cos⁡\\phi } \\frac{\\partial }{\\partial \\phi} \\left( -2 \\pi a^2  \\cos⁡\\phi ~ D ~ \\frac{\\partial T_s}{\\partial \\phi} \\right) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "If we assume that $D$ is a constant (does not vary with latitude), then this simplifies to\n",
    "\n",
    "$$ \\frac{\\partial E(\\phi)}{\\partial t} = \\text{ASR}(\\phi) - \\text{OLR}(\\phi) + \\frac{D}{\\cos⁡\\phi } \\frac{\\partial }{\\partial \\phi} \\left(   \\cos⁡\\phi  ~ \\frac{\\partial T_s}{\\partial \\phi} \\right) $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Surface temperature is a good measure of column heat content\n",
    "\n",
    "Let's now make the same assumption we made [back at the beginning of the course](Lecture01 -- Planetary energy budget.ipynb) when we first wrote down the zero-dimensional EBM.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "*Most of the heat capacity is in the oceans, so that the energy content of each column $E$ is proportional to surface temperature*:\n",
    "\n",
    "$$ E(\\phi) = C(\\phi) ~ T_s(\\phi) $$\n",
    "\n",
    "where $C$ is **effective heat capacity** of the atmosphere - ocean column, in units of J m$^{-2}$ K$^{-1}$. Here we are writing $C$ are a function of latitude so that our model is general enough to allow different land-ocean fractions at different latitudes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### A heat equation for surface temperature\n",
    "\n",
    "Now our budget becomes a PDE for the surface temperature $T_s(\\phi, t)$:\n",
    "\n",
    "$$ C(\\phi) \\frac{\\partial T_s}{\\partial t} = \\text{ASR}(\\phi) - \\text{OLR}(\\phi) + \\frac{D}{\\cos⁡\\phi } \\frac{\\partial }{\\partial \\phi} \\left(   \\cos⁡\\phi  ~ \\frac{\\partial T_s}{\\partial \\phi} \\right) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Notice that if we were NOT on a spherical planet and didn’t have to worry about the changing size of latitude circles, this would look something like\n",
    "\n",
    "$$ \\frac{\\partial T}{\\partial t} = K \\frac{\\partial^2 T}{\\partial y^2} + \\text{forcing terms} $$\n",
    "with $K = D/C$ in m$^{2}$ s$^{-1}$.\n",
    "\n",
    "Does equation look familiar?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "This is the *heat equation*, one of the central equations in classical mathematical physics. \n",
    "\n",
    "This equation describes the behavior of a diffusive system, i.e. how mixing by random molecular motion smears out the temperature. \n",
    "\n",
    "In our case, the analogy is between the random molecular motion of a metal rod, and the net mixing / stirring effect of weather systems.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Take the global average...\n",
    "\n",
    "Take the integral $\\int_{-\\pi/2}^{\\pi/2} \\cos\\phi ~ d\\phi$ of each term.\n",
    "\n",
    "\n",
    "$$ C \\frac{\\partial \\overline{T_s}}{\\partial t} d\\phi = \\overline{\\text{ASR}} - \\overline{\\text{OLR}} + D \\int_{-\\pi/2}^{\\pi/2} \\frac{\\partial }{\\partial \\phi} \\left(   \\cos⁡\\phi  ~ \\frac{\\partial T_s}{\\partial \\phi} \\right) d\\phi$$\n",
    "\n",
    "The global average of the last term (heat transport) must go to zero (why?)\n",
    "\n",
    "Therefore this reduces to our familiar zero-dimensional EBM.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "____________\n",
    "<a id='section3'></a>\n",
    "\n",
    "## 3. Solving the temperature diffusion equation with `climlab`\n",
    "____________\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "`climlab` has a pre-defined process for solving the meridional diffusion equation. Let's look at a simple example in which diffusion is the ONLY process that changes the temperature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import climlab\n",
    "from climlab import constants as const"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Temperature (deg C)')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#  First define an initial temperature field\n",
    "#   that is warm at the equator and cold at the poles\n",
    "#   and varies smoothly with latitude in between\n",
    "\n",
    "from climlab.utils import legendre\n",
    "sfc = climlab.domain.zonal_mean_surface(num_lat=90, water_depth=10.)\n",
    "lat = sfc.lat.points\n",
    "initial = 12. - 40. * legendre.P2(np.sin(np.deg2rad(lat)))\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lat, initial)\n",
    "ax.set_xlabel('Latitude')\n",
    "ax.set_ylabel('Temperature (deg C)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "climlab Process of type <class 'climlab.dynamics.meridional_heat_diffusion.MeridionalHeatDiffusion'>. \n",
      "State variables and domain shapes: \n",
      "  default: (90, 1) \n",
      "The subprocess tree: \n",
      "Diffusion: <class 'climlab.dynamics.meridional_heat_diffusion.MeridionalHeatDiffusion'>\n",
      "\n"
     ]
    }
   ],
   "source": [
    "##  Set up the climlab diffusion process\n",
    "\n",
    "# make a copy of initial so that it remains unmodified\n",
    "Ts = climlab.Field(np.array(initial), domain=sfc)\n",
    "# thermal diffusivity in W/m**2/degC\n",
    "D = 0.55\n",
    "# create the climlab diffusion process\n",
    "#  setting the diffusivity and a timestep of ONE MONTH\n",
    "d = climlab.dynamics.MeridionalHeatDiffusion(name='Diffusion', \n",
    "            state=Ts, D=D, timestep=const.seconds_per_month)\n",
    "print( d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "#  We are going to step forward one month at a time\n",
    "#  and store the temperature each time\n",
    "niter = 5\n",
    "temp = np.zeros((Ts.size, niter+1))\n",
    "temp[:, 0] = np.squeeze(Ts)\n",
    "for n in range(niter):\n",
    "    d.step_forward()\n",
    "    temp[:, n+1] = np.squeeze(Ts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11d92ecc0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#  Now plot the temperatures\n",
    "fig,ax = plt.subplots()\n",
    "ax.plot(lat, temp)\n",
    "ax.set_xlabel('Latitude')\n",
    "ax.set_ylabel('Temperature (deg C)')\n",
    "ax.legend(range(niter+1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "At each timestep, the warm temperatures get cooler (at the equator) while the cold polar temperatures get warmer!\n",
    "\n",
    "Diffusion is acting to **reduce the temperature gradient**.\n",
    "\n",
    "If we let this run a long time, what should happen??\n",
    "\n",
    "Try it yourself and find out!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Mathematical aside: the Legendre Polynomials\n",
    "\n",
    "Here we have used a function called the “2nd Legendre polynomial”, defined as\n",
    "\n",
    "$$ P_2 (x) = \\frac{1}{2} \\left( 3x^2-1 \\right) $$\n",
    "\n",
    "where we have also set\n",
    "\n",
    "$$ x = \\sin\\phi $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Just turns out to be a useful mathematical description of the relatively smooth changes in things like annual-mean insolation from equator to pole.\n",
    "\n",
    "In fact these are so useful that they are coded up in a special module within `climlab`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '$P_2(x)$')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-1,1)\n",
    "fig,ax = plt.subplots()\n",
    "ax.plot(x, legendre.P2(x))\n",
    "ax.set_title('$P_2(x)$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "____________\n",
    "<a id='section4'></a>\n",
    "\n",
    "## 4. Parameterizing the radiation terms\n",
    "____________"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's go back to the complete budget with our heat transport parameterization\n",
    "\n",
    "$$ C(\\phi) \\frac{\\partial T_s}{\\partial t} = \\text{ASR}(\\phi) - \\text{OLR}(\\phi) + \\frac{D}{\\cos⁡\\phi } \\frac{\\partial }{\\partial \\phi} \\left(   \\cos⁡\\phi  ~ \\frac{\\partial T_s}{\\partial \\phi} \\right) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We want to express this **as a closed equation for surface temperature $T_s$**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "First, as usual, we can write the solar term as\n",
    "\n",
    "$$ \\text{ASR} = (1-\\alpha) ~ Q $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For now, we will **assume that the planetary albedo is fixed (does not depend on temperature)**. Therefore the entire shortwave term $(1-\\alpha) Q$ is a fixed source term in our budget. It varies in space and time but does not depend on $T_s$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the solar term is (at least in annual average) larger at equator than poles… and transport term acts to flatten out the temperatures."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now, we almost have a model we can solve for T!  Just need to express the OLR in terms of temperature.\n",
    "\n",
    "So…  what’s the link between OLR and temperature????\n",
    "\n",
    "[ discuss ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We spent a good chunk of the course looking at this question, and developed a model of a vertical column of air.\n",
    "\n",
    "We are trying now to build a model of the equator-to-pole (or pole-to-pole) temperature structure."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We COULD use an array of column models, representing temperature as a function of height and latitude (and time).\n",
    "\n",
    "But instead, we will keep things simple, one spatial dimension at a time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Introduce the following simple parameterization:\n",
    "\n",
    "$$ OLR = A + B T_s $$\n",
    "\n",
    "With $T_s$ the zonal average surface temperature in ºC, A is a constant in W m$^{-2}$ and B is a constant in W m$^{-2}$ ºC$^{-1}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### OLR versus surface temperature in NCEP Reanalysis data\n",
    "\n",
    "Let's look at the data to find reasonable values for $A$ and $B$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<xarray.Dataset>\n",
      "Dimensions:             (lat: 94, lon: 192, nbnds: 2, time: 12)\n",
      "Coordinates:\n",
      "  * lon                 (lon) float32 0.0 1.875 3.75 ... 354.375 356.25 358.125\n",
      "  * time                (time) float64 -6.571e+05 -6.57e+05 ... -6.567e+05\n",
      "  * lat                 (lat) float32 88.542 86.6531 ... -86.6531 -88.542\n",
      "Dimensions without coordinates: nbnds\n",
      "Data variables:\n",
      "    climatology_bounds  (time, nbnds) float64 ...\n",
      "    skt                 (time, lat, lon) float32 ...\n",
      "    valid_yr_count      (time, lat, lon) float32 ...\n",
      "Attributes:\n",
      "    title:                          4x daily NMC reanalysis\n",
      "    description:                    Data is from NMC initialized reanalysis\\n...\n",
      "    platform:                       Model\n",
      "    Conventions:                    COARDS\n",
      "    not_missing_threshold_percent:  minimum 3% values input to have non-missi...\n",
      "    history:                        Created 2011/07/12 by doMonthLTM\\nConvert...\n",
      "    References:                     http://www.esrl.noaa.gov/psd/data/gridded...\n",
      "    dataset_title:                  NCEP-NCAR Reanalysis 1\n"
     ]
    }
   ],
   "source": [
    "import xarray as xr\n",
    "## The NOAA ESRL server is shutdown! January 2019\n",
    "ncep_url = \"http://www.esrl.noaa.gov/psd/thredds/dodsC/Datasets/ncep.reanalysis.derived/\"\n",
    "ncep_Ts = xr.open_dataset( ncep_url + \"surface_gauss/skt.sfc.mon.1981-2010.ltm.nc\", decode_times=False)\n",
    "#url = 'http://apdrc.soest.hawaii.edu:80/dods/public_data/Reanalysis_Data/NCEP/NCEP/clima/'\n",
    "#ncep_Ts = xr.open_dataset(url + 'surface_gauss/skt')\n",
    "lat_ncep = ncep_Ts.lat; lon_ncep = ncep_Ts.lon\n",
    "print( ncep_Ts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "Ts_ncep_annual = ncep_Ts.skt.mean(dim=('lon','time'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "ncep_ulwrf = xr.open_dataset( ncep_url + \"other_gauss/ulwrf.ntat.mon.1981-2010.ltm.nc\", decode_times=False)\n",
    "ncep_dswrf = xr.open_dataset( ncep_url + \"other_gauss/dswrf.ntat.mon.1981-2010.ltm.nc\", decode_times=False)\n",
    "ncep_uswrf = xr.open_dataset( ncep_url + \"other_gauss/uswrf.ntat.mon.1981-2010.ltm.nc\", decode_times=False)\n",
    "#ncep_ulwrf = xr.open_dataset(url + \"other_gauss/ulwrf\")\n",
    "#ncep_dswrf = xr.open_dataset(url + \"other_gauss/dswrf\")\n",
    "#ncep_uswrf = xr.open_dataset(url + \"other_gauss/uswrf\")\n",
    "OLR_ncep_annual = ncep_ulwrf.ulwrf.mean(dim=('lon','time'))\n",
    "ASR_ncep_annual = (ncep_dswrf.dswrf - ncep_uswrf.uswrf).mean(dim=('lon','time'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best fit is A = 214 W/m2 and B = 1.6 W/m2/degC\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import linregress\n",
    "slope, intercept, r_value, p_value, std_err = linregress(Ts_ncep_annual, OLR_ncep_annual)\n",
    "\n",
    "print( 'Best fit is A = %0.0f W/m2 and B = %0.1f W/m2/degC' %(intercept, slope))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We're going to plot the data and the best fit line, but also another line using these values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#  More standard values\n",
    "A = 210.\n",
    "B = 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax1 = plt.subplots(figsize=(8,6))\n",
    "ax1.plot( Ts_ncep_annual, OLR_ncep_annual, 'o' , label='data')\n",
    "ax1.plot( Ts_ncep_annual, intercept + slope * Ts_ncep_annual, 'k--', label='best fit')\n",
    "ax1.plot( Ts_ncep_annual, A + B * Ts_ncep_annual, 'r--', label='B=2')\n",
    "ax1.set_xlabel('Surface temperature (C)', fontsize=16)\n",
    "ax1.set_ylabel('OLR (W m$^{-2}$)', fontsize=16)\n",
    "ax1.set_title('OLR versus surface temperature from NCEP reanalysis', fontsize=18)\n",
    "ax1.legend(loc='upper left')\n",
    "ax1.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Discuss these curves...\n",
    "\n",
    "Suggestion of at least 3 different regimes with different slopes (cold, medium, warm).\n",
    "\n",
    "Unbiased \"best fit\" is actually a poor fit over all the intermediate temperatures.\n",
    "\n",
    "The astute reader will note that...   by taking the zonal average of the data before the regression, we are biasing this estimate toward cold temperatures.  [WHY?]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's take these reference values:\n",
    "\n",
    "$$ A = 210 ~ \\text{W m}^{-2}, ~~~ B = 2 ~ \\text{W m}^{-2}~^\\circ\\text{C}^{-1} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Note that in the **global average**, recall $\\overline{T_s} = 288 \\text{ K} = 15^\\circ\\text{C}$\n",
    "\n",
    "And so this parameterization gives \n",
    "\n",
    "$$ \\overline{\\text{OLR}} = 210 + 15 \\times 2 = 240 ~\\text{W m}^{-2} $$\n",
    "\n",
    "And the observed global mean is $\\overline{\\text{OLR}} = 239 ~\\text{W m}^{-2} $\n",
    "So this is consistent.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "____________\n",
    "<a id='section5'></a>\n",
    "\n",
    "## 5. The one-dimensional diffusive energy balance model\n",
    "____________\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Putting the above OLR parameterization into our budget equation gives\n",
    "\n",
    "$$ C(\\phi) \\frac{\\partial T_s}{\\partial t} = (1-\\alpha) ~ Q - \\left( A + B~T_s \\right) + \\frac{D}{\\cos⁡\\phi } \\frac{\\partial }{\\partial \\phi} \\left(   \\cos⁡\\phi  ~ \\frac{\\partial T_s}{\\partial \\phi} \\right) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "This is the equation for a very important and useful simple model of the climate system. It is typically referred to as the (one-dimensional) Energy Balance Model.\n",
    "\n",
    "(although as we have seen over and over, EVERY climate model is actually an “energy balance model” of some kind)\n",
    "\n",
    "Also for historical reasons this is often called the **Budyko-Sellers model**, after Budyko and Sellers who both (independently of each other) published influential papers on this subject in 1969."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Recap: parameters in this model are\n",
    "\n",
    "- C: heat capacity in J m$^{-2}$ ºC$^{-1}$\n",
    "- A: longwave emission at 0ºC in W m$^{-2}$\n",
    "- B: increase in emission per degree, in W m$^{-2}$ ºC$^{-1}$\n",
    "- D: horizontal (north-south) diffusivity of the climate system in W m$^{-2}$ ºC$^{-1}$\n",
    "\n",
    "We also need to specify the albedo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Tune albedo formula to match observations\n",
    "\n",
    "Let's go back to the NCEP Reanalysis data to see how planetary albedo actually varies as a function of latitude."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "days = np.linspace(1.,50.)/50 * const.days_per_year\n",
    "Qann_ncep = climlab.solar.insolation.daily_insolation(lat_ncep, days ).mean(dim='day')\n",
    "albedo_ncep = 1 - ASR_ncep_annual / Qann_ncep\n",
    "\n",
    "albedo_ncep_global = np.average(albedo_ncep, weights=np.cos(np.deg2rad(lat_ncep)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The annual, global mean planetary albedo is 0.354\n"
     ]
    },
    {
     "data": {
      "image/png": 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EATGUlleycneO21GMMafhUG4xa/Ye45LhzevkdDUrEH4osXdHQoMC+GrHEbejGGNOw+LUquYlKxCm0YQFBzK+d0crEMY0c59sPsiAuEj6xTavq5eqWYHwUz8YEMOuIwUcOF7kdhRjzCk4fKKY1XuONtujB7AC4bcmDogBsKMIY5qpxSmHUG2+zUtgBcJv9Y+NpHPbMCsQxjRT/9mSRd+YCAbERbkd5ZRZgfBTIsLEAdEsTcumvKLS7TjGmAZQVTZl5DK+d/MY96EuViD82MQBMZwoLmdjxnG3oxhjGiDjWBG5RWUM69bO7SinxQqEHzu7XzQBAl/uyHY7ijGmATYfyAVgeEsvECLSXUTeF5EjIpIlIu+KSHdfnlxEJovIdhFJE5EHvCxPEpFcEdng+fkfX7dtDdqHhzCie3u+3mnnIYxpTjYfyCUoQBjYufmefwDfjiBeBhYAXYBuwEeeeSclIoHAM8DFwBBguogM8bLq16o6yvPzcAO3bfHO7NuJTRm51rurMc1IyoFcBsRFERrU/Droq8mXAhGjqi+rarnn5xUgxoftxgNpqpquqqXAPGCqj7lOZ9sWJbFPJyoqlbV7j7kdxRjjA1Ul5UBus29eAvCle8FsEbkBeNMzPR3wpZOgbkDNPqszgEQv650hIhuBTOCXqpragG0RkRnADIC4uDiSk5N9iNa08vPzTzlXcbkSIDA/eT2VmSGNG8yL08na1CyrMyzr6ckuquRYYRmhhVnfyeaPWevjS4G4FXga+D9AgeWeefXxNq6e1ppeB/RS1XwRuQT4AOjv47ZVM1XnAHMAEhISNCkpyYdoTSs5OZnTyTVi+zIOVghJSWc2Xqg6nG7WpmRZnWFZT8+ilIPAOq6YNI5RPdp/O98fs9an3iYmVd2nqlNUNUZVY1X1MlXd68NzZwA9akx3p+oooeZz56lqvufxQiBYRKJ92bY1mdCnE5syjlNYauchjPF3mw/kEhggDGrmJ6jhJEcQIvIUdXxrB1DVn9Xz3KuB/iLSGzgATAOuq/UanYEsVVURGU9VwcoBjte3bWuS2Kcjs7/cxbq9xzm7f7TbcYwxJ5FyII/+sZGEBTfvE9Rw8iOINcBaIAwYA+z0/IwC6h3JRlXLgVnAYmArMF9VU0VkpojM9Kx2FZDiOQfxD2CaVvG67an8gS1BQq8OBAYI39j4EMb4tZZ0ghpOcgShqq8CiMjNwCRVLfNMzwb+48uTe5qNFtaaN7vG46epOr/h07atVVRYMMO6tuWb9KNuRzHGnMTB3GJyCkoZ3r1lFAhfLnPtCtRsTIv0zDNNaEKfTmzYf5ziMhuG1Bh/VX0HdXPvYqOaLwXiUWC9iLwiIq9QdeXRnx1NZb4nsU9HSisqWbfP7ocwxl+lHsglQGBw57ZuR2kUvlzF9DJV9yC87/k5o7r5yTSdhPiOBAistGYmY/zW5gO59I+Nok1I8z9BDb71xSTA+cBIVf0QCPFccWSaUNuwYIZ2bcc36Xai2hh/pKpsPpDXYpqXwLcmpn8CZ1B1BzXACar6STJNLLF3R9bbeQhj/NLenEKy80sY1bN9/Ss3E74UiERVvQsoBlDVY4DzfT6Y70mI70hpeSWpmXluRzHG1LI0rapb/rP7tZx7lXwpEGWe3lUVQERiABvizAVjelV9M1lvJ6qN8TvL0rLp1r4N8Z3C3Y7SaHwpEP+g6uR0nIj8CViKXcXkitioMLp3aGNXMhnjZyoqleW7cjirXyeqTtu2DPV21qeqc0VkLXCeZ9ZlqrrV2VimLmN6dmDVbruSyRh/knIgl9yiMs5qQc1L4PuQo+FAoGf9Ns7FMfUZ07M9h/KKyTxe5HYUY4xH9fmHM/u2sgLhGQb0VaAjEA28LCIPOh3MeDe6ZwcA1u877nISY0y1ZWnZDOocRUxUqNtRGpUvRxDTgXGq+ntVfQiYAFzvbCxTl8Fd2hIaFGDnIYzxE0WlFazZc4xzWmBPy74UiD1U9ehaLRTY5UgaU6+QoABGdG9nBcIYP7F6z1FKKypb3PkH8G08iBIgVUQ+9UxfQNWVTMYlY3p24OVleygpr2j2g6Ib09wtS8smOFAY37uj21Ea3cmuYlrj+b2WqstcqyU7lsb4ZHTPDjz3VTopB/IY26uD23GMadWWpmUzpmcHwkN8GcG5eal3PAjjf2reMGcFwhj3HC0oJTUzj19cMMDtKI44WRPTZuoeclRVdaQzkUx9qm+YsyuZjHHXZ1uzADhnQIzLSZxxsmOiH3mZJ0B34De+PLmITAaepOoeihdU9dE61hsHrASuVdV3PPP2UNUxYAVQrqoJvrxmazG6ZwfW7LEb5oxx0/zV++kTE8HIFjKCXG11XsWkqnurf4AOwF1UnX/4Iz4MBerpv+kZ4GJgCDBdRIbUsd5jVI0/XdskVR1lxeH7xvRsz8HcYg7m2g1zxrgh7XA+a/Ye49qEHi2qe42a6iwQIjJARP5HRLZSNW70fkBUdZJnLOn6jAfSVDVdVUuBecBUL+vdDbwLHG54/Nar+tyDjVNtjDvmr9lPUIBwxZjubkdxzMmamLYBXwOXqmoagIjc14Dn7kZVUamWQdXIdN8SkW7A5cC5wLha2yvwHxFR4DlVnePtRURkBjADIC4ujuTk5AZEbBr5+fmNnqtSlfahwqtLNtM+d2ejPa8TWZ1iWZ1hWetXXqnMW1nIiOhAUteu8Gmb5rRfq52sQFwJTAOWiMgiqo4AGnIc5W3d2ie9/w7cr6oVXg7RzlLVTBGJBT4VkW2q+tX3nrCqcMwBSEhI0KSkpAZEbBrJyck4kevy/FTmrtzHmAln0TYsuFGe06msTrCszrCs9VuUcoi80rXMumQ0SYPifNqmOe3Xaic7B/G+ql4LDKLq3MN9VHX5/ayIXOjDc2cAPWpMdwcya62TAMzznJC+CviniFzmef1Mz+/DVN2HYcOc1vKjEV0prajk09Qst6MY06q8tXofcW1Dmdi/ZV69VK3erjZUtUBV56rqj6j6kN8APODDc68G+otIbxEJoepoZEGt5+6tqvGqGg+8A/xUVT8QkQgRiQIQkQjgQiClIX9YazCmZ3u6tW/Dx5tq111jjFMO5Rbz5Y4jXDW2O0GBvnaI3Tw16K9T1aOq+pyqnuvDuuXALKquTtoKzFfVVBGZKSIz69k8DlgqIhuBVcAnqrqoIVlbAxHhhyO68PXObI4Xlrodx5hW4c1V+6hUuCahR/0rN3OO3huuqgupdUmsqs6uY92bazxOB+xGPB/8aEQX5nyVzuLUQ1w7rqfbcYxp0Y6cKOGFr9O5cEgcvTpFuB3HcS37+KgVGN6tHT07hvPxpoNuRzGmxXvy8x2UlFfywMWD3I7SJKxANHMiwo9GdGH5rhxy8kvcjmNMi5V2+ARvrtrP9Yk96RMT6XacJmEFogX40YiuVFQqC1MOuR3FmBbrkYXbCA8O5Gfn9Xc7SpOxAtECDO4SxeAubXn+q3SKyyrcjmNMi7M8LZvPtx3mrnP70SmyZQ0rejJWIFoAEeG3lwxm39FCXlq22+04xrQoRaUV/OGjLXRr34abz4x3O06TsgLRQpzdP5oLhsTx9BdpZOUVux3HmBZBVXngvU3sOHyCP10+jLDg1jWCoxWIFuTBHw6mvEJ5bNE2t6MY0yK8tGwPH27I5BcXDCBpYKzbcZqcFYgWpFenCG47pzfvrTvA+n3H3I5jTLO2Mj2HPy/cyoVD4vhpUj+347jCCkQLc9ekfsRGhfLLtzey7VCe23GMaZbSj+Rz19x19OoUzt+uGUlAQMsc76E+ViBamMjQIJ64ZhTHCsu49KmlPPnZTkrLK92OZUyzsTu7gOnPrwRgzo0JRDVST8nNkRWIFujs/tF8et9ELh7Whf/7bAdTn1lmfTUZ44O9OQVMn7OSsgpl7h2J9IttHTfE1cUKRAvVKTKUf0wfzXM3jmVn1gke/miL25GM8WsHjhcxfc5KSsormHt7IoM6t3U7kuusQLRwFw3tzE+T+vLe+gN8sc3GjTDGG1Xlwfc3k1tUxuu3JzK4ixUHsALRKtx1bj8GxEXym/dSyCsuczuOMX5nceohlmw/wn0XDGBo13Zux/EbViBagdCgQB6/aiSHTxTzyMKtbscxxq8UlJTzh4+2MKhzVKu7U7o+ViBaiZE92nPHxD68uWo/i1Ksa3Bjqv39sx0czC3mT5cPa/EjxDWU7Y1W5L7zBzCyR3vuemM9H6w/4HYcY1y39WAeLy3bw7RxPRjbq6PbcfyOFYhWJCw4kLm3JzI+viP3zd/Av1bscTuSMa7Zf7SQma+vpW1YEPdPbh0DADWUowVCRCaLyHYRSRORB06y3jgRqRCRqxq6rWmYyNAgXr5lHOcNiuV3H6bywLubWLv3GKrqdjRjmkza4RNcPXsFxwpKefHmcXSICHE7kl9ybExqEQkEngEuADKA1SKyQFW3eFnvMWBxQ7c1pyYsOJBnbxjLwx9t4a01+5m3ej/dO7Rh+vieDMYKhWnZNmfk8uOXVxEgwlt3nmGXtJ6EYwUCGA+kqWo6gIjMA6YCtT/k7wbeBcadwrbmFAUHBvDHy4bxq8kD+U9qFh+sP8Dji7czoUsg50ysJNhO1pkWJCe/hH+nHOKjjZms2nOUru3a8PrtifSOjnA7ml9zskB0A/bXmM4AEmuuICLdgMuBc/lugah32xrPMQOYARAXF0dycvLp5m50+fn5fpmrWjRwez/oLMG8s7OMa578Dz8dFUqwn3dQ5u/7tSbL6oz6sqoqS/aX88bWUsoVukQIl/UN5gc9YG/KavY2XdRmtV+rOVkgvH261G6/+Dtwv6pWiHxndV+2rZqpOgeYA5CQkKBJSUkNT+qw5ORk/DFXbUlJEPbqp7y+tZTXdofz3I1jCQ9x8i1yeprLfgXL6pSTZS0pr+B/PkjlrS37SRoYw/2TBzGocxS1PmuaTHPar9Wc/N+fAfSoMd0dyKy1TgIwz/MPFg1cIiLlPm5rHHB+r2BGDh3E/e9u4rrnv+FlO4FnmqGsvGJmvr6W9fuOM2tSP+67YACBfn5E7I+cLBCrgf4i0hs4AEwDrqu5gqr2rn4sIq8AH6vqByISVN+2xjlXJ/SgbZtg7n5zPVfNXs5rtyXSrX0bt2MZ45PUzFxue2UNecVlzL5hDJOHdXE7UrPl2JlIVS0HZlF1ddJWYL6qporITBGZeSrbOpXVfN9FQzvzr1vHc/hECVc9u5zth064HcmYen2+NYurZ69ABN6ZeaYVh9Pk6KUqqrpQVQeoal9V/ZNn3mxVne1l3ZtV9Z2TbWuaVmKfTsy/8wwqKpWrnl3OlzuOuB3JmDq9smw3d7y2hr4xkXx411kM6WqXr54uu5bRnNTgLm354K6z6N4xnFtfWW13Xxu/o6r8dfF2fv/RFs4fHMdbd04gtm2Y27FaBCsQpl5d27fhnZlnkDQght99mMrji7e5HckYACpV+e0HKTy9JI3p43vw7A3+feVdc2MFwvgkIjSIOTclMG1cD55Zssuam4zryisqeXZjCW98s4+7JvXlz5cPtyuVGpkVCOOzwADh91OG0j82kv/3zkZyC23wIeOe//1kK6sPVfDbSwbzq4sGuXZ/Q0tmBcI0SFhwIE9cM4qc/FIeWpDidhzTSr2ybDevLN/D5Pgg7pjYx+04LZYVCNNgw7u34+5z+/PBhkwWbrbBh0zT+mJbFg9/vIULhsRxzUC7idNJViDMKfnppL6M6N6O376/may8YrfjmFZiZ9YJ7n5jPUO6tuXJaaMIsGYlR1mBMKckODCAJ64ZRXFZJb+Yv5HKSusm3DirpLyCe+ZtICw4kBduGmdXKzUBKxDmlPWLjeShS4ewNC2bOV+nux3HtHBPfLqDLQfzeOzKEXRuZ/c5NAUrEOa0XDuuB5cM78xfF29n4/7jbscxLdTK9BzmfJXO9PE9OH9InNtxWg0rEOa0iAiPXD6CuLZh/GzeevJLyt2OZFqYvOIyfjF/I706hvPgD4e4HadVsQJhTlu78GD+Pm0U+48W8ov5G+x8hGlUjyzcxqG8Yp64dhQRoXbeoSlZgTCNYlx8R35zyWAWp2bxzJI0t+OYFiLlQC7zVu/j5jPjGdOzg9txWh0rEKbR3HZ2by4f3Y2/fUXuL+0AABS2SURBVLqDz7ZkuR3HNHOqyh8+SqVjeAg/O6+/23FaJSsQptGICI9cMZzh3dpx71sbSDtsY0iYU/fRpoOs3nOMX140kHZtgt2O0ypZgTCNKiw4kOduHEtoUAC/eHuTnY8wp6SwtJxHFm5laNe2XJPQo/4NjCOsQJhG17V9G359yWA27j/Oe+sPuB3HNEOzk3dxMLeYhy4daj20usjRAiEik0Vku4ikicgDXpZPFZFNIrJBRNaIyNk1lu0Rkc3Vy5zMaRrfFaO7MbJHex5btM0ufTUNknIgl2e/3MWUkV0Z37uj23FaNccKhIgEAs8AFwNDgOkiUvsi5s+Bkao6CrgVeKHW8kmqOkpVE5zKaZwRECD8YcpQjpwo4akvdrodxzQThaXl/OzN9XSKCOUPU4a6HafVc/IIYjyQpqrpqloKzAOm1lxBVfNVtbqROgKwBusWZFSP9lw1tjsvLd3N7uwCt+OYZuCPH29hd04BT1w7kg4R1lOr2+S/n8+N/MQiVwGTVfV2z/SNQKKqzqq13uXAI0As8ENVXeGZvxs4RlXReE5V59TxOjOAGQBxcXFj582b58jfczry8/OJjIx0O4ZPGjvr8ZJKHviqiIEdA7l3TGijDurSmverk9zKuvpQOc9sKOGS3sE+d+Nt+/X0TZo0aW2drTSq6sgPcDXwQo3pG4GnTrL+ROCzGtNdPb9jgY3AxPpec+zYseqPlixZ4nYEnzmRdc6Xu7TX/R/rJ5syG/V5W/t+dYobWfdk5+uI3y/WS5/6WkvKKnzezvbr6QPWaB2fqU42MWUANa9P6w5k1rWyqn4F9BWRaM90puf3YeB9qpqsTDN0y1nxDOvWlocWpJJbZMOUmu/KLSzjlldWIwL/mDaakCC7uNJfOPkvsRroLyK9RSQEmAYsqLmCiPQTT5uDiIwBQoAcEYkQkSjP/AjgQsDGt2ymggIDePSKERwtKOXRf29zO47xI6Xllcx8fS37jxby3A1jiY+OcDuSqcGxAqGq5cAsYDGwFZivqqkiMlNEZnpWuxJIEZENVF3xdK3nkCcOWCoiG4FVwCequsiprMZ5w7q147aze/Pmqn18k57jdhzjB1SVBz/YzIr0HB69YgSJfTq5HcnU4mjXiKq6EFhYa97sGo8fAx7zsl06MNLJbKbp3Xf+AP6dcpBfv7+ZhT87h7DgQLcjGZeoKn9euJX5azL42bn9uHJsd7cjGS+ssc80mTYhgTxy+QjSjxTw0IepbscxLimvqOSXb2/i+a93c9MZvbjvggFuRzJ1sAJhmtTZ/aOZNakfb63Zz/zV+92OY5pYcVkFd/5rLe+uy+C+8wfwhylDG/XSZ9O4rECYJnffBQM4q18nfvdhCqmZuW7HMU1EVbn7zfV8sf0wf7xsGPec39+Kg5+zAmGaXGCA8OS00XQID+Enr68jt9AufW0N3l6bwadbsvjNxYO5cUIvt+MYH1iBMK6IjgzlmetHk3m8iJteXmVFooXLOFbIwx9tIbF3R247u7fbcYyPrEAY14zt1ZF/Xj+GrZl5TH9+JTn5JW5HckVJeQXLd2Uz95u9/O/HW/jN+5s5nFfsdqxGU1mp/OrtTagqf716JAHWfXezYSOAG1ddOLQzz/84gRmvrWHanJXMvT2R2LZhbsdqMjn5Jfz45VWkHMgDIDQoAAWWp2Xz+u2JdO8Q7m7ARvDaij2eex2G06Nj8/97WhM7gjCu+8GAGF65ZTwHjhdxzXMryDhW6HakJnEot5hrnlvBzqx8/nb1SJY9cC5bH57MvBkTOFpQyjWzV5B+JN/tmKfl861Z/HnhNiYNjOHacTYyXHNjBcL4hTP6duL12xPJ8XwwtvTuwfdkF3DV7OVk5ZXw6q3juXJsd7q1b0NAgDCmZwfenDGBkvJKrnluRbMd2/uLbVn85PV1DOoSxd+njbYrlpohKxDGb4zp2YE375hAcXklV89ewbZDeW5HcsSB40VMm7OSgpJy3rgjkQleupgY2rUdb915BgB3v7mB0vLKpo55Wr7YlsXMf1UVh3/dlki7NsFuRzKnwAqE8SvDurVj/p0TCAyAaXNWknKgZd0ncayglJte/IaC0nLeuGMCI7q3r3PdfrGR/Pny4Ww9mMfTS9KaMGXDVVYqG/cf55klaVz3/EpmvLaWgZ2j+NetVhyaMysQxu/0i43i7TvPJCIkiOueX8mG/cfdjtQoikoruO3V1ew/VsTzNyUwuEvbere5cGhnrhjdjWeWpLE5wz+LZcqBXK6cvZypzyzj8cXbOVZYxm1n9+b12xJpF27FoTmzAmH8Us9O4bx15wTah4dwwwvfsGbPUbcjnZaySuXuN9exfv9xnrx2lNdmpbo8dOlQoiND+MXbGygpr3AwZcPkFpXx0IcpTHl6KfuPFvKny4ex+rfn8+97zuHXlwy24tAC2GWuxm917xDO/DvP4LrnV3LTS6t4/fZExvTs4GqmotIKPtuaxdc7jxAeEkR0ZAidIkMZ07MDA+IivZ6Izcor5tFvitmVW8gfLxvGxcO7NOg124UH8+iVI7jl5dU8+dlO/t/kQY3155yyRSmH+N2HKeTkl3DjhF78/MKB1pTUAlmBMH6tc7sw5t05gatnr+C2V1bz7k/OpE9M04/rm3IglxeX7mZx6iEKSytoHx5MRaVyorj823X6xkTww+FdOLt/DD07hhMbFcq6fcf4ydx1nCisZPYNY5g8rGHFodqkgbFcOaY7z3+dztUJPejt0sA6R06U8NCCFBZuPsSQLm15+eZxDOvWzpUsxnlWIIzfi40K49VbxnPls8v58cureO8nZxETFdokr52VV8xfFm3nvfUZRIYGMWVkV6aM6kpi704EBggl5RUczisheccRFm46yNNL0vjHF1UnlEMCA6hQpWfHcO4dGXDKxaHa/RcPZFHKQf70yVZe+LH3Meadoqq8vSaDPy3cSlFpBb+6aCAzJvYhONBaqVsyKxCmWYiPjuDFm8cxfc5Kbn1lNfNmTHD09YpKK3j+63SeTd5FRaUy45w+3HVuP9qGfbcZJTQokB4dw7lxQi9unNCLIydKSM3MZf+xom9v+PtpUj/Wf7PstDPFRoUx69z+PLZoG1/vPMI5/WNO+zl9setIPr99fzMr048yLr4Dj1wxnH6xUU3y2sZdjhYIEZkMPAkEAi+o6qO1lk8F/ghUAuXAvaq61JdtTeszqkd7nrl+NHe8tpY7XlvDzX200V9DVVmwMZPH/r2NzNxiLh7WmV9fPJienXzrIiImKpSkgbGNnqvarWfHM2/1Ph7+aAv/vuccghz+Br9gYya/nL+RsOAAHrliONcm9LC+lFoRx95dIhJI1TjTFwNDgOkiMqTWap8DI1V1FHAr8EIDtjWt0LmD4vjr1SNYkZ7DU+tLGvWqns0ZuVz57HLumbeBDhEhvDVjAs/eMNbn4tAUQoMC+c0lg9l5OJ+53+xz9LXeWZvBvfPWM6pnez77xQ+YPr6nFYdWxsmvH+OBNFVNV9VSYB4wteYKqpqvqtVfAyMA9XVb03pdPro7j14xnM3ZFdw1dz1lFad3l/HxwlJ++/5mpjyzlH1HC/nLlSNYMOtsEhtwKWpTunBIHGf168RfF29nWVq2I6/xxjf7+NU7GzmzbzSv3jKe2KjW04Gi+S/57+dzIz+xyFXAZFW93TN9I5CoqrNqrXc58AgQC/xQVVf4uq1n2QxgBkBcXNzYefPmOfL3nI78/HwiI5v+yptT0ZyyLtyZz/xdwujYQGaMCKVNUMO+3aoqSw+U89b2UgrL4byeQVzWL4SI4Mb/ltzY+zW7qJIn1hZzqECZPjCE83sFNUpfR+WVyrtbC/j3fmFETCCzRoUSEui/Rw3N6f3qr1knTZq0VlW9XvXg5DkIb++q71UjVX0feF9EJlJ1PuJ8X7f1bD8HmAOQkJCgSUlJp5rXMcnJyfhjLm+aU1ZIZtiweH6/IJW/bhSeu3GszydP9+YU8Jv3N7MsLYeEXh3442XDfLqz+ZSTOrBfJ59bzn1vbWDulixKImJ54OJBREee+tVd6/Yd44F3N7EjS7h8dDcevXI4oUGBjZi48TWn92tzylrNyQKRAdTs37c7kFnXyqr6lYj0FZHohm5rWq+bzoinX2wkP3tzPVOeXsYjVwxnysiudX6bLi6r4MWlu3nqi50EBQTwv5cN47pm2rYeGRrEczeM5e+f7+Qfn+/kg/UHOG9wLNck9CAhviNtw/57VFFcVsHenEK2Z50g5UAumzNy2ZF1gtCgADpFhhIRGsg3u4/SuW0Y944J5d5rRrn81xl/4GSBWA30F5HewAFgGnBdzRVEpB+wS1VVRMYAIUAOcLy+bY2pdmbfaD6++xx+Onct98zbwP99uoNrx/XkyrHdvm07V1UWp2bxp4Vb2H+0iMlDO/P7KUPp3K55t60HBAg/v2AAU0Z2Yf6aDN5bl8Hi1CwA2gQH0rldGJWq7D9aSKXnGDwkMIBBXaI4f3AcZZWVHC0o5VhBKTefGc/PLxjA2pWnf0muaRkcKxCqWi4is4DFVF2q+pKqporITM/y2cCVwE0iUgYUAdd6Tlp73daprKb569wujLfuPIOPNmYyb9V+Hlu0jb8s3kZkSBBtQgIJChAyc4sZEBfJ3NsTOatftNuRG1W/2Ch+c8lgfnXRQJbuzCbtcD6H8oo5lFsMAlNHdaNvTAT9YiPpHxtFSJDd4Gbq5+h9EKq6EFhYa97sGo8fAx7zdVtjTiY4MIArxnTnijHd2XUkn4WbDnK0sJSi0gqKyipIiO/I9HE9HL93wE3BgQFMGhTLpEHO3YthWg+7k9q0SH1jIrn7vP5uxzCmWWu5X6WMMcacFisQxhhjvLICYYwxxisrEMYYY7yyAmGMMcYrKxDGGGO8sgJhjDHGKysQxhhjvHKsu283iMgRYK/bObyIBpzpuL/xWVZnWFZnWNbT10tVvY5f26IKhL8SkTV19bfubyyrMyyrMyyrs6yJyRhjjFdWIIwxxnhlBaJpzHE7QANYVmdYVmdYVgfZOQhjjDFe2RGEMcYYr6xAGGOM8coKhINE5C0R2eD52SMiGzzz40WkqMay2fU9VxNk/b2IHKiR6ZIay34tImkisl1ELnIzpyfP4yKyTUQ2icj7ItLeM98f9+tkz35LE5EH3M5Tk4j0EJElIrJVRFJF5B7P/DrfC27y/B/a7Mm0xjOvo4h8KiI7Pb87+EHOgTX23QYRyRORe/11v56MnYNoIiLyNyBXVR8WkXjgY1Ud5m6q/xKR3wP5qvrXWvOHAG8C44GuwGfAAFWtaPKQ/810IfCFZ9zzxwBU9X5/268iEgjsAC4AMoDVwHRV3eJqMA8R6QJ0UdV1IhIFrAUuA67By3vBbSKyB0hQ1ewa8/4CHFXVRz0FuIOq3u9Wxto874EDQCJwC364X0/GjiCagIgIVf/p3nQ7yymYCsxT1RJV3Q2kUVUsXKOq/1HVcs/kSqC7m3lOYjyQpqrpqloKzKNqf/oFVT2oqus8j08AW4Fu7qZqsKnAq57Hr1JV4PzJecAuVfXHHh7qZQWiaZwDZKnqzhrzeovIehH5UkTOcStYLbM8zTYv1ThU7wbsr7FOBv71IXIr8O8a0/60X/19333Lc/Q1GvjGM8vbe8FtCvxHRNaKyAzPvDhVPQhVBQ+IdS2dd9P47hdDf9yvdbICcZpE5DMRSfHyU/Ob4nS++yY5CPRU1dHAz4E3RKSty1mfBfoCozz5/la9mZencrxd0pf9KiK/BcqBuZ5ZruzXk3Bl3zWUiEQC7wL3qmoedb8X3HaWqo4BLgbuEpGJbgc6GREJAaYAb3tm+et+rVOQ2wGaO1U9/2TLRSQIuAIYW2ObEqDE83itiOwCBgBrHIxab9ZqIvI88LFnMgPoUWNxdyCzkaN9jw/79cfAj4Dz1HMiza39ehKu7LuGEJFgqorDXFV9D0BVs2osr/lecJWqZnp+HxaR96lqwssSkS6qetBzTuWwqyG/62JgXfX+9Nf9ejJ2BOG884FtqppRPUNEYjwnrxCRPkB/IN2lfNWZutSYvBxI8TxeAEwTkVAR6U1V1lVNna8mEZkM3A9MUdXCGvP9bb+uBvqLSG/Pt8lpVO1Pv+A5N/YisFVVn6gxv673gmtEJMJzIh0RiQAupCrXAuDHntV+DHzoTkKvvtNy4I/7tT52BOG82m2QABOBh0WkHKgAZqrq0SZP9l1/EZFRVDWB7AHuBFDVVBGZD2yhqjnnLjevYPJ4GggFPq36jGOlqs7Ez/ar5yqrWcBiIBB4SVVT3crjxVnAjcBm8VyCDfwGmO7tveCyOOB9z793EPCGqi4SkdXAfBG5DdgHXO1ixm+JSDhVV6/V3Hde/4/5M7vM1RhjjFfWxGSMMcYrKxDGGGO8sgJhjDHGKysQxhhjvLICYYwxxisrEMZ4ISL5DVg3SUTOrDE9U0Ru8jy+WUS6nsLr7xGR6IZuZ0xjsvsgjDl9SUA+sBxAVWt2M34zVTdE+dUd1Mb4wgqEMT4SkUuBB4EQIAe4HmgDzAQqROQG4G6qevDMp+pmqARgrogUAWdQ1WNqgqpmi0gC8FdVTRKRTlTdUBlD1Z3qUuN1bwB+5nndb4Cf+sHNiqYVsCYmY3y3FJjg6QxwHvD/VHUPMBv4P1UdpapfV6+squ9Q1Q/U9Z5lRSd57oeApZ7nXgD0BBCRwcC1VHVUN4qqO8Svb/w/zZjvsyMIY3zXHXjL06dOCLC7EZ97IlWdOqKqn4jIMc/886jq6HG1p5uJNvhXh3SmBbMCYYzvngKeUNUFIpIE/P4UnqOc/x65h9Va5q3fGwFeVdVfn8JrGXNarInJGN+1o2r4SPhvD6IAJ4CoOrapvWwP/+36/coa87/C03QkIhcD1YPJfA5cJSKxnmUdRaTXKeY3pkGsQBjjXbiIZNT4+TlVRwxvi8jXQHaNdT8CLpeqgehrj2L3CjDbs6wN8AfgSc9z1DzR/Adgooiso6or630AnvGrH6RqJLVNwKdAzW6jjXGM9eZqjDHGKzuCMMYY45UVCGOMMV5ZgTDGGOOVFQhjjDFeWYEwxhjjlRUIY4wxXlmBMMYY49X/B6YCPfEWKCjvAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print( 'The annual, global mean planetary albedo is %0.3f' %albedo_ncep_global)\n",
    "fig,ax = plt.subplots()\n",
    "ax.plot(lat_ncep, albedo_ncep)\n",
    "ax.grid();\n",
    "ax.set_xlabel('Latitude')\n",
    "ax.set_ylabel('Albedo');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**The albedo increases markedly toward the poles.**\n",
    "\n",
    "There are several reasons for this:\n",
    "\n",
    "- surface snow and ice increase toward the poles\n",
    "- Cloudiness is an important (but complicated) factor.\n",
    "- Albedo increases with solar zenith angle (the angle at which the direct solar beam strikes a surface)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Approximating the observed albedo with a Legendre polynomial\n",
    "\n",
    "Like temperature and insolation, this can be approximated by a smooth function that increases with latitude:\n",
    "\n",
    "$$ \\alpha(\\phi) \\approx \\alpha_0 + \\alpha_2 P_2(\\sin\\phi) $$\n",
    "\n",
    "where $P_2$ is the 2nd Legendre polynomial (see above).\n",
    "\n",
    "In effect we are using a truncated series expansion of the full meridional structure of $\\alpha$. $a_0$ is the global average, and $a_2$ is proportional to the equator-to-pole gradient in $\\alpha$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We will set\n",
    "\n",
    "$$ \\alpha_0 = 0.354, ~~~ \\alpha_2 = 0.25 $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Add a new curve to the previous figure\n",
    "a0 = albedo_ncep_global\n",
    "a2 = 0.25\n",
    "ax.plot(lat_ncep, a0 + a2 * legendre.P2(np.sin(np.deg2rad(lat_ncep))))\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Of course we are not fitting all the details of the observed albedo curve. But we do get the correct global mean a reasonable representation of the equator-to-pole gradient in albedo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "____________\n",
    "<a id='section6'></a>\n",
    "\n",
    "## 6. The annual-mean EBM\n",
    "____________\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Suppose we take the **annual mean of the planetary energy budget**.\n",
    "\n",
    "If the albedo is fixed, then the average is pretty simple. Our EBM equation is purely linear, so the change over one year is just\n",
    "\n",
    "$$ C \\frac{\\Delta \\overline{T_s}}{\\text{1 year}} = \\left(1-\\alpha(\\phi) \\right) ~ \\overline{Q}(\\phi) - \\left( A + B~\\overline{T_s} \\right) + \\frac{D}{\\cos⁡\\phi } \\frac{\\partial }{\\partial \\phi} \\left(   \\cos⁡\\phi  ~ \\frac{\\partial \\overline{T_s}}{\\partial \\phi} \\right) $$\n",
    "\n",
    "where $\\overline{T_s}(\\phi)$ is the annual mean surface temperature, and $\\overline{Q}(\\phi)$ is the annual mean insolation (both functions of latitude).\n",
    "\n",
    "Notice that once we average over the seasonal cycle, there are no time-dependent forcing terms. The temperature will just evolve toward a steady equilibrium."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The equilibrium temperature is then the solution of this Ordinary Differential Equation (setting $\\Delta \\overline{T_s} = 0$ above):\n",
    "\n",
    "$$ 0 = \\left(1-\\alpha(\\phi) \\right) ~ \\overline{Q}(\\phi) - \\left( A + B~\\overline{T_s} \\right) + \\frac{D}{\\cos⁡\\phi } \\frac{d }{d \\phi} \\left(   \\cos⁡\\phi  ~ \\frac{d \\overline{T_s}}{d \\phi} \\right) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "You will often see this equation written in terms of the independent variable\n",
    "\n",
    "$$ x = \\sin\\phi $$\n",
    "\n",
    "which is 0 at the equator and $\\pm1$ at the poles. Substituting this for $\\phi$, noting that $dx = \\cos\\phi~ d\\phi$ and rearranging a bit gives\n",
    "\n",
    "$$  \\frac{D}{B} \\frac{d }{d x} \\left(   (1-x^2)  ~ \\frac{d \\overline{T_s}}{d x} \\right) - \\overline{T_s} = -\\frac{\\left(1-\\alpha(x) \\right) ~ \\overline{Q}(x) - A}{B}  $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "This is actually a 2nd order ODE, and actually a 2-point Boundary Value Problem for the temperature $T(x)$, where the boundary conditions are no-flux at the boundaries (usually the poles).\n",
    "\n",
    "This form can be convenient for analytical solutions. As we will see, the non-dimensional number $D/B$ is a very important measure of the efficiency of heat transport in the climate system.  We will return to this later."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Numerical solutions of the time-dependent EBM\n",
    "\n",
    "We will leave the time derivative in our model, because this is the most convenient way to find the equilibrium solution!\n",
    "\n",
    "There is code available in `climlab` to solve the diffusive EBM."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Animating the adjustment of annual mean EBM to equilibrium\n",
    "\n",
    "Before looking at the details of how to set up an EBM in `climlab`, let's look at an animation of the adjustment of the model (its temperature and energy budget) from an **isothermal initial condition**.\n",
    "\n",
    "For reference, all the code necessary to generate the animation is here in the notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "#  Some imports needed to make and display animations\n",
    "from IPython.display import HTML\n",
    "from matplotlib import animation\n",
    "\n",
    "def setup_figure():\n",
    "    templimits = -20,32\n",
    "    radlimits = -340, 340\n",
    "    htlimits = -6,6\n",
    "    latlimits = -90,90\n",
    "    lat_ticks = np.arange(-90,90,30)\n",
    "\n",
    "    fig, axes = plt.subplots(3,1,figsize=(8,10))\n",
    "    axes[0].set_ylabel('Temperature (deg C)')\n",
    "    axes[0].set_ylim(templimits)\n",
    "    axes[1].set_ylabel('Energy budget (W m$^{-2}$)')\n",
    "    axes[1].set_ylim(radlimits)\n",
    "    axes[2].set_ylabel('Heat transport (PW)')\n",
    "    axes[2].set_ylim(htlimits)\n",
    "    axes[2].set_xlabel('Latitude')\n",
    "    for ax in axes: ax.set_xlim(latlimits); ax.set_xticks(lat_ticks); ax.grid()\n",
    "    fig.suptitle('Diffusive energy balance model with annual-mean insolation', fontsize=14)\n",
    "    return fig, axes\n",
    "\n",
    "def initial_figure(model):\n",
    "    #  Make figure and axes\n",
    "    fig, axes = setup_figure()\n",
    "    # plot initial data\n",
    "    lines = []\n",
    "    lines.append(axes[0].plot(model.lat, model.Ts)[0])\n",
    "    lines.append(axes[1].plot(model.lat, model.ASR, 'k--', label='SW')[0])\n",
    "    lines.append(axes[1].plot(model.lat, -model.OLR, 'r--', label='LW')[0])\n",
    "    lines.append(axes[1].plot(model.lat, model.net_radiation, 'c-', label='net rad')[0])\n",
    "    lines.append(axes[1].plot(model.lat, model.heat_transport_convergence, 'g--', label='dyn')[0])\n",
    "    lines.append(axes[1].plot(model.lat, \n",
    "            model.net_radiation+model.heat_transport_convergence, 'b-', label='total')[0])\n",
    "    axes[1].legend(loc='upper right')\n",
    "    lines.append(axes[2].plot(model.lat_bounds, model.heat_transport)[0])\n",
    "    lines.append(axes[0].text(60, 25, 'Day 0'))\n",
    "    return fig, axes, lines\n",
    "\n",
    "def animate(day, model, lines):\n",
    "    model.step_forward()\n",
    "    #  The rest of this is just updating the plot\n",
    "    lines[0].set_ydata(model.Ts)\n",
    "    lines[1].set_ydata(model.ASR)\n",
    "    lines[2].set_ydata(-model.OLR)\n",
    "    lines[3].set_ydata(model.net_radiation)\n",
    "    lines[4].set_ydata(model.heat_transport_convergence)\n",
    "    lines[5].set_ydata(model.net_radiation+model.heat_transport_convergence)\n",
    "    lines[6].set_ydata(model.heat_transport)\n",
    "    lines[-1].set_text('Day {}'.format(int(model.time['days_elapsed'])))\n",
    "    return lines   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "#  A model starting from isothermal initial conditions\n",
    "e = climlab.EBM_annual()\n",
    "e.Ts[:] = 15.  # in degrees Celsius\n",
    "e.compute_diagnostics()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x720 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#  Plot initial data\n",
    "fig, axes, lines = initial_figure(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "ani = animation.FuncAnimation(fig, animate, frames=np.arange(1, 100), fargs=(e, lines))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HTML(ani.to_html5_video())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "###  Example EBM using `climlab`\n",
    "\n",
    "Here is a simple example using the parameter values we just discussed.\n",
    "\n",
    "For simplicity, this model will use the **annual mean insolation**, so the forcing is steady in time.\n",
    "\n",
    "We haven't yet selected an appropriate value for the diffusivity $D$. Let's just try something and see what happens:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "climlab Process of type <class 'climlab.model.ebm.EBM_annual'>. \n",
      "State variables and domain shapes: \n",
      "  Ts: (90, 1) \n",
      "The subprocess tree: \n",
      "Untitled: <class 'climlab.model.ebm.EBM_annual'>\n",
      "   LW: <class 'climlab.radiation.aplusbt.AplusBT'>\n",
      "   insolation: <class 'climlab.radiation.insolation.AnnualMeanInsolation'>\n",
      "   albedo: <class 'climlab.surface.albedo.P2Albedo'>\n",
      "   SW: <class 'climlab.radiation.absorbed_shorwave.SimpleAbsorbedShortwave'>\n",
      "   diffusion: <class 'climlab.dynamics.meridional_heat_diffusion.MeridionalHeatDiffusion'>\n",
      "\n"
     ]
    }
   ],
   "source": [
    "D = 0.1\n",
    "model = climlab.EBM_annual(A=210, B=2, D=D, a0=0.354, a2=0.25)\n",
    "print( model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'timestep': 350632.51200000005,\n",
       " 'S0': 1365.2,\n",
       " 's2': -0.48,\n",
       " 'A': 210,\n",
       " 'B': 2,\n",
       " 'D': 0.1,\n",
       " 'water_depth': 10.0,\n",
       " 'a0': 0.354,\n",
       " 'a2': 0.25}"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.param"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Integrating for 900 steps, 3652.4220000000005 days, or 10 years.\n",
      "Total elapsed time is 9.999999999999863 years.\n"
     ]
    }
   ],
   "source": [
    "model.integrate_years(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1,2, figsize=(12,4))\n",
    "ax = axes[0]\n",
    "ax.plot(model.lat, model.Ts, label=('D = %0.1f' %D))\n",
    "ax.plot(lat_ncep, Ts_ncep_annual, label='obs')\n",
    "ax.set_ylabel('Temperature (degC)')\n",
    "ax = axes[1]\n",
    "energy_in = np.squeeze(model.ASR - model.OLR)\n",
    "ax.plot(model.lat, energy_in, label=('D = %0.1f' %D))\n",
    "ax.plot(lat_ncep, ASR_ncep_annual - OLR_ncep_annual, label='obs')\n",
    "ax.set_ylabel('Net downwelling radiation at TOA (W m$^{-2}$)')\n",
    "for ax in axes:\n",
    "    ax.set_xlabel('Latitude'); ax.legend(); ax.grid();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def inferred_heat_transport( energy_in, lat_deg ):\n",
    "    '''Returns the inferred heat transport (in PW) by integrating the net energy imbalance from pole to pole.'''\n",
    "    from scipy import integrate\n",
    "    from climlab import constants as const\n",
    "    lat_rad = np.deg2rad( lat_deg )\n",
    "    return ( 1E-15 * 2 * np.math.pi * const.a**2 * \n",
    "            integrate.cumtrapz( np.cos(lat_rad)*energy_in,\n",
    "            x=lat_rad, initial=0. ) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Latitude')"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(model.lat, inferred_heat_transport(energy_in, model.lat), label=('D = %0.1f' %D))\n",
    "ax.set_ylabel('Heat transport (PW)')\n",
    "ax.legend(); ax.grid()\n",
    "ax.set_xlabel('Latitude')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The upshot: compared to observations, this model has a much too large equator-to-pole temperature gradient, and not enough poleward heat transport!\n",
    "\n",
    "Apparently we need to increase the diffusivity to get a better fit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "____________\n",
    "<a id='section7'></a>\n",
    "\n",
    "## 7. Effects of diffusivity in the annual mean EBM\n",
    "____________\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### In-class investigation:\n",
    "\n",
    "- Solve the annual-mean EBM (integrate out to equilibrium) over a range of different diffusivity parameters.\n",
    "- Make three plots:\n",
    "    - Global-mean temperature as a function of $D$\n",
    "    - Equator-to-pole temperature difference $\\Delta T$ as a function of $D$\n",
    "    - Maximum poleward heat transport $\\mathcal{H}_{max}$ as a function of $D$\n",
    "- Choose a value of $D$ that gives a reasonable approximation to observations:\n",
    "    - $\\Delta T \\approx 45$ ºC\n",
    "    - $\\mathcal{H}_{max} \\approx 5.5$ PW"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### One possible way to do this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "Darray = np.arange(0., 2.05, 0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "model_list = []\n",
    "Tmean_list = []\n",
    "deltaT_list = []\n",
    "Hmax_list = []\n",
    "for D in Darray:\n",
    "    ebm = climlab.EBM_annual(A=210, B=2, a0=0.354, a2=0.25, D=D)\n",
    "    ebm.integrate_years(20., verbose=False)\n",
    "    Tmean = ebm.global_mean_temperature()\n",
    "    deltaT = np.max(ebm.Ts) - np.min(ebm.Ts)\n",
    "    energy_in = np.squeeze(ebm.ASR - ebm.OLR)\n",
    "    Htrans = inferred_heat_transport(energy_in, ebm.lat)\n",
    "    Hmax = np.max(Htrans)\n",
    "    model_list.append(ebm)\n",
    "    Tmean_list.append(Tmean)\n",
    "    deltaT_list.append(deltaT)\n",
    "    Hmax_list.append(Hmax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OaYuxY1r7IsZHfmtnYCVbp0d/LyJSAyutT4bt2Y9KvxDVccC4oISlHXZ7z/9EpJ6qLoqatDZbNsUS+W4ix4olFJ7Dou2OrUtskhNv/TJZafelZImcq1oSdXUlQlWXi8ibWHI/UVV/LMvMw0rSxmA/vpWqOq2Y6d4DbhKRA1T1uyKmWQdUKuVyPwK6iki7mATkHOwgW6aNh5XyzcaSzeg2t84g8dv2N+AMEdlBVdcDiEgH7F6muFR1OnCDiFxOYdF4UUYC54rI8VhiNaiE6cG2fdzlq+ovIvIedhPzgcDAUhTxTgjm2Q0rAYo4C9ueH5UiptIoKu5IlegfVHVNgpZVlDYiUldVZwOIyE5YRYFI0f50LLHdT1Xv2cZlRJKx6JNbY+yEEF1CHflnGu939Btb7zsnlSGGsdh9ZXur6tgyfA7sEqJiFTDuixretQzziLcNamD7eLTPsft4zmDLS5zdSrGMMdi/6d+DP0nbq7jvI1a89auA/eHaFqk6po0BrgOqq+oHxUxXGbsMvTmxEGuEdm+2TNzLss3A/uSUdtpIHFDyflRmQYnTh0Fp3RvYzebRSdqZWIWZiG5YqdGU4P1HQN8guZsVxFYeO25OCm6lKElZzqOJtr3LLu2+lCwtg+fimiV5DCtNe76sMy/Lj+5AEakZZ/jEoCi8LJ7Hanh9ICKDsaLrHbB/hZ2xm4lXAw9iCdT7InIndi26JvbDuDzY+aYCu4jIFViV37Wq+n3sAgPDsH+7/xGRG7EDUnfsvpnL4lyqKZaqbhKR24GhIvIsdnDfFyv9WF7sh8vuJaxG6jNirX7Xx0qqlkUmEJHqWKnL89i9UBuwbVWDwuvzRXkf+8fxNHZAir0vLJ6pwD9E5CysxtCKIDGMeBw76GygFA3HquoSEXkAGCAiq7DLHM2wyzifsPW9CduqqLhvwS65jxeRx7AkqQaWpDRQ1UT2UjAfeE9EbsMOUtdhtY/vAKtpIyK9gDdEZAesyHwR9i/6cCwhKKnxx/exUogRwe9sD6xU9Xe2vNXhp2C6C0VkSRDP9OD39RL2R+lGLIluj9WwLpUgWb8XeCwo2f0I+9dbF/vdDQ1KFOJ9drqIvADcEVzW+xq7nBcpJSrNfR2fYb/F/xORW7FtfBO2LatHLWusiHwC/Ds4zv2MneRK+nMDdpw6C/hYRB7EEuwqWBMt7VW1rCfy4r6PWD9iifRdIlKA/db6lXF5m6XqmKaq+SLyIjA6+M1/iX2f9YC/Adep6k/YCbgvMCyIpzFWUWNuzCwj9w71EpHh2HaYHPlDG8dU4CQRGYOV8P6hqsWVuJRqPyqt4I9zB+wYNxs7rw3AjsFTYia/JNj/v8IukV6MVeaJlCQ+iN3MPzaIbTlWC7Uxpf9DNRVoLyInY5dJF0USvhQoyzl8K2XYl4pTU0TaxBn+Z8x22Clquh2wBC2yPxbZEHBQ+vpJUeOLVVLNAoqv3alAzWC6UtfuDIbviNU2ibRrsgTbCW8jquordqljCFYMvx7boYdTWOuwCnaD5F/B8meVsD57YKVGcdtJK25diplnH+xAGWlT6AhKaCctGFbq2p3BuMuwk8ca7KBxcPRysHsj/o0Vv67EfqxfEVW7hjg186LGDQrGfRZn3Fafw4rT38ZqGilbtx1VHrvXbVRptmPwmXjtpP0fRbSTVlKMRSyjyLixm6aHYj+6yPLHEr8tvdgq2rOIqSFFnJp6kemwg+0vwX44CTgqTqxtsZuY/wr2r1nYibNt1DT5xKmtGow7E/uNrQ32i27Yn5XY/e4y7JLKRqJqM2K/04eD7bACeBm7UTZ2XxhGMTWVsBtmJwT7w0osuXiMYmr7Bp+LtJO2JPjcm9iJR4mqgVfc8rHEbhL2u/kFq3F7G1vXOt8NO5asoLCdtC7R2yNqe8fu6zWwk+XMYL9ZgF067xvnGLBvzGfjxRL3+yhi/Q7ETgCrsT+eA4N9K14NvK1q8BG/Bm+Jx7QiYulEnJqpxD/+lQuWE2k/b1nw+j6sVCQyXe9gu67BjmfHFPEd3Ir9bgtilxUnznZY0r82ev0TtB+VeGzCftdvUNj+5zzsHsboJnhuCz6zP9ZO2hosgbqD+O2kvR5sw7UU307aVk0UYX8oPg72IS3uey7iuyz1vhVnmrjn8GTsS0UsfxZF5zePxfzuo8etD/aDfxNzHKOYY3LUNEXua9GPSBVW5xJORI7FSvCO0XCKodOSiMzCfsDnljSt25qIXIvdN1hPo2rIOpdNglL2W7GmPMJqLcCFLKx70lwWE5GGWGOND2Lt9HiC5rZJcPllf6zJgk3Y5dZrsOZhPEFzzmU1T9JcMtyM1RD9DmvSwrlttQLrkeF67LLIXKwx21vDDMo551LBL3c655xzzqWhsjRm65xzzjnnUsSTNOecc865NOT3pCVJuXLltFKlxLUNuGnTJsqVS++cOt1jTPf4IP1jTPf4wGNMhHSPD9I/xnSPLxlWr16tqppbK51knqQlSaVKlVi1alXC5pefn0+nTp0SNr9kSPcY0z0+SP8Y0z0+8BgTId3jg/SPMd3jSwYRSXZPLTnHM17nnHPOuTTkSZpzzjnnXBryJM0555xzLg15kuacc845l4Y8SXPOOeecS0OepDnnnHPOpSFP0pxzzjnn0pAnac4555xzaciTNOecc865NJSTSZoIz4iwQIQpccZdI4KKUDNq2AARZogwXYTjUxutc84553JRTiZpwDDghNiBItQFjgV+jxrWHOgG7Bd85nERyqcmTOecc87lqpxM0lQZDyyJM+pBoD+gUcO6AC+psk6VmcAM4NDkR+mcc865XOYdrAdE6AzMVeU7kS1G7QVMiHo/JxjmXEL17duXOXPm5FynzM65JNiwAebNg7lzi36ceioMGhR2pK4YnqQBIlQGbgSOizc6zjCNMwwRuRS4FCAvL4/8/PxEhcjKlSsTOr9kSPcY0z2+/Px8CgoK0jrGdN+G4DEmQrrHB+kfYzLjk/XrqbhoERUXLqTiggWbX++4YAEVFy5kh0WL2OGvvxDd8lS1qUIF1tWsybqaNVlfty5LypfnzzTehs6TtIiGQH3YXIpWB/hGhEOxkrO6UdPWAf6INxNVHQIMAahSpYomskQkPz8/7UtY0j3GdI9v5513ZunSpWkdY7pvQ/AYEyHd44P0j3Gb49u40UrAfv8dZs/e8nnOHHu9cOHWn6teHerWhfr1oX172Gsve9Sps/l1uV13pZIIlYKP1AKabsc6uuTzJA1Q5XtsfwVAhFlAa1UWifAm8IIIDwB7Ao2AL0MJ1DnnXGZbsQJ++63w8fvvWz7++AMKCrb8TCQBq1sXWre2xKtOHXsfScJ22imc9XFJlZNJmggvAp2AmiLMAW5V5el406rygwivAFOBjUAvVQriTeuccy6HqcKSJTBzJrt99BF8/fXWCdlff235mR12KEzAjjzSnvfee8vnatXCWR8XupxM0lQ5u4Tx9WLe3wXclcyYnHPOZYClS2HWLJg5056jX8+cCStXAtZmE2AlXPvsY4927QpfRx61a0O5nGxowZVCTiZpzjnnXFwbNth9X7/+Gv8RWxJWtardB1a/vpWE1a8P9eoxcdEiWp9xBuy8M0i8+mfOlcyTNOecc7ll1Sr45Rd7zJhhj19/tfe//77lPWEVKlji1aABHHZYYUJWr54916gRNwlbmZ9v45zbDp6kOeecyz7Ll8PPPxcmYTNmFCZl8+ZtOW3NmtCwIbRtC927W0IWeey5J5T3TmZcODxJc845l5nWrLHE6+ef4aefCp9/+gnmz99y2j33hH33hRNOsOfIo2FDqz3pXBryJM0551z6UrXW8adNg+nTNz+3mTwZFiyw8RG1a0PjxnDSSfbcqJE9GjSAKlXCWwe3bUR2BNoC9YBKwELgG1R/CTOsVPIkzTnnXPjWrrUSsGnTtkrIWLWqcLpq1aBJE5a1aMGO7dtbEhZJyLypiuwg0g7oA5wCVACWAWuAXYCKiPyKNRz/JKorQoszBTxJc845lzorV1ryNXUq/PijPU+dajfub9pk04hY8xRNmljr+U2b2uumTWH33UGEH/PzqZ3GPQ64bSTyBtAaeAHrqnEiqmuixjcA2gNnA1cj0gPVsWGEmgqepDnnnEu8Vass+ZoyxR6RpOy33wqnqVDBSsFatbIb9ps1s0SsUSOoXDm82F2Y3gO6oro+7ljVX4FfgeGI7If1BJS1PElzzjm37davt8uUU6bA998XJmUzZxbeL7bjjpZ8tWsHl1wCzZtbQtawoSVqzkWo/l8Zpv0B+CF5wYTPkzTnnHMlU7V+JSdPhu++s+fJk+2esY0bbZry5e2yZOvW0LMn7L+/PRo08GYsXOmJDAM+BMahOjvkaELlSZpzzrktyPr1MGlSYTL23Xf2WLy4cKJ99oEWLaBzZ0vEWrSwS5cVK4YXuMsWjbB7zvIQmYklbJGkbX6xn8wynqQ551wuW74cvv3WkrJvvoFJk+jwww+FN/FXqmRJ2GmnwQEHQMuW9th553DjdtlLtR0ilbAKAp2AI4GeQHlEpgHjgA9R/U9oMaaIJ2nOOZcrFiywZCwqIWPGjMLxe+wBrVrxe8uW7NO5syVl++7rlypd6lmNzveCB4hUwZK244CLgCuArN8xPUlzzrlstGQJfP01fPUVTJxoz3PmFI5v0MBqVfbsCQcdZK933x2Amfn57OPNW7h0IFIOOBgrTeuEJWorgLdDjCplPElzzrlMt2KFlYxFErKJE627pIjGjaFDBzj4YEvIDjzQL1e61BNpArwcNaQBcAuqD8VM1wpLyo6iMCn7CHgd6IvqTymJNw14kuacc5mkoAB++AEmTLDHF19Y+2OR5i722QcOOcSaujjkEEvKPCFz6UB1OnAgACLlgbnAa3Gm/Br4DRiMJWUz4kyTEzxJc865dPbnn5aIRZKyr74q7CapZk047DDo1s2avWjdGnbbLdx4nSudo4FfUP0tzrhngY7A/UBXRPKxygKfo7oudSGGz5M055xLFxs3WoOwn3wCn35qSVmkhf68PLtv7MILLTFr08buKxMJN2bntk034MW4Y1QvAkCkLnbZ80gscdsdkS+BfCAf1XGpCDRMnqQ551xYVq60UrJIUvb55zYMYK+94PDD4aqrLCFr1cqaw3AufeWJyMSo90NUdchWU4nsAHQGBhQ7N2vIdkTwAJF6WM3OvsCN5EAOk/Ur6JxzaWP+fBg/nn1fegmuucbaJysosNKwFi2gRw/rOumII2DvvcOO1rmy2qiqrUsx3YnAN6VqmFakDoWlaZ2AesAarDQt63mS5pxzyTJvHnz0EeTn2/O0aQDsUbGilZINGGAJWZs2UL16uLE6lzpnU9SlTgCRsylMzBoAG4AvgOHYvWkTiuyAPct4kuacc4kyZ44lY5HE7OefbXi1apaMXXghdOzIJ8uX0/GYY0IN1blQiFQGjgUuK2aq4cBXWHMd44BPUV2bgujSjidpGWDDBliwwPvDcy7tLFoE48bB++/DBx8Utk1Wvbq1S3bZZdCxo7VLlld4uNX8/HDidS5sqquBXUuYqgaqq1IRTrrzJC0DHH88LFjQnDPPDDsS53Lc6tV2k/8HH1hiNmmStU9WrRp06gS9etlzy5belZJz2241ItcCpwIVgPeBgblYmuZJWgY45hi48cbqzJ4NdeuGHY1zOaSgwLpWev99e3z6KaxfDxUq2D1lAwfaD7R16y1Kypxz2+V64E7gA6ySwNVATeDSMIMKgx9VMkDXrnDjjfDqq9C3b9jROJfl5s+Hd9+Fd96B996zPjDBOhvv3duSsvbtoUqVcON0Lnv1BHqj+jgAIicAryNyGRrpWiM3eJKWARo1goYNVzJqVFVP0pxLtI0bra2yd96xxzff2PDateGUU+x+g6OPhlq1wo3TudyxD/BW1Pt3AQH2xLqSyhmepGWITp0W8PTTVZkzB+rUCTsa5zLcn38WJmVjx8LSpXYPWdu2cNddcMIJdrN/uXJhR+pcLtoBu8xpVBWR9UDO1aDzJC1DdOy4kKefbsDo0X7J07kyU4WpU+HNN+3xxRc2bI894PTTLSk79ljviNy59HE3Iquj3u8A3IrIss1DVK9KeVQp5klahqhbdw0HHACjRlzdclYAACAASURBVHmS5lypbNxoNTHfeMMSs19/teGHHGI3/J98st1n5n1fOpduxgMNY4Z9BkR3w5ET96Z5kpZBunaFm27CL3k6V5Tly9ktPx+GDoW334a//oKKFe2esv797R6zPfcMO0rnXHFUO4UdQrrwJC2DRJK0V1+FPn3Cjsa5NLF0Kfz3v1bM/O677Ld+Pey6K3TuDF262GXMqlXDjtI558rMk7QM0rixtZE5apQnaS7HLVlilzBHjbIb/zdssEYEe/ViUr16tOrVyxuTdS4TidwEPFiqHgdE2gG7oPrfpMcVkpysuiTCMyIsEGFK1LBBIkwTYbIIr4mwc9S4ASLMEGG6CMeHE7Xp2tXa05wzJ8wonAvBokXw9NN2k3/t2nDBBfDDD/aPZcIEmDULHniAZd7av3OZbF/gd0SGIHIyIrtvHiOyIyIHIXIVIl8CI4C/wgo0FXIySQOGASfEDBsL7K9KS+AnYACACM2BbsB+wWceFyG0M0DXrvb86qthReBcCi1fDsOHW1tlu+8OF19snZb/85/w1VcwcyYMGgSHHebNZTiXDVR7Ap2wigEjgbmIbERkDbAKmAj0AIYCzVD9JKRIUyInL3eqMl6EejHD3ot6OwH4e/C6C/CSKuuAmSLMAA4FPk9FrLGaNPFLni7LrV8PY8bA88/bJc21a6FBA7vxv2tXa7/Ma2Q6l71UvwcuQ+QKoCXWuG0lYBHwLaqLwgwvlXIySSuFC4GXg9d7YUlbxJxgWGi6doWbb4a5c2GvUCNxLkE2bYLPPrPE7JVX7J6zmjXhoouge3do08YTM+dyjeom4NvgkZM8SYshwo3ARuD5yKA4k8Vtn0VELiXoADYvL4/8/PyExbVy5crN89t770rAYdxzz8+ccUb69JARHWM6Svf4li5dSkFBQVrHmOhtWPm336g9diy133+fHefPp6BiRRa1a8f8Y47hr0MOQfPyYN06+Oij0GJMhnSPMd3jg/SPMd3jcxlCVXPyAVoPdErMsPNBPwetHDVsAOiAqPfvgrYtaf6VK1fWRBo3btwW71u0UD3iiIQuYrvFxphu0j2+jh076gEHHBB2GMVKyDZctkx1yBDVww5TBdVy5VSPP1515EjVFSvSI8YkS/cY0z0+1fSPMd3jSwZglabB+T2bHn6nbUCEE4DrgM6qRHdF8SbQTYSKItQHGgFfhhFjtK5drTH1uelTkOZc0VTh44+hZ0/riunSS2HFChg8GP74w+5BO/dcb8/MOeei5GSSJsKL2I3/TUSYI8JFwGPATsBYEb4V4UkAVX4AXgGmAmOAXqoUhBT6Zl7L02WEP/+Ee++Fpk2hQwfbYbt3tyYzpkyBq6+25jScc85tJSfvSVPl7DiDny5m+ruAu5IXUdk1bQotWlgtz6uyvotZl1E2brQumZ5+Gv73PygogCOOgAED7N9FlSphR+icywQitwD3o7o6Zngl4FpUB4YSVwrlZElatog0bPvHH2FH4hywcCHcfbc1l9GlC3zxhbVnNm1a4aVOT9Ccc6V3KxDvHojKwbis50laBuva1W718UueLlRffgk9ekCdOnDDDdCoke2Us2fbpc4mTcKO0DmXmYT4rSm0ApakOJZQ5OTlzmzRtCnsv79d8uzdO+xoXE5Zu9baM3vsMWv5v2pVuOQS+Mc/oHnzsKNzzmUykRVYcqbAr4hEJ2rlgR3B7hvPdp6kZbiuXeG22+yS5557hh2Ny3YV//zT7i0bOtT60mzWzBK1886DatXCDs85lx2uxErRngFuBJZFjVsPzEI1lF5/Us2TtAzXtSvceqtdXfLSNJc0X30FgwbRJnJtvUsXuPJKOPJI7wnAOZdYqsMRyQOqAG+gOifskMLi96RluGbNCi95OpdQqvDOO5aIHXoovPces886yzo1/89/4KijPEFzziWH6kbgPuzyZs7yJC0LRBq2nTcv7EhcVli/HkaMgJYt4W9/gxkzrNHZ2bP59dJLYe+9w47QOZcbJgAHhx1EmDxJywJey9MlxPLllow1bAjnn2/DRoyAX36xRmd32inc+JxzueYp4H5E+iLSHpGDtnjkAL8nLQs0awb77WeXPK+8MuxoXMb58094+GF44glYtswubz71FBx/vF/OdM6F6YXg+YE445QcuBTqSVqW6NoVbr/dLnnusUfY0biMMH8+3HefJWfr1sHf/w7XXgutW4cdmXPOAdQPO4Cw+eXOLOGXPF2pLVhgyVj9+vDQQ7bzTJsGL7/sCZpzLn2o/lbsIwd4kpYlmjcvvOTpXFyLFsF111ly9sADcMYZ8OOPMHy49RLgnHPJJrIzIqMRmYbIj4i0LWH6loiMQGQiIl8hMhyRFimKNnSepGWRs86C8eOthQTnNlu82BqgrVcPBg2CU0+FqVNh5Eho3Djs6JxzueVhYAyqTYEDgB+LnFKkM/ANUBd4BxgD7A18g8gpyQ81fJ6kZZGePe0+72eeCTsSlxaWLIEbb7Tk7N574ZRT4Icf4PnnvT9N51zqiVQDOgBPA6C6HtWlxXziTuAuVI9E9ebgcSRwdzAu63mSlkXq1oUTToBnn4WNG8OOxoVm3Tq7nNmwIdx9t7V19v338OKLVhXYOefC0QBYCDyLyCREhiJSpZjpGwMj4wwfCeTEP01P0rLMJZfA3Lnw7rthR+JSTtU6PW/WDP75T2jbFr77zioE7Ldf2NE557JfnohMjHpcGjseOAh4AtVWwCrg+mLmt4D4jdkeDMxPSMRpzpvgyDInnwy1aln/1yedFHY0LmU+/RSuuQYmTLCeAt57D449NuyonHO5ZaOqFldFfA4wB9UvgvejKT5Jewr4NyL7Ap9hbaMdAVwDDEpAvGnPS9KyTIUKdm/af/9rbZS6LDdjhrVvdsQR8PvvdkPiN994guacSz+qfwKzEYlcqjwamFrMJ+4EbgeuAD4APgQuB24F/pXESNOGJ2lZ6KKLoKDAWlZwWWrxYujXz9peGTMGBg6En36CCy6A8lnfCLdzLnP1Bp5HZDJwIMUlW6qK6oOo1gGqA9VRrYPqw6hqasINl1/uzEKNG0OHDnbJs39/79knq2zcCI8+aknZ8uVw8cXW1cTuu4cdmXPOlUz1W6BsrWaLNASaBa+novpr4gNLT16SlqUuvtiuhI0fH3YkLmE++wwOPtg6O2/TBiZPhn//2xM051x2EtkVkdeBn4HXg8fPiLyByK7hBpcanqRlqTPOgOrVrTTNZbjFi63abrt28Ndf8Npr8PbbXmPTOZfthgL7Au2BHYNHB6xPz6dCjCtlPEnLUpUrQ/fuMHq0ndddBlKFYcOgaVNr/O6aa6yngFNP9WvYzrlccDxwCaqforoxeHwKXBaMy3qepGWxiy+GtWvhhRfCjsSV2Q8/QMeOVhGgcWOrsTloEFStGnZkzjmXKguxttRirQYWpziWUHiSlsVatYKDDoKnnrJCGZf+diwogOuvhwMPtERt6FD4+GNr+8w553LLQOAhRPbaPMReDw7GZT2v3ZnlLr4Y/vEP+PpraF22+jQuxdouXkzv6dNhyhRr7O6++2C33cIOyznnwtIXqAfMQmRuMGwvYC1QC5GrNk+pmpX/ZD1Jy3LnnGM9BA0d6kla2lq2DPr04e4pU/ilYkX46CNrQ8U553Lb6LADCJsnaVmuenU480y7L23wYKhSXFe2LvU++MDuO5s7l5F7783D1asz0RM055wD1dvDDiFsfk9aDrj4YlixAkaNCjsSt9nq1dC7NxxzDFSqBJ99xtP167OxnP8knXMOAJHdENkt6n0LRO5E5OwQo0opPyPkgHbtoEkTbzMtbUyYYLU6HnsMrroKJk2Cww4LOyrnnEs3rwCnACBSExgPnAY8icg/Q4wrZTxJywEiVpr26afw449hR5PD1q+HG2+0rHntWrvU+fDD1qidc865WC2BCcHrvwMzUN0P6IG1lZb1PEnLET16QF4ePP102JHkqO+/h0MPhX/9y76MyZPhqKPCjso559JZJWBl8PoY4M3g9TdA3VAiSrGMStJEqChCfRGai+BtE5RBrVrQpQsMH24FOi5FNm2ypjRat4Z58+CNN6z3gOrVw47MOefS3c/A6YjUBY4D3guG1waWhhZVCqV9kibCTiJcIcJ4YBkwA5gC/CnCbBGeEuGQcKPMDBdfDIsWwZtvljytS4DFi+Gkk+C66+Dkk639s86dw47KOecyxe3AvcAsYAKqXwTDjwcmhRVUKqV1kiZCP+zLuRAYC3QBDgQaA22BW7FmRMaKMEaERqWc7zMiLBBhStSwXUQYK8LPwXONqHEDRJghwnSRzO0v7NhjoW5dr0CQEl98YZUDPvwQnnjCOlH1hmmdc670VP8D7A20Bk6IGvM+cHUoMaVYWidpwOFAR1UOUeUOVd5V5XtVZqjypSrPqHIBsDt2rbpjKec7jC2/cIDrgQ9UaQR8ELxHhOZAN2C/4DOPi1B+u9csBOXLw4UXwnvvwW+/hR1NllK1Wpvt20O5clZb4/LLvUN055zbFqrzUZ2E6qaoYV+gOi3EqFImrZM0VbqqFpZ2FTPdWlUeV6VUZUSqjAeWxAzuAgwPXg8HTo0a/pIq61SZiV1uPbRUK5CGLrjAnp99Ntw4stLKldbFQ+/ecNxx1im6d/PgnHPbTuQsRIYg8joib27xyAFpnaTFEuFEEd4SYaqI1ewQ4WIRjk7A7GurMg8geK4VDN8LmB013ZxgWEbaZx84/nh45hnYuDHsaLLI1KlwyCHwyitWg/PNN2GXXcKOyjnnMpfIIOA5rP/OpcDimEfWy5huoUToDjwJDAWOBioEo8oD/bFLlElZdJxhGndCkUuBSwHy8vLIz89PWBArV65M2PzatavJmDH7M3DgVI46akFC5gmJjTEZkhVfrfffp8ngwRRUqsTU++9naatWMH58meezdOlSCgoKcnIbJpLHuP3SPT5I/xjTPb4M0QM4G9Xc7cNTVTPiAfodaLfg9QrQBsHrA0Dnb8P86oFOiXo/HXSP4PUeoNOD1wNAB0RN9y5o25LmX7lyZU2kcePGJWxeBQWqzZurtmhhrxMlkTEmQ8LjW7tW9YorVEG1fXvVuXO3a3YdO3bUAw44IEHBJUe6f8eqHmMipHt8qukfY7rHlwzAKk3kuR8WKuyb0Hlm2COTLnc2Aj6PM3wlUC0B838TOD94fT7wRtTwbpE22oI4vkzA8kJTrhwMGGDtq771VtjRZKg5c6xywBNPwLXXWi3OPfcMOyrnnMsmQ4Bzww4iTBlzuRP4A2t6I7ZeYgfgl7LMSIQXgU5ATRHmYE153AO8IsJFwO9AVwBVfhDhFWAqsBHopUrBdqxHWujWDW65Be66C045xSsflsm331r7ZytWwGuvwamnlvwZ55xzZbUzcA4ixwKTgQ1bjFW9KoygUimTkrQhwCMiXBy8rytCe+A+4LayzEiVs4sYFbcCgip3AXeVZRnpLi/P2li9/HIrBDo6EVUvcsE778CZZ0KNGta8RosWYUfknHPZqjnwbfC6acy4uPeGZ5uMSdJUuU+E6lijtjsC44B1wP2q/F+owWWonj3h9tutNM2TtFJ48km48kpo2dKuE/vlTeecSx7VI8MOIWyZdE8aqtwI1MTaKWsD7KbKzeFGlbkqVoRrroFx4+DzeHf7ObNpE/TvD1dcASecYDU3PUFzzjmXZBmVpAGoslqViWo9DqwMO55Md9llsOuu1rSXi2PNGjjrLBg0CP7xD3j9dahaNeyonHMuN4gcGTRmOwaRD7d45IC0vtwpQqlbFFbFe67eBlWqQN++cPPN8N13cMABYUeURhYutA7Rv/gCBg+Gfv28hoVzzqWKSE+sfdTXsMp+b2AVCOtjjdxmvXQvSYttXbi4h9tGvXrBTjt5adoWpk+HNm2sJufo0XD11Z6gOedcal0DXInq2VjNzgGotsIStJy4kpbWJWlqnae7JKtRwxK1e++FO+6Axo3Djihk48dbsxp5eXbDXps2YUfknHO5qAHwfvB6HRC51+QxIB+4PoSYUirdS9JcivTrZxUJ7rkn7EhC9uqrcOyxUKsWTJjgCZpzzoVnMbBT8HousH/welegUigRpVhGJWki1BZhoAijRRglwu0i1A47rmxQqxZccgmMHAm/xTYXnCteftkqCRx8MHz2GTRoEHZEzjmXXURmIfI9It8iMrGEqT8GjgtevwI8gsizwItYc1xZL2OSNBHaATOAc4A1wFqgO/CzCG3DjC1bXHut3XY1aFDYkYTg+efhnHPg8MPh3Xdhl13Cjsg557LVkageiGrrEqa7EkvIAO4GBmGlaK/A5obts1rGJGnA/diX1ViV81Q5D6vl8RIwONTIskTdutCjBwwdCn/+GXY0KTR8OJx3HnToYD0K7LRTyZ9xzjmXPCJ5QLfN71U3oXovqp1RvQbVpeEFlzqZlKQdCAxWZVNkQPD6AaBVaFFlmeuugw0b4MEHw44kRZ55Bi64AI46Cv73P2uTxDnnXLIo8B4iXyNyadFT6Uas5KxCqgJLR5mUpC3D2kaJVR/IiYw6FRo1sq4pH38cliwJO5okGzIELrrIKgr8979QuXLYETnnXCbLE5GJUY94SVg7VA8CTgR6IdKhmPlNAA5OSqQZIpOStJeAp0XoLkJ9EeqJcC7wFIXXrF0CDBgAK1fCY4+FHUkSPf64dbdw4onwxhtQKScqCjnnXDJtVNXWUY8hW02h+kfwvABrpPbQYub3FHA/In0RaY/IQVs8ckBat5MWoz8gwDMUxr0BeIIcaCsllVq2hFNOgYcftjZcs64XpEcegT59bCVHjbK2R5xzziWXSBWgHKorgtfHAQOL+cQLwfMDccYpUD7BEaadjEnSVFkP9BFhANAQS9hmqLI63Miy0403WhNhTz5pnbBnjQcegH/+0xqrffll2GGHsCNyzrlcURt4Lei9JQ94AdUxxUwf7xannJIxSVqEKqtFmBl5HXY82eqww+Doo63LyiuvhB13DDui7Vf3xRftPrQzzoAXX4QKOX0/qnPOpZbqr0BZeojeB/gsqERQyGp+Hg5kfauemXRPGiL0FeF3rBLBMhFmi9BPBO9UMQluusma4njoobAjSYDBg2k4ZIg1VusJmnPOZYJxQLxGK6sH47JexiRpItwH3Ab8Gzg2eDwJ3ALcG15k2atTJ+jSBe68E/74I+xotsMLL8A117CgY0d47jlP0JxzLjMIdu9ZrF2BVSmOJRSZdLnzYuBiVUZHDftQhOlY4tY/nLCy2+DB0Lw5XH89jBgRdjTb4MMPoWdP6NCBaTfcQK28TNrlnXMuB4m8GbxS4DlE1kWNLY/14flZyuMKQcaUpAUmFzEs09YjYzRsaPfZjxxp/Y1nlMmT4bTToHFjeP11NnklAeecywSLg4cAf0W9XwzMwa6inRtadCmUScUKI4BeQJ+Y4VcAI1MfTu644QbrOemqqyxRK5cJKfHs2fC3v1n7Ie+8AzVqhB2Rc8650lC9ALDO2OF+VHPi0mY8mXC6jagI9BRhmgjDgsePwIVAngiPRB4hx5l1qlaFe++Fr76yZC3tLV1qjdSuWGEJWt26YUfknHOurFRvz+UEDTIrSWsKfAPMw6rl7gP8GQxrBrQIHvuHFWA2694d2ra13giWLw87mmKsW2dtoP30E7z+urXM65xzzmWgjLncqcqRYceQy0Ssof5DD4U77oBBg8KOKI5Nm6BHD/joI6vReaTvMs455zJXJpWkuZC1bg0XXGDdRf30U9jRxHHttfDKK3DffXD22WFH45xzzm0XT9JcmfzrX9YXeb9+YUcS46GHrMun3r2zrB8r55zLUSIdgt4FYofnIdIhhIhSzpM0Vya1a8Mtt8Dbb9sjLYwebT3Bn346PPggQb9wzjnnMpv3OBB2AC7z9O4NTZpYadr69SEH8/HHcO65cPjh1ptA+fIhB+Sccy5BvMeBsANwmWeHHazA6m9/s8oEoV1dnDvXOkuvVw/efNOuwzrnnMts3uPAZhmVpIlQG2vQtjn25U0FHldlfqiB5aATT4STToKBA60ga/fdUxzAhg3WWfrq1TB+POwSr0TcOedcBlocPEd6HFgTNW498AnwVKqDCkPGJGkitAPGAPOBz4PB3YF+IhyvunmYS5EHH4T99rMeCZ55JsULHzAAPv0UXnwRmjZN8cKdc84ljfc4sFkm3ZN2P/Ai0FiV81Q5D2gMvAQMDjWyHNWoEfTtC88+a70RpMx//mM9v195JXTrlsIFO+ecSxnvcSCjkrQDgcGqbIoMCF4/ALQKLaocd9NNVuPzqqusLdmk+/lna6zt0EPh/vtTsEDnnHOhEbkAkfcQmYbIr1s8ckAmJWnLgPpxhtcHliZqISL0E+EHEaaI8KIIO4qwiwhjRfg5ePbeugPVqsE991jH6++8s0dyF7ZmDfz975CXZ43WVqyY3OU555wLj8i12JWyr4F6wOvAFKxZjlTfZBOKTErSXgKeFqG7CPVFqCfCudjNgy8mYgEi7AVcBbRWZX+sFkk34HrgA1UaAR8E712gRw/rgen//q8hvybzv82VV8LkydbUxj77JHFBzjnn0sAlwKWoDgA2AI+h2hlL3HLiJJBJSVp/YDSWPc8AfgGGAqNIbNKUB1QSIQ+oDPwBdAGGB+OHA6cmcHkZr1w5GD7cns87DwoKkrCQZ56xx003WdVS55xz2a4O8GXweg1QLXj9InBGKBGlWCYlabsD/YAa2P1prbAiz6uDcdtNlblYBYXfgXnAMlXeA2qrMi+YZh5QKxHLyyZ160Lfvj/x2Wdw770Jnvl330GvXnDUUXDbbQmeuXPOuTT1J1AzeP0b0DZ4vS/xG7nNOqKaGespQgGwhyoLYobvCixQZbubmg/uNXsVOAu7z20UVnr3mCo7R033l+rW96WJyKXApQB5eXkHjx07dntD2mzlypVUrVo1YfNLhhUrVvLgg4cyfnxNHn/8Gxo3Xrnd8yy/ciUHX3455detY+KQIWyose23A6b7Nuzbty8FBQU8+uijYYdSpHTfhuAxJkK6xwfpH2O6x5cMRx555GpVrZKwGYoMBeagehsilwMPAhOAg4BXUL0kYctKV6qaEQ/QTaC7xRm+D+iqBC2jK+jTUe97gD4OOh10j2DYHqDTS5pX5cqVNZHGjRuX0Pklw7hx43TxYtW99lJt1kx19ertnOGmTaqnn65avrzqxx8nJL501rFjRz3ggAPCDqNY6b4NVT3GREj3+FTTP8Z0jy8ZgIScizc/oJxCXtT7sxQeUbhSoUJCl5Wmj7RvzFaER4KXCtwtwuqo0eWBQ4FvE7S434E2IlTGrn8fDUzE+gg7H7gneH4jQcvLOrvsAsOGwbHHwnXXWbdR2+zBB61NtPvvhyOOSFSIzjnnMoHqJihsdgvVl4GXQ4snBGmfpAEtgmcBmmFdQkSsB77B7iPbbqp8IcLoYJ4bgUnAEKAq8IoIF2GJXNdELC9bHXMM9OkDDz8MJ58Mxx23DTP55BPo3x9OPRWuvjrhMTrnnMsAIi2Ay4CGwIWozkPkVOA3VCeFG1zypX2SpsqRACI8C/RRZXmSl3crcGvM4HVYqZorpbvvhrFjrd3Z778vY9eay5fDOedYx+nPPgsiyQrTOedcuhI5DngTeAc4CqgUjGkI9CQHWlrImNqdqlyQ7ATNJU6lStac2cKFcPnloGWpn3LddTBnjs1g551Lnt4551w2ugO4GtXT2PIqWj52q1PWy5gkzWWeVq3g9tth1Ch4/vlSfig/H5580joFbdMmmeE555xLb/sBb8cZvgRrgivreZLmkqp/f7vnv1cv+P33EiZetQouuggaNoQ770xJfM4559LWX8BecYYfBMxJcSyh8CTNJVX58jBihHW+fv75JXTCfvPN8OuvMHQoVK6cshidc86lpReAQYjUwVp4yEOkI1ZZcESokaVIRiRpIlQQ4QsRmoQdiyu7+vWtKY78fGtVI64JE+Chh+wGtk6dUhidc865lBIpj8gkRN4qYcqbgJlYbwNVganAh8AnwF3JDTI9ZESSpsoGoD450g1ENurZE047DW64wfpI38K6dXDhhVCnThL6lHLOOZdm+gA/ljiV6gZUuwONgTOBc4CmqJ6HajJ6iU47GZGkBYYD2d8FRJYSgX//G3bd1ZK1xYujRt5xB/z4o01QrVqR83DOOZfh7NLlScDQUn9G9RdUR6P6Cqo/Jy22NJT27aRFqQJ0F+FY4GusF4DNVLkqlKhcqe22m3Ug0KkTdO0K774LFX74Fu65B3r0gBNPDDtE55xzyfUQ0B/YqVRTi5yFtVNai9iCJdXOCY4t7WRSktYM6wkAoEHMOL8MmiHatIGnnrKc7OreG3j0ywuhZs1iblZzzjmXIfJEZGLU+yGqOmTzO5GTgQWofo1IpxLnJjII6AuMA/4gB8/1GZOkRXoecJnvvPOsF4K8QYOASfDqq2XsksA551wa2qiqrYsZ3w7ojMjfgB2Baog8h+q5RUzfAzgb1dGJDjRTZNI9aS6L3N3jR24vdzujpCv5u5wedjjOOeeSTXUAqnVQrQd0Az4sJkEDy1G+TUlsaSqjkjQRaoswUITRIowS4XYRaocdlyujggLKX3Ih5atX5ZF9H+WMM6x5NOeccy7KEKC4JC7rZczlThHaAWOA+cDnweDuQD8RjlfdPMylu0cfhQkTKPfcczx7WG0OPRQ6d4bPP4edSncrqXPOuUymmo/1wbklkUei3pUDuiNyLDAZ2BAzj6yvMJgxSRrWwvCLwOWqbAIQoRzwJDAYODzE2Fxp/fKLNZZ20klwzjnsK9a35/HHw7nnwmuvQbmMKt91zjmXQC1i3kcudzaNGZ4TlQgyKUk7EOgZSdAAVNkkwgPApPDCcqWmCpdeChUqWCfqIgAcfbR1NtC7N9x0E/zrXyHH6ZxzLhyqXkkwSiYlacuwXgemxwyvDyxNfTiuzF5/HT78EB5/3HoXibljAgAAIABJREFUiNKrl9X4vPtu2H9/OOeckGJ0zjnn0kQmXVh6CXhahO4i1BehngjnAk9hl0FdOtuwAa67Dpo1g0u27jhCxG5V69ABLroIvvoqhBidc865NJJJJWn9AQGeoTDuDcATwPVhBeVKacgQ+Pln+O9/IS/+brfDDjB6NBx6KHTpAhMnwp57pjhO55xzLk1kTEmaKutV6QPUwO5PawXsoko/VdaHG50r1vLlcPvt1h/USScVO+luu8Ebb9hH/vY3WLIkNSE655xz6SZjkjQR9hZBVFmtyveqTFZldWRc2PG5Ytx3HyxcCIMGba4sUJyWLa2Pzx9/hBNOsITNOeecyzWZdLlzJrAHsCB6oAi7BuPKhxGUK8HcufDAA3D22dC6uN5CtnTccXbp8/TTrfBtzBioUiWJcTrnnAufSIdST6s6PomRpIVMStKE+O2iVAXWpjgWV1o33wwFBdvUrsYpp8Dzz1t+16ULvPUW7LhjEmJ0zjmXLvKxc33kskvkvB/7HnKgcCbtkzQRIq0PK3C3iF3iDJQHDiXH+/ZKW5Mnw7BhcPXVUK/eNs3izDNh7Vo4/3z4+9/tMugOOyQ0Suecc+ljt6jXh2EN2d9FYU9DbYEbsMqEWS/tkzQKWx8WoBlsUUlgPfAN9iW6dHPddbDzznDjjds1mx49YM0auPxyK1V7+eUiK4g655zLZKqLN78WuQPog+rYqCl+RWQBcB/wvxRHl3Jpf6pT5UgAEZ4F+qjit5FngvfftxvJBg+GGjW2e3aXXWaJWr9+Vqo2YgSUz/qCbuecy2nNgTlxhs9l626islLaJ2kRqlwgQp4IhwN7AzvEjB8RTmRuK5s2wbXX2iXOXr0SNtu+fS1Ru+EGqFTJml7zfj6dcy5r/QDcisgFqK4BQKQScEswLutlTJImQlPgv1g3UAIUYPFvANaBJ2lp47nn4Ntv4YUXoGLFhM56wABYvRruvNMStUceKVWrHs455zLPFcBbwFxEJgfDWmDn/+Ib3cwSGZOkAQ8BX2MN2f4ZPFfHehy4KcS4XLQ1a6yX9Nat4ayzkrKIgQMtUXvgAUvU7r3XEzXnnMs6ql8hUh84F7u8KcDzwAuorgo1thTJpCTtEKCjKqtE2ATkqfKNCP2BR4GW4YbnACvamj0bRo5M2rVIEbj/fssHBw2ywrqBAz1Rc865rCFSAXgOuAHVIWGHE5ZMuqNHYHPzGwuBvYLXc4B9Q4nIbaHCsmXWHtopp0DHjkldlgg89ph1xn7nnXbrW0FBUhfpnHMuVVQ3AMcRv33UnJFJJWlTgAOAX4EvgetEKAAuAWaEGZgz+4wYAStXwj33pGR5/9/efYdJVZ5vHP8+sIDSQRBpCiKgiIKCFIm6CLFHY8PYNRqNJZHEGP0ZY4kaU0yi0ahBo6IxsUdQVhCRtSArIiJFIiAqgojSVIrSnt8f76xbWHaHMDvnnJn7c13nmpkzZ/bcu+wwz77nLXXqwL33wk47hZWnli4Nk99qwlsRkZzwNHACeTzNVpKKtJuB0oWBriF0JpwILAOGRRVKUubPp92oUXD++dCjR9ZOaxb6pLVtG6bnOOwwGD06TM8mIiKJthC4BrODgKlAxX5o7n+OIlQ2JaZIc2dcufsLgB5mtARWuud3c2gsXH01Xq8e3HBDJKcfPhx22SVMfHvQQWGKtvbta36diIjE1jnASkKf88r9zh3I+SItSX3StuDOikwXaGY0N+NJM/5rxhwzBprR0ozxZsxL3W7/7Ky5ZPp0eOIJPj7llFApReQHP4Dnn4ePPoKBA2HOnMiiiIjI9nLvXM22e9TxsiExRZoZo6vbMniq24Gx7uxJ6AM3B7gKmOBOV2BC6rGUuvVWaNKEj086KeokDBkCL78M69fDd74DkyfX/BoREZE4SszlTmB5pcf1CEVUR0Lnwu1mRlPgYEITK+6sB9abcRxQmDpsJFAMXJmJcybewoXw6KNw2WVsatw46jQA7LcfvP46HHFEKNoeeywMOBURkYQx6wacRBUrDeH+wygiZVNiijR3zq1qvxl/Ar7K0Gl2J0zv8YAZvQiT514GtHFnSSrHEjN2ztD5ku/228PtZZfBggXRZiln991h0iQ4+mg4/nj4+9+hS5eoU4mISNrMjgaeAt4G+gBvAl2ABsCrESbLGnNPdp97M7oBr7lvf+FkRl+gBBjkzhtm3A58CfzEnebljlvpvmW/NDO7ALgAoKCgoM/48eO3N9K3Vq9eTeOYtFSVKli9mgHDhrF80CDm/OpXscy4bl1drr++B1Om7MTpp7/Heectie2kt8OHD2fTpk3ccccdUUfZqjj+G1emjNsv7vkg/hnjnq82DB48eK27N6r5yDSZvQU8ifstmH1FuHr2CfAwMDkfRnfi7onewL8H/lmGvtYu4B+We3wQ+Bjw98Dbpva1BX+vpq/VsGFDz6SJEydm9OtlxO9/7w7u06a5e0wzuvv69e5nnRWinnii+5dfRp2oaocccoj36tUr6hjViuu/cXnKuP3ins89/hnjnq82AGs8k5/xsNph99T9FQ49U/f3cViY0XPFdEvM5U4z/lp5F9AWOBK4PxPncOdTMz42o7s77wFDgHdT29nA71K3ozJxvkRbvz5c6hwyJHQCi7F69eDBB6FRo/mMGLEHs2fDf/4De+4ZdTIREanGV0Dp9ORLCKsLzSJ01cqLWRYSU6QB+1R6vJnQf+xnZKhIS/kJ8IgZ9QmrG5xLGAX7uBnnESbXOzmD50umf/8bPvkE7s/kj772mMGwYYsYNmwPhg2Dfv1g5MjQX01ERGLpDeA7hIaSMcCfMOsFHA/kxdj9xBRp7gzO0nmmA32reGpINs6fCO5h2o199glT/CdIYSFMmwYnnQQnnABXXRXW/qxbN+pkIiJSyc+B0o591wNNgBOBuanncl5iijSJkXHjYNas0BQV11741ejQIcyldtllYZnRqVNDw2CrVlEnExGRb7kvKHd/LXBRdGGikZgizSz9S5ru5PzcKZG69VZo1y5M8Z9QDRrAPfdA//5w0UXQpw88/XS4FRGRWmC2A/AKYQqNAsLIzeuqOf7/CGt0v4n7pqxkjJnErDgAtCY0cx5P6Dy4B/B94ITUc+U3qS3TpsGECaEZqn79mo+PuXPPDfOpAQwalJgudiIiSfQNcCjuvYDewBGYDajm+KOBl4FVmI3D7P8wG4hZ3nRQSVKR9jowDujgzsHuHExYbWAsUOLO90q3SFPmuj/9CZo0gQsvjDpJxvTpA2+9FRZmP++88K2tWxd1KhGRHBPmlVidelQvtW19slb37wDNCY0xbxKKtomEom1s7YaNhyQVaT8FrndnTemO1P0bCSMypbYtXBjWWPrRj6BZs6jTZFSrVjB2bBhIMGIE7L9/6KsmIiIZZFYXs+nAZ8B43N+o9nj3dbiPB+4E/gY8SZiW4+DajhoHSSrSGgPtqtjfFmiY5Sz56bbbwkCB4cOjTlIr6taFW26B8ePhq69g4EC48UbYuDHqZCIiiVBgZlPLbRdscYT7Jtx7Ax2Afpj13OpXMzsZs7swmwO8T1jRZz7wXTRPWuw8RVhT8wrC0k0AA4Dfk6EF1qUaq1bBvffCKadAx45Rp6lVQ4fCzJlwySVw7bUwZgw8/DB07Rp1MhGRWNvo7lVNYbUl91WYFQNHECaorcpjhPlQ/wTcmRrhmVeS1JJ2EfAs8CBhktn3gZGECe4uji5Wnvj732H1avjFL6JOkhUtWsC//gWPPgpz50Lv3mE0qCd7qVsRkeiYtcaseer+jsBQ4L/VvOJCYDyhS9MnmD2L2eWY7Y8lcP6n/0FiijR31rlzMbATYVTI/kBLdy52J++q66wqXQJq6NBQreSRU04JrWrf+U6YquPoo2HJkqhTiYgkUltgImYzCAMBxuP+3FaPdr8X9zNw70iYZH4U0I9wNW15FvJGLjFFGoAZRxKaPx8FVrizxozzzbQaQK36179CZZInrWiVtW8fBhXceScUF0PPnvDkk1GnEhFJGPcZuO+H+76498T9NzW+xqwOZv0JU3CdTBjhCfBeLSaNjcQUaWacDjwOzAM6E4buAtQFfhlVrpyX4CWgMsks9FF7+23o0gVOPhnOPBOW58XfciIiETArAlYCrxLmSH0bOAlogfvAKKNlS2KKNEIh9iN3fgaUH29XQrj8KbVh7FiYPTu0ouVHF4Bqde8eJr+97rqwlNSee4bVsdRXTUQk42YApxCKsgG4X4X7WNzX1PTCXJGkIq0rVa96vxpomuUs+ePWW8P1vgQvAZVp9erB9deHxRe6doVzzoHBg+Hdd6NOJiKSQ/KwKKssSUXaJ0C3KvYfTBjpKZk2fTq89FLOLAGVafvuC6+9Fia/nTEDevWCq6+GtRrGIiKSGWYXYzYbs7WY7Z7adxVmwyJOlhVJKtJGAH81Y1DqcUczzgb+ANwdXawc9sADoTg777yok8RWnTphAYb33oPTTw+T4e69d5hbTUREtoPZcOAawud/+f42i4FLI8mUZYkp0tz5A2HS2vFAI8L6XfcA97jztyiz5aQNG8KozmOPhZYto04Te61bw4MPhtGfO+4IxxwDJ5wAH38cdTIRkcT6MfAj3G+nYl/0acDe0UTKrsQUaQDu/ApoRZgnZQDQ2p1fR5sqRz3/PCxbBmefHXWSRDnkkHCV+JZbwpiLvfYKa9Jv2BB1MhGRxNmNqlcj2ADsmOUskUhUkQbgzlp3prozxZ3VUefJWQ89FJqHDj886iSJU79+WKh99uxQtP3iF2FutWee0ShQEZFtsIAwcX1lRwF5MVQr1kWaGZ234VgzI7cXlcyWFSvg2WfhtNPCUEb5n3TuDM89B6NGhb5rxx8PBx8Mb7wRdTIRkUS4FbgTs9MJfdIGYnYdcDPwx0iTZUmsizRgshn/MGOrk9aZ0cKMiwhV9XHZi5bDHn88LAV11llRJ0k8s9Ctb+bMsPbnvHkwYEBYbup9jUkWEdk69weA64HfAg2Bh4HzgZ/i/liEybIm7kXansAKYIwZn5sx1owHzLjbjEfNmAF8BpwBDHfnzkjT5oqRI8P1uf32izpJzigogAsvDEXatdeGFra99oLhw7VqgYjIVoX1O3cDdgZ2wb0j7v+IOla2xLpIc2eVO1cA7YGLgP8CzQnLQm0ERgL7uTPInXHRJc0hc+dCSUloRdMKAxnXpAnccEMo1s4+G+64Iywz9Yc/wObNUacTEYkp92W4fxZ1jGwriDpAOtxZBzyZ2qQ2Pfxw6EB1+ulRJ8lp7drBvfeGeYKvvDJsDRrAzjvXZ8MGdQUUkTxlNhNIb4iV+761GyZ6iSjSJEs2bw5F2tChoYqQWtezZ5j49qWX4Ljj4OOPG9K9e1i54KyztNCDiOQdNcaUoyJNyrzyCnz0Efz2t1EnyTuHHgp9+sDChWvYaaewisFNN4Vi7ZxzVKyJSJ5wvyHqCHES6z5pkmUPPQSNG8P3vx91krzVtOkGpkwJrWtt2oTBBnvsAXffDd98E3U6EZEImO2O2TGYHf3t+p15IvZFmhmnm6nFr9atXQtPPAEnnwwNG0adJq+ZwVFHhfEbY8dChw5w8cWhWPvb3+Drr6NOKCKSBWZNMXsCmA88A4wC5mH2OGZNog2XHbEv0oCHAC0eWdueeQZWr9YyUDFiFhZ8mDQJxo+HTp3g0kvDaNA//xm+/DLqhCIitep2YF9gMGEZqB2BIal9t0WYK2uSUKRpHohsGDkSdtsNDjoo6iRSiVkYy/HKK2GAQbducPnl0LFjWHJq4cKoE4qI1IpjgfNxfxn3DamtGLgAyIt+OUko0qS2LV4ML74IZ54Zpt+QWDKDwYNh4kR48004+mi47TbYfXc49VSYOjXqhCIiGbUjUNV03yuAHbKcJRJJ+US+3IzjzOgQdZCc9K9/hek3zjwz6iSSpr59wz/bggXws59BUREccEBYG3TUKNi0KeqEIiLbbRJwI2ZlHaXNGgE3AK9HFSqbklKk/QB4GvjIjM9Sy0PdbMaJ27IIu1TBPVzqHDgwXEeTRNl1V/jjH+Hjj0M/tYULw+DcPfeEu+6CNWuiTigi8j/7GdAfWIzZy5gVA4tS+4ZHGSxbklKkHQC0AIYCvyc0f54APAa8b8aKCLMl29tvw+zZWkw94Zo2DS1q8+fDY49By5ZwySXQvn1Y1eDdd6NOKCKyjdxnAV2BXwJTgWnAFUBX3GdHGS1bkjC1hQO48yUwMbUBYEYjYH9AK4H/rx56KMyUOmxY1EkkAwoKwj/lySfD66+H1rR77oG//jVcCv3xj+GEE8ISVCIisee+Drg36hhRSUJL2lZHd7qzxp1X3flrxk5m1DXjbTOeSz1uacZ4M+albltk6lyR27AhdGw69tjQ9CI5wwwGDYJHHoFFi8IC7osXw2mnhXnXfvnL0OomIhJrZvtj9hBmU1Pbw5jtH3WsbElCkXY48EV1B5gxNIPnuwyYU+7xVcAEd7oCE1KPc8O4cfD557rUmeNat4YrroC5c+GFF0KL2p//DF27wmGHwdNPh3pdRCRWzE4H3gTaAkWprQ0wBbMzooyWLbEv0twZ784WC+KY0d6Ma8xYAIzNxLlSo0ePBu4rt/s4YGTq/khyaW6WkSOhVSs44oiok0gW1KkD3/0uPPVUGGDwm9/AnDlw4olhAMIVV8CsWVGnFBH51s3Ar3H/Lu7XprbDgF8DN0WcLStiX6SVl7oUebwZY4APgfOBV8nchLe3EToobi63r407SwBStztn6FzRWrkSRo8O17/q1Ys6jWRZu3bw61/DBx+EX4P+/cOca/vsExZ6v/320MgqIhKh1sDjVex/glz5LK6BuXvUGWpkRnfgPOAsoB7wJPBPd141oyfwjjt1t/McxwBHuXOxGYXAL9w5xoxV7jQvd9xK96r7pZnZBYSZkCkoKOgzfvz47YlUwerVq2ncuHHGvl7b0aPp/pe/MPXvf2d1hqbeyHTGTIt7vuHDh7Np0ybuuOOOSM6/alU9JkzYmXHjdmHevCbUrbuZ/v1XcPjhnzJw4HLq1fPY/wwh/v/OEP+Mcc8H8c8Y93y1YfDgwWvdvVHGvqDZc8AzuN9Xaf/5wIm4H5mxc8VU7Is0M14F+gBjgEeAMe5sKPf83sCMDBRptwBnAhsJMxk3JczNdgBQ6M4SM9oCxe50r+nrNWrUyNdkcJKq4uJiCgsLM/b1GDQIvvgCZs4MvcwzIOMZMyzu+QoLC1m1ahXTp0+POgqzZoWr4f/8J3z6aRhXcuqp0LPnW1x4YZ9M/crUirj/O0P8M8Y9H8Q/Y9zz1QYzy3SRdglwPfAUUJLaO4AwBdf1wKffHuv+dMbOGyNJuNw5CHgGuM2dZ8oXaJnkzv+508GdToTJc19y5wxgNFC66vjZwKjaOH9WzZsX5mc466yMFWiSW3r2LJskt6go9GW77z646KI+dO0KV18N77wT5kIWEUmLWUfMJmI2B7PZmF1WwyvuAHYiXKG6P7VdALQC7iRcVXuScPkzJyWhSNsfWAk8Z8YCM24yY68snv93wHfNmAd8N/U42R5PXeI//fRoc0jsFRTAkUfCo4+GFrUrrvgvXbqEKT1694a99oJrrw3zIYuI1GAjcDnuexFaxC7BrMdWj3avk+a2XVfS4iz2RZo70925hDAE9zrgO8BsM6aZ8TOgXS2cs9idY1L3l7szxJ2uqdvkr24wZkxY/LF9+6iTSII0bw5HHfUp48bBkiVhktx27eDmm0PLW8+ecOONYaoPEZEtuC/BfVrq/leE6a70QVSN2Bdppdz52p2H3SkEugEvEJaHGBdpsKRZtgxKSuDoo6NOIgnWujVceCG89FKYJPeOO6BFi9Cq1r077LdfKNhmztQlURGpglknwmpBb0QbJN4SU6SV5858d64COgLHQ1gdQNLwwgvhU/Ooo6JOIjlil13g0kvh1VfD6gZ/+Qs0bAjXXQf77gt77AE//zm88gps2hR1WhGpRQVmNrXcdkGVR5k1JgwGGI77l1lNmDCJLNJKubPJnVHuHBd1lsQoKgrNIH37Rp1EclD79jB8OEyaBJ98AiNGwJ57wt/+BoccEgq6H/4wzM22bl3UaUUkwza6e99y24gtjjCrRyjQHsnVEZmZlOgiTbbRpk0wdmzoCV5H//RSu3bZBX70o9AFctmyMF6ldBmq444Li10cfzz84x+hoBORHGdmwD+AObj/Oeo4SVAQdQDJoilTYPlyXeqUrGvSBE4+OWzr14dLn888A6NGhVsIo0WPPDL8eg4YEEaWikhOGUSYj3QmZqUTQl6Ne1GNrzTbgcoNS+5rMx0wbtSckk+KikIL2mGHRZ1E8lj9+jB0KNx5Z1hDdMYM+N3voGnTMLXHQQeFK/KnnBIm1F26NOrEIpIR7q/hbrjvi3vv1Lb1As1sN8xGYfYlsAb4qtKW8/S3aj4pKoIDDwzD8ERiwCysF7rPPnDllbBqFbz4YvhVff75sin9+vSBww8Pxd2BB0KDBtHmFpGs+CdhBaCfAEuBvBsrriItXyxZAtOmwS23RJ1EZKuaN4eTTgrb5s1hVYPnnw9F2+9/D7/9Ley4Ixx8cCjYhg4NI0jVxVIkJ+0HHID7nKiDREVFWr54/vlwq/5okhB16oT51vbbLyxD9eWX8PLLoaVt/Hi44opwXOvWMGRIWdEmIjnjHaA1YdLbvKQiLV8UFUGHDuG6kkgCNW0K3/te2CBMojthQijaXnwxLF0F0K5dfw4/HAoLw7Qfu+0WWWQR2T4XAH/F7K/ALKi0drf7wihCZZOKtHywfn2YxPbUU7WguuSM9u3hrLPC5g7vvhuKtSeeWMMzz+zIAw+E43bbraxgO+QQ6NxZbwORhKgD7Az8h4r90Sz1OGfX7CylIi0fTJoEX32lS52Ss8xg773D1qvXLA4+uJBZs6C4OFwiHTMmjBSF0KBcWrANGhQm21WfNpFYGgl8DnwPDRyQnFVUBPXqhY47InmgTp0woGDffeGnPw2DEObMKSvaxo+HRx4Jx7ZoAQMHhoJt0CA44ICwrJWIRG5PoDfuc6MOEhUVafmgqCg0GzRuHHUSkUjUqVPW0nbJJeHy6Lx5oZG5dCtKzdZUUAD7719WtB14ILRtG21+kTw1BegMqEiTHPXhh6Gzzo9+FHUSkdgwg27dwnbuuWHf8uXw+uthmzQJ7r47LBYP0LEj9O9ftvXpo9Y2kSy4G7gNsz8BM9ly4MC0KEJlk4q0XFfaPKD+aCLV2mmniqNH168PUwtOngxvvBG2J58Mz9WtGwZK9+tXVrjttZf6tolk2L9Tt1su1K6BA5ITioqgSxfo2jXqJCKJUr9+WEN0wICyfUuXhiVwp0wJRdtjj8GI1MdHkybhMmmfPmHr2xf22EOFm8h26Bx1gKipSMtl69bBSy/B+edrzgGRDGjTpmJr2+bNMHduKNimTIG33oK77oKvvw7PN226ZeHWpUt0+UUSxf2jqCNETUVaLisuDoXa0UdHnUQkJ9WpE6bw2HNPOPvssG/DhtAN9K23YOrUcHvnnfDNN+H5pk2hU6feFBZC795hRYUePULLnYiUY3ZCtc+7P52lJJFRkZbLiorCQoeHHBJ1EpG8Ua8e9OoVth/+MOzbsAFmzw4F21tvwSuvGPfdB2vXlr2mR49QtJVuvXqF6UFE8tiTW9lfOl+a+qRJQrmHIm3IENhhh6jTiOS1evXKiq/zzoPi4rc56KBC3n8fpk8v2154oWzSXQijSvfZJ8z3ts8+YeveXa1ukifcK/boNCsgLLr+R+BXUUTKNhVpuWruXFiwoGwVahGJlbp1y6YBGTasbP/SpfDOO/D22zBzZtjGjw+tcRAKvu7dKxZvPXuGgk6DFCSnuW8E3sTsasL0HL0iTlTrVKTlqjFjwu2RR0abQ0S2SZs2cNhhYSu1YQO8915Z0TZjRpjL7d//LjumUaNwybR023vvcLvbbireJOesAvJiCI6KtFxVVBT+l95tt6iTiMh2qlcvtJb17Amnnlq2/4svYNas0N9t9uwwYKHyJdOGDcMcbqXFW+lAhy5dwtcViS2z/SvvAdoCVwJvZz9Q9qlIy0VffQWvvALDh0edRERqUbNmZctXlbdyZSjY3n23rHibMAEefrjsmIKCMI9badFWfhOJiamEQQKV55AqAc7NfpzsU5GWi158MVwf0dQbInmpRYuqi7cvvgiXTf/734rbmDFlfd4AWrYcSM+eYQ7s0n5z3bqF1rcGDbL7vUheqzyZ7Wbgc9y/jiJMFFSk5aKiojAZ04EHRp1ERGKkWbOwlFW/fhX3b9gAH3xQVrQVF69g9eq2PPdcGMhQyiz0oCgt2rp2Da1xe+wBnTpp1KlkmCazVZGWc0qn3jjsMHU4EZG01KtXVngdeyz06/cehYVtgdD6Nm9eGDA+d27Z/Ycegi+/LPsadeqEAq5Ll7LCbY89wuPdd9eC9PI/MtsFOBDYGag4BMb9rigiZZOKtFwzYwZ88okWVBeRjGjWLCxn1bdvxf3u8Nln8P77MH9+2e38+fD447BiRcXj27YNxVrp1rlz2f22bTUCVapgdgZwH6FP2krKJrEldV9FmiSMpt4QkSwwC9OFtGlTdc+KlSsrFm4ffBCmbnz5ZfjnP0ORV6pBg1C0lW6dOpVtnTvDTjtp+eE8dTPwB+A3qTnS8o6KtFxTVBRWct5ll6iTiEgea9Gi6hY4gPXr4aOPQtG2YEFZAff++1BSEgq88ho1qli4deoEq1e3pmFD2HVX2HlntcTlqKbAg/laoIGKtNyyYgVMngy/yovVMkQkoerXD4MOunat+vkvvghF3AcfwIcfVtwmTYJVqwD25oYbwvENGoQVF3bdNfSLK3+7667QoUNYxlgS5xHgaOCOqINERUVaLnnhBdi8WVNviEiiNWsWlrzad9+qn1+1Cp566k3atDmAjz6ChQv59nbcOFiypOLlVIBWrUIhV9XWoQNNYLojAAAUs0lEQVS0b6/RqTH0c+AZzIYAM4ENFZ51/00UobJJRVo5ZnQEHgJ2IczHMsKd281oCTwGdAI+BIa5s3JrXycy48dDy5ZVX18QEckRzZtDly5rKCys+vn162HRolC4ffxxxe2DD8Jc36E1rqI2bUKx1qFDWeFW/n779tC4ca1+a1LRhcARwDJgD7YcOKAiLc9sBC53Z5oZTYC3zBgPnANMcOd3ZlwFXEVYliJeSkpg4MCwcrOISJ6qX79s5OjWrF5dsXhbtChsixeHQu7VV7fsGwehla9du1CwtWtX9X11Cc6YXwOX4/6XqINERUVaOe4sAZak7n9lxhygPXAcUJg6bCRQTNyKtFWrwtovp50WdRIRkdhr3DisabrXXls/Zu3aULQtXlxWwC1aFGY5+uQTKC4OtxsrdWs3g+bND2TXXcP0IqVbu3YVH++yC+ywQ61+m0lXFxgddYgoqUjbCjM6AfsBbwBtUgUc7iwxY+cos1VpypRwO2BAtDlERHJEw4bVD3CA0A142bJQrC1eXFbAvfnmMszasWRJmL5y6VLYtGnL17doUVawtWkTbqvaWrXKgRGsZvcDxwCf4d4zjVc8AJxOHlzW3Brzyr0rBTMaAy8DN7vztBmr3Gle7vmV7rTY8nV2AXABQEFBQZ/x48dnLNPq1atpXE1niN1GjqTTyJG89uyzbGrUKGPn3RY1ZYxa3PMNHz6cTZs2cccd8R3IFPefIShjJsQ9H8Q/Y+V8mzbBF1/UY8WKBixfXj+1hfsrV9ZnxYqy7euvt+yyUqeO07z5elq02ECLFutp0WI9LVtWfBz2baBZsw3UrZv9z/bBgwevdfetfwCZHQysBh5Kq0gzuws4DZgNzGDLgQM/3Y64iaAirRIz6gHPAePc+XNq33tAYaoVrS1Q7E736r5Oo0aNfM2aNRnLVVxcTOHWeslCmLx28eLwJ1tEaswYsbjnKywsZNWqVUyfPj3qKFsV958hKGMmxD0fxD/j9uRbvRo+/bTitmRJaI2rvH3zzZavNwtjyHbeufqtU6cwKCJTzKz6Ii0c1Al4Ls0ibWI1zzruh25LviTS5c5yzDDgH8Cc0gItZTRwNvC71O2oCOJt3ebNYdDAySdHnURERLZT48Zla59Wxz2sn1q5cPv887BkV+k2Y0a4rTwQ4txz4f77a+/72G7ug6OOEDUVaRUNAs4EZppR2pxxNaE4e9yM84CFQLyqoblzw8CBgQOjTiIiIlliFkabNmsG3brVfPz69aH/XGnx1rp1xiMVmNnUco9HuPuIjJ8lj6hIK8ed1wgLuVZlSDazbJPJk8OtBg2IiMhW1K9fNlVILdno7ts3UafZaOAM3L9M3d8692O361wJoCItF5SUhNkdu1fbTU5ERCTullM2ae3yKIPEgYq0XFBSAv3758D4bBERyVlm/ybMOdoKs0XAdbj/o8Ix7udWeT9PqUhLuq++glmz4Pjjo04iIiKyde6nbtPxZp1w/3Arzx2I++vbHyre1PSSdG++GUZ3atCAiIjklncwO6PCHrM6mP0GqG56jpyhIi3pSgcN9OsXbQ4REZHMuhK4B7N/YdYUsy7AZOCHwNHRRssOFWlJV1ISFp9rscUCCCIiIsnlfg/QF+gOzALeBhYB++L+YpTRskVFWpK5hyJNU2+IiEhu+hT4EGgD7AiMxX1FpImySEVakr3/fpiZUP3RREQk14S1PmcAHYC9CZc5/4jZfzDbKdJsWaIiLck0ia2IiOSuF4GHgEG4z8f9YaA30BqYGWmyLNEUHElWUgJNmkCPHlEnERERybShuL9SYY/7h6kWtqujiZRdKtKSbPLkMKqzbt2ok4iIiGRW5QKtbP9m4KbshomGirSkWrMGZsyAq66KOomIiEjtMGsJHAHsCtSv8Jz7b6KIlE0q0pLqrbdg0yYNGhARkdxkNgAYA3xD6Ie2GGibevwhkPNFmgYOJFXpoIH+/aPNISIiUjv+CDwCtAe+Bg4ltKhNBX4fYa6sUZGWVCUl0LUrtGoVdRIREZHasC9wJ+4ObAIa4L6UsBLB9VEGyxYVaUnkHlrSNPWGiIjkrvXl7i8FdkvdXw20y36c7FOftCT66CNYulT90UREJJdNAw4A5gLFwE2YtQHOIExym/NUpCXE8OG9ad483D/0s8lcCzy+cADDgLVr4aijtnzNOeeEbdkyOOmkLZ+/6CI45RT4+GM488wtn7/8cvje9+C99+DCC7d8/pprYOhQmD4dhg+HVavKMgL89rdw4IHw+utwdRUz2tx2G/TuDS++CDdVMZj673+H7t3h2WfhT3/a8vmHH4aOHeGxx+Duu7d8/sknw9XgBx8MW+V8RUXQsCHcdRc8/viWry8uDre33grPPVfxuR13hOefD/dvvBEmTKj4/E47wVNPhfv/939lXQhLdegA//xnuD98ePgZTp8OGzc2prAQunWDESPC8xdcAHPnVnx9797h5wdwxhmwaFHF5wcOhFtuCfdPPBGWL6/4/JAh8Otfh/tHHgnr1lV8/phj4Be/CPcLC8v2l/4Mhw2Diy+Oz+9eeatW9eauu+L1u1fZVVeFixhx+d0rr1s3OO20cD9Ov3ulSn/3vv66TpXPR/m7B2X/782a1ZTrr9/y+ah/98r/v3fxxVs+HzO/Apqk7l9DmNj2DkLRdm5UobJJRVoC9fiyhHV1GrK83T5RRxEREakd7lPL3f8cODK6MNGw0B9PMq1Ro0a+Zs2ajH294uJiCkv/bOzXL/wpVPrndkxUyBhDcc9XWFjIqlWrmF65aSNG4v4zBGXMhLjng/hnjHu+2mBma929UdQ5cola0pJm3Tp4++3QJi8iIpJrzEandZz7sbWcJHIq0pLm7bdh40YNGhARkVx1DPARYbBAXlORljSlvYA1/YaIiOSmWwkjOA8GHgAexH1R9S/JTZonLWlKSqBzZ2jTJuokIiIimef+S6Aj8DOgLzAPs+cxOwmzetGGyy4VaUmjSWxFRCTXuW/CfTTu3wc6AxOBm4DFmDWONlz2qEhLkkWLYPFi9UcTEZF80ghoDjQmrDaQN9NSqEhLEvVHExGRfGC2I2ZnY/YKMJOwJNTZuO+Oe+bmt4o5DRxIkpIS2GEH6NUr6iQiIiK1w2wEcAowD/gHcCzuq6INFQ0VaUkyeTL06QP160edREREpLacDywElhBWGTgSsy2P0jxpEhe2fj1MmwaXXhp1FBERkdr0EHnU76w6KtISovH778M332jQgIiI5Db3c6KOEBcaOJAQTWfPDnc0aEBERCQvqEhLiKZz5kDHjtC+fdRRREREJAtUpCVEs9mz1YomIiKSR1SkpcmMI8x4z4z5ZlyV1ZMvWcIOS5eqP5qIiCSb2RGYvYfZfMyy+1maQCrS0mBGXeBvhKHAPYBTzeiRtQAlJeFWLWkiIpJUZlt8lmKWvc/SBFKRlp5+wHx3FrizHngUOC5rZy8pYXNBAey3X9ZOKSIikmH9gPm4L8A9+5+lCaQpONLTHvi43ONFQP/KB5nZBcAFAAUFBRQXF2fk5L3HjcO7dOGd0ha1mFq9enXGvufaEPd8rVq1olmzZrHOGPefIShjJsQ9H8Q/Y9zz1ZICM5ta7vEIdx9R7nFan6VSRkVaeqqY6njLifZSv4wjABo1auSFhYWZOfukSZSMGkXGvl4tKS4ujnXGuOcrLCyMfca45wNlzIS454P4Z4x7vlqy0d37VvN8Wp+lUkaXO9OzCOhY7nEH4JOsnb1RI75u1y5rpxMREakF0X6WJpCKtPS8CXQ1o7MZ9YEfAKMjziQiIpIkbwJdMeuMmT5L06DLnWlwZ6MZlwLjgLrA/e7MjjiWiIhIcrhvxKzCZynu+iythoq0NLlTBBRFnUNERCSx3PVZug10uVNEREQkhlSkiYiIiMSQijQRERGRGFKRJiIiIhJDKtJEREREYkhFmoiIiEgMqUgTERERiSEVaSIiIiIxpCJNREREJIbMXQvQ1wYz2wysy+CXLAA2ZvDr1Ya4Z4x7Poh/xrjnA2XMhLjng/hnjHu+2rCju6vxJ4NUpCWEmU11975R56hO3DPGPR/EP2Pc84EyZkLc80H8M8Y9nySDKl4RERGRGFKRJiIiIhJDKtKSY0TUAdIQ94xxzwfxzxj3fKCMmRD3fBD/jHHPJwmgPmkiIiIiMaSWNBEREZEYUpEWM2Z2hJm9Z2bzzeyqKp43M/tr6vkZZrZ/zPKdnso1w8xeN7Ne2cyXTsZyxx1gZpvM7KS45TOzQjObbmazzezlbOZLJ6OZNTOzZ83snVTGc7Oc734z+8zMZm3l+UjfJ2lmjPS9UlO+csdF8j5JnbvGjFG+V9L4N470fSI5wN21xWQD6gLvA7sD9YF3gB6VjjkKeB4wYADwRszyHQi0SN0/Mpv50s1Y7riXgCLgpDjlA5oD7wK7ph7vHLefIXA18PvU/dbACqB+FjMeDOwPzNrK85G9T7YhY9TvlWrzlftdyPr7ZBt+hlG/V2rKF+n7RFvyN7WkxUs/YL67L3D39cCjwHGVjjkOeMiDEqC5mbWNSz53f93dV6YelgAdspQt7YwpPwGeAj7LZjjSy3ca8LS7LwRw9zhmdKCJmRnQmPDhk7WJO939ldQ5tybK9wlQc8ao3ytp/AwhuvcJkFbGSN8raeSL9H0iyaciLV7aAx+Xe7wotW9bj6kt23ru8witGdlUY0Yzaw8cD9yTxVyl0vkZdgNamFmxmb1lZmdlLV2QTsY7gb2AT4CZwGXuvjk78dIS5fvkfxHFe6VaEb9P0hX1e6UmcX+fSMwVRB1AKrAq9lUefpvOMbUl7XOb2WDCB893ajVRFaeuYl/ljLcBV7r7pvAHblalk68A6AMMAXYEJptZibvPre1wKelkPByYDhwKdAHGm9mr7v5lbYdLU5Tvk20S4XulJlG+T9IV9XulJnF/n0jMqUiLl0VAx3KPOxD+AtvWY2pLWuc2s32B+4Aj3X15lrKVSidjX+DR1AdPK+AoM9vo7s/EJN8iYJm7rwHWmNkrQC8gWx886WQ8F/iduzsw38w+APYEpmQnYo2ifJ+kLeL3Sk2ifJ+kK+r3Sk3i/j6RmNPlznh5E+hqZp3NrD7wA2B0pWNGA2elRq8NAL5w9yVxyWdmuwJPA2dG9NdsjRndvbO7d3L3TsCTwMVZ/OBJ5994FHCQmRWYWUOgPzAnS/nSzbiQ0HqBmbUBugMLspixJlG+T9ISg/dKtSJ+n6Qr6vdKTeL+PpGYU0tajLj7RjO7FBhHGFV1v7vPNrMfp56/hzDK6ihgPrCW8JdanPJdC+wE3JX6C3yjZ3GR4TQzRiadfO4+x8zGAjOAzcB97l7tNAnZzgjcCDxoZjMJlxavdPdl2cpoZv8GCoFWZrYIuA6oVy5fZO+TbcgY6XsljXyRqylj1O+VNH6Gkb5PJPm04oCIiIhIDOlyp4iIiEgMqUgTERERiSEVaSIiIiIxpCJNREREJIZUpImIiIjEkIo0ERERkRhSkSYiIiISQyrSRCQvmVnH1MLc75rZO2Z2QpbOO9rMVprZk9k4n4gklyazFZG8ZGZtgTbuPt3MdgbeArq7+9paPu9goDFwtrufVJvnEpFkU0uaiGSMmbUws6Vm1iXqLDVx9yXuPj11/zNgJWEh8do+70Tgq6qeM7MnzezntZ1BRJJBRZqIfMvMHjQzT20bzOwzM5toZpeYWb00vsTVQJG7v29mPzazNalF2ku/fn0zW5tay7D8ebumznlopr+ndJhZX8Kaix/XcNyDZvZcpX3HpL6nmzMQ5QbgGjNrloGvJSIJpwXWRaSyF4EzCYurtwYOJRQPZ5rZEHdfU9WLzKwhcD7wvdSul4CGQD/gtdS+/sAXQDcza+3un6f2FwLfAK9n8hsxs60ttn2ku3+cOmYn4CHgPN/G/h9mdiZwH/BLd7893XNujbvPNLMFwBnA37Yli4jkHhVpIlLZN+7+aer+YmC6mb0ATAN+CVy3ldcdBWwGJgG4+1wz+wQYTFmRNphQBO5OKMyeKLd/srt/XdUXNrNiYA6wFjgX2ATcBNwD/Bk4HfgS+JW7P1z6OnfvWd03amYNgP8At7j7NhWIZnYZ8Afg/G05ZxpGA6eiIk0k7+lyp4jUyN1nAWOBE6s57CDgrUqtURMJBVipwUBxaiu/vzB1bHVOJ/Tl6g/8DrgNeAaYC/QFRgL3mVm7Gr4OAGZmwIPAS+WLrDRfeyNwC3DCtr42DVOAfma2Y4a/rogkjIo0EUnXu4QWsK3ZDVhSad9EYKCZNTCzHYABhALtZVJFmpntCbQlXB6tzmx3v97d5xFaz5YBG9z9dnefD/wGMODANL+fQcApwPfNbHpq2yeN130XuAY42d3HpHmub5nZi4QWxKPMbJGZDax0yCeE/nFpFZsikrt0uVNE0mVAdX22dgSWVto3EdgBGJh6/bLUoIJPgS5mtguhWFsLvFHD+WeU3nF3N7PPgJnl9m0ws5XAzul8M+7+Gv/bH6qzgGbAdWY2yd1XbcuL3X1oDYesS92qJU0kz6klTUTS1QNYUM3zy4AW5Xe4+wLgI8LlzEJCKxqpwQdvldv/mrtvqOH8lZ/3reyr7f/XlgCHEAq1F82sRQ3Hb6uWqdvPqz1KRHKeijQRqZGZ9QSOAKqbJf9tQiFXWWm/tNL+aKWKCSNHC6n5UmesuPtiQu5GwITUCNFM6Ql84u6VWyVFJM+oSBORyhqY2S5m1s7MeqUmVy0mtHzdWs3rxgF7VVGwTCT0RetPxSLtZeAHhMuTNQ0aiB13X0Io1OoDL5lZpibCPYgwSENE8pyKNBGpbCjhkt5CYAJwLGGetIO3NkcahDm+CCMTf1DpqYmEQuYzd3+/3P7XCP2uviQUgImTau0qHaU6MbW81P8sNbjieODe7c0mIsmntTtFJGPM7AjgdqCHu2+KOk/SmNklwHHufljUWUQkempJE5GMcfexhElYO0SdJaE2AD+JOoSIxINa0kRERERiSC1pIiIiIjGkIk1EREQkhlSkiYiIiMSQijQRERGRGFKRJiIiIhJDKtJEREREYkhFmoiIiEgMqUgTERERiSEVaSIiIiIx9P9fcbi4tTSKoAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "color1 = 'b'\n",
    "color2 = 'r'\n",
    "\n",
    "fig = plt.figure(figsize=(8,6))\n",
    "ax1 = fig.add_subplot(111)\n",
    "ax1.plot(Darray, deltaT_list, color=color1)\n",
    "ax1.plot(Darray, Tmean_list, 'b--')\n",
    "ax1.set_xlabel('D (W m$^{-2}$ K$^{-1}$)', fontsize=14)\n",
    "ax1.set_xticks(np.arange(Darray[0], Darray[-1], 0.2))\n",
    "ax1.set_ylabel('$\\Delta T$ (equator to pole)', fontsize=14,  color=color1)\n",
    "for tl in ax1.get_yticklabels():\n",
    "    tl.set_color(color1)\n",
    "ax2 = ax1.twinx()\n",
    "ax2.plot(Darray, Hmax_list, color=color2)\n",
    "ax2.set_ylabel('Maximum poleward heat transport (PW)', fontsize=14, color=color2)\n",
    "for tl in ax2.get_yticklabels():\n",
    "    tl.set_color(color2)\n",
    "ax1.set_title('Effect of diffusivity on temperature gradient and heat transport in the EBM', fontsize=16)\n",
    "ax1.grid()\n",
    "\n",
    "ax1.plot([0.6, 0.6], [0, 140], 'k-');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "When $D=0$, every latitude is in radiative equilibrium and the heat transport is zero. As we have already seen, this gives an equator-to-pole temperature gradient much too high.\n",
    "\n",
    "When $D$ is **large**, the model is very efficient at moving heat poleward. The heat transport is large and the temperture gradient is weak.\n",
    "\n",
    "The real climate seems to lie in a sweet spot in between these limits.\n",
    "\n",
    "It looks like our fitting criteria are met reasonably well with $D=0.6$ W m$^{-2}$ K$^{-1}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
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   "source": [
    "Also, note that the **global mean temperature** (plotted in dashed blue) is completely insensitive to $D$. Look at the EBM equation and convince yourself that this must be true, since the transport term vanishes from the global average, and there is no non-linear temperature dependence in this model."
   ]
  },
  {
   "cell_type": "markdown",
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     "slide_type": "slide"
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   "source": [
    "____________\n",
    "<a id='section8'></a>\n",
    "\n",
    "## 8. Summary: parameter values in the diffusive EBM\n",
    "____________"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Our model is defined by the following equation\n",
    "\n",
    "$$ C \\frac{\\partial T_s}{\\partial t} = (1-\\alpha) ~ Q - \\left( A + B~T_s \\right) + \\frac{D}{\\cos⁡\\phi } \\frac{\\partial }{\\partial \\phi} \\left(   \\cos⁡\\phi  ~ \\frac{\\partial T_s}{\\partial \\phi} \\right) $$\n",
    "\n",
    "with the albedo given by\n",
    "\n",
    "$$ \\alpha(\\phi) = \\alpha_0 + \\alpha_2 P_2(\\sin\\phi) $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We have chosen the following parameter values, which seems to give a reasonable fit to the observed **annual mean temperature and energy budget**:\n",
    "\n",
    "- $ A = 210 ~ \\text{W m}^{-2}$\n",
    "- $ B = 2 ~ \\text{W m}^{-2}~^\\circ\\text{C}^{-1} $\n",
    "- $ a_0 = 0.354$\n",
    "- $ a_2 = 0.25$\n",
    "- $ D = 0.6 ~ \\text{W m}^{-2}~^\\circ\\text{C}^{-1} $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "There is one parameter left to choose: the heat capacity $C$. We can't use the annual mean energy budget and temperatures to guide this choice.\n",
    "\n",
    "[Why?]\n",
    "\n",
    "We will instead look at seasonally varying models in the next set of notes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<div class=\"alert alert-success\">\n",
    "[Back to ATM 623 notebook home](../index.ipynb)\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "____________\n",
    "## Version information\n",
    "____________\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading extensions from ~/.ipython/extensions is deprecated. We recommend managing extensions like any other Python packages, in site-packages.\n"
     ]
    },
    {
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       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>3.7.3 64bit [Clang 4.0.1 (tags/RELEASE_401/final)]</td></tr><tr><td>IPython</td><td>7.6.0</td></tr><tr><td>OS</td><td>Darwin 17.7.0 x86_64 i386 64bit</td></tr><tr><td>numpy</td><td>1.16.4</td></tr><tr><td>scipy</td><td>1.3.0</td></tr><tr><td>matplotlib</td><td>3.1.1</td></tr><tr><td>xarray</td><td>0.12.1</td></tr><tr><td>climlab</td><td>0.7.5</td></tr><tr><td colspan='2'>Wed Jul 03 14:55:59 2019 EDT</td></tr></table>"
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       "\\begin{tabular}{|l|l|}\\hline\n",
       "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
       "Python & 3.7.3 64bit [Clang 4.0.1 (tags/RELEASE\\_401/final)] \\\\ \\hline\n",
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       "OS & Darwin 17.7.0 x86\\_64 i386 64bit \\\\ \\hline\n",
       "numpy & 1.16.4 \\\\ \\hline\n",
       "scipy & 1.3.0 \\\\ \\hline\n",
       "matplotlib & 3.1.1 \\\\ \\hline\n",
       "xarray & 0.12.1 \\\\ \\hline\n",
       "climlab & 0.7.5 \\\\ \\hline\n",
       "\\hline \\multicolumn{2}{|l|}{Wed Jul 03 14:55:59 2019 EDT} \\\\ \\hline\n",
       "\\end{tabular}\n"
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       "Software versions\n",
       "Python 3.7.3 64bit [Clang 4.0.1 (tags/RELEASE_401/final)]\n",
       "IPython 7.6.0\n",
       "OS Darwin 17.7.0 x86_64 i386 64bit\n",
       "numpy 1.16.4\n",
       "scipy 1.3.0\n",
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       "Wed Jul 03 14:55:59 2019 EDT"
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   ],
   "source": [
    "%load_ext version_information\n",
    "%version_information numpy, scipy, matplotlib, xarray, climlab"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   },
   "source": [
    "____________\n",
    "\n",
    "## Credits\n",
    "\n",
    "The author of this notebook is [Brian E. J. Rose](http://www.atmos.albany.edu/facstaff/brose/index.html), University at Albany.\n",
    "\n",
    "It was developed in support of [ATM 623: Climate Modeling](http://www.atmos.albany.edu/facstaff/brose/classes/ATM623_Spring2015/), a graduate-level course in the [Department of Atmospheric and Envionmental Sciences](http://www.albany.edu/atmos/index.php)\n",
    "\n",
    "Development of these notes and the [climlab software](https://github.com/brian-rose/climlab) is partially supported by the National Science Foundation under award AGS-1455071 to Brian Rose. Any opinions, findings, conclusions or recommendations expressed here are mine and do not necessarily reflect the views of the National Science Foundation.\n",
    "____________"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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