ECS_TCR_with_GHF.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "this function computes the equilibrium climate sensitivity based on the estimates from Otto Nature Geo (2013) and our new ground heat flux estimates "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "N_MCMC  = 1000000\n",
    "area_land  = 148300000; # km^2 Coble et al., 1987\n",
    "area_Earth = 510064472\n",
    "mu_T, Delta_T = 0.75,0.2\n",
    "sigma_T = Delta_T/2\n",
    "mu_OHS, Delta_OHS = 0.65,0.27\n",
    "sigma_OHS = Delta_OHS/2\n",
    "mu_RAD, Delta_RAD = 1.95,0.58\n",
    "sigma_RAD = Delta_RAD/2\n",
    "mu_RAD_CO2x, Delta_RAD_CO2x = 3.44,0.34\n",
    "sigma_RAD_CO2x = Delta_RAD_CO2x/2\n",
    "mu_GHS, Delta_GHS = 0.24,(0.08+0.16)/2 # 0.18*2\n",
    "sigma_GHS = Delta_GHS/2\n",
    "DeltaT   = np.random.normal(mu_T ,sigma_T ,N_MCMC)\n",
    "OHS = np.random.normal(mu_OHS ,sigma_OHS ,N_MCMC)\n",
    "RAD = np.random.normal(mu_RAD ,sigma_RAD ,N_MCMC)\n",
    "RAD_CO2x = np.random.normal(mu_RAD_CO2x ,sigma_RAD_CO2x ,N_MCMC)\n",
    "GHS = area_land/area_Earth*np.random.normal(mu_GHS ,sigma_GHS ,N_MCMC) # only applies over ~1/3rd of the globe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "check distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "now estimate lambda and its spread"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "lambda_est = -(OHS-RAD)/DeltaT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "count, bins, ignored = plt.hist(lambda_est, 100, density=True)\n",
    "#plt.plot(bins, 1/(sigma_OHS * np.sqrt(2 * np.pi)) *\n",
    "#                   np.exp( - (bins - mu_OHS)**2 / (2 * sigma_OHS**2) ),\n",
    "#                   linewidth=2, color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "now estimate TCR doubling CO2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "indices_good = ~((OHS>RAD-0.1) | (OHS>RAD_CO2x-0.1) | (RAD>RAD_CO2x-0.3) | (OHS+GHS>RAD-0.1))\n",
    "DeltaT_TCR = DeltaT[indices_good] * RAD_CO2x[indices_good] / ( RAD[indices_good] )\n",
    "DeltaT_ECS = DeltaT[indices_good] * RAD_CO2x[indices_good] / ( RAD[indices_good] - OHS[indices_good])\n",
    "DeltaT_ECS_with_GHF = DeltaT[indices_good] * RAD_CO2x[indices_good] / ( RAD[indices_good] - OHS[indices_good] - GHS[indices_good])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAEMJJREFUeJzt3X+MZWddx/H3h6UFIwgJO8amu8vWuCTWpto6lJomUn4l20J2Y6yyjYAlxU3QggoqRU2L5R9+JIpIsS7YFFBaaiFkrdvUH5TUqK075UftD0vWUu2kJDsUKBIUXPz6x9wt18udvWdmzsydefb9Sia555xn7/nm2bmf+8xzz3luqgpJUlueMu0CJEn9M9wlqUGGuyQ1yHCXpAYZ7pLUIMNdkhpkuEtSgwx3SWqQ4S5JDXrqtE68devW2rlz57ROL0mb0j333PPlqpqZ1G5q4b5z507m5uamdXpJ2pSS/HuXdk7LSFKDDHdJapDhLkkNMtwlqUGGuyQ1yHCXpAYZ7pLUIMNdkhpkuEtSg6Z2h6pWbueVf/Xk40fe8fIpViJpo3LkLkkNcuS+yTmKlzSOI3dJapDhLkkNMtwlqUHOuW8Sw3PrXdo4/y6d3By5S1KDDHdJapDhLkkNmhjuSa5PcjTJfRPaPT/Jd5Jc0l95kqSV6DJyvwHYfaIGSbYA7wRu76EmSdIqTQz3qroT+MqEZm8APg4c7aMoSdLqrPpSyCSnAz8DvBh4/qorUi9GL5300kjp5NLHB6rvAd5SVd+Z1DDJ/iRzSeYWFhZ6OLUkaZw+bmKaBW5KArAVuDjJsar65GjDqjoAHACYnZ2tHs4tSRpj1eFeVWccf5zkBuDWccEuSVo/E8M9yY3AhcDWJPPA1cApAFV13ZpWd5LrsuSAJI0zMdyr6tKuT1ZVl62qGklSL7xDVZIaZLhLUoMMd0lqkOEuSQ0y3CWpQYa7JDXIcJekBvkdqicJv19VOrk4cpekBhnuktQgw12SGmS4S1KDDHdJapDhLkkNMtwlqUFe577B+AUdkvrgyF2SGmS4S1KDDHdJalCXL8i+HngFcLSqzhpz/BeAtww2vwG8vqo+32uV6pXrzEjt6zJyvwHYfYLjXwReWFVnA28HDvRQlyRpFSaO3KvqziQ7T3D8H4c27wK2rb4sSdJq9D3nfjlw21IHk+xPMpdkbmFhoedTS5KO6y3ck7yIxXB/y1JtqupAVc1W1ezMzExfp5YkjejlJqYkZwMfBC6qqsf7eE5J0sqteuSeZAfwCeDVVfWF1ZckSVqtLpdC3ghcCGxNMg9cDZwCUFXXAVcBzwHenwTgWFXNrlXBkqTJulwtc+mE468DXtdbRZKkVfMOVUlqkOEuSQ0y3CWpQYa7JDXIcJekBhnuktQgw12SGmS4S1KD/ILsDWCaX4rtF3dIbXLkLkkNMtwlqUGGuyQ1yHCXpAYZ7pLUIMNdkhpkuEtSgwx3SWqQ4S5JDZoY7kmuT3I0yX1LHE+S9yY5kuTeJOf2X6YkaTm6jNxvAHaf4PhFwK7Bz37gj1dfliRpNSaGe1XdCXzlBE32Ah+uRXcBz05yWl8FSpKWr4+Fw04HHh3anh/s+1IPz6115CJiUjv6+EA1Y/bV2IbJ/iRzSeYWFhZ6OLUkaZw+wn0e2D60vQ14bFzDqjpQVbNVNTszM9PDqSVJ4/QR7geB1wyumjkfeKKqnJKRpCmaOOee5EbgQmBrknngauAUgKq6DjgEXAwcAb4JvHatipUkdTMx3Kvq0gnHC/iV3iqSJK2ad6hKUoMMd0lqkOEuSQ0y3CWpQX3coaoVGL4bVJL65shdkhpkuEtSgwx3SWqQ4S5JDTLcJalBhrskNchwl6QGeZ27xvJbmaTNzZG7JDXIcJekBhnuktQgw12SGmS4S1KDDHdJalCncE+yO8lDSY4kuXLM8R1J7kjy2ST3Jrm4/1IlSV1NDPckW4BrgYuAM4FLk5w50ux3gZur6hxgH/D+vguVJHXXZeR+HnCkqh6uqm8DNwF7R9oU8AODx88CHuuvREnScnW5Q/V04NGh7XngBSNt3gb8dZI3AN8PvLSX6iRJK9Jl5J4x+2pk+1LghqraBlwMfCTJ9zx3kv1J5pLMLSwsLL9aSVInXcJ9Htg+tL2N7512uRy4GaCq/gl4OrB19Imq6kBVzVbV7MzMzMoqliRN1CXcDwO7kpyR5FQWPzA9ONLmP4CXACT5URbD3aG5JE3JxDn3qjqW5ArgdmALcH1V3Z/kGmCuqg4CbwY+kOTXWZyyuayqRqduTnrDKy1uJq4QKW0+nZb8rapDwKGRfVcNPX4AuKDf0iRJK+UdqpLUIMNdkhpkuEtSgwx3SWqQ4S5JDTLcJalBhrskNchwl6QGGe6S1CDDXZIaZLhLUoMMd0lqkOEuSQ3qtCqkdJzL/0qbgyN3SWqQ4S5JDTLcJalBhrskNahTuCfZneShJEeSXLlEm59P8kCS+5N8tN8yJUnLMfFqmSRbgGuBlwHzwOEkBwffm3q8zS7grcAFVfXVJD+4VgVLkibrMnI/DzhSVQ9X1beBm4C9I21+Cbi2qr4KUFVH+y1TkrQcXcL9dODRoe35wb5hzwOel+QfktyVZHdfBUqSlq/LTUwZs6/GPM8u4EJgG/D3Sc6qqq/9vydK9gP7AXbs2LHsYiVJ3XQJ93lg+9D2NuCxMW3uqqr/Ab6Y5CEWw/7wcKOqOgAcAJidnR19g2jS8B2dkrReukzLHAZ2JTkjyanAPuDgSJtPAi8CSLKVxWmah/ssVJLU3cRwr6pjwBXA7cCDwM1VdX+Sa5LsGTS7HXg8yQPAHcBvVtXja1W0JOnEUjWd2ZHZ2dmam5ubyrnX08kyLeMiYtL6SHJPVc1OaucdqpLUIMNdkhpkuEtSgwx3SWqQ4S5JDTLcJalBhrskNchwl6QGGe6S1CDDXZIa1GVVSGmi4WUWXIpAmj5H7pLUIMNdkhpkuEtSgwx3SWqQ4S5JDTLcJalBXgq5Bk6Wb1+StHE5cpekBnUK9yS7kzyU5EiSK0/Q7pIklWTi9/tJktbOxHBPsgW4FrgIOBO4NMmZY9o9E3gjcHffRUqSlqfLnPt5wJGqehggyU3AXuCBkXZvB94F/EavFWrTcSkCafq6TMucDjw6tD0/2PekJOcA26vq1h5rkyStUJdwz5h99eTB5CnAHwBvnvhEyf4kc0nmFhYWulcpSVqWLuE+D2wf2t4GPDa0/UzgLODTSR4BzgcOjvtQtaoOVNVsVc3OzMysvGpJ0gl1CffDwK4kZyQ5FdgHHDx+sKqeqKqtVbWzqnYCdwF7qmpuTSqWJE00Mdyr6hhwBXA78CBwc1Xdn+SaJHvWukBJ0vJ1ukO1qg4Bh0b2XbVE2wtXX5YkaTW8Q1WSGmS4S1KDXDhMa8obmqTpcOQuSQ0y3CWpQYa7JDXIOfee+AUdkjYSR+6S1CDDXZIa5LSM1o2XRUrrx5G7JDXIcJekBhnuktQgw12SGmS4S1KDDHdJapDhLkkN8jp3TYXXvEtry5G7JDWoU7gn2Z3koSRHklw55vibkjyQ5N4kf5fkuf2XKknqamK4J9kCXAtcBJwJXJrkzJFmnwVmq+ps4BbgXX0XKknqrsuc+3nAkap6GCDJTcBe4IHjDarqjqH2dwGv6rPIjcplfiVtVF3C/XTg0aHteeAFJ2h/OXDbuANJ9gP7AXbs2NGxRLXOD1el/nWZc8+YfTW2YfIqYBZ497jjVXWgqmaranZmZqZ7lZKkZekycp8Htg9tbwMeG22U5KXA7wAvrKpv9VOeJGkluozcDwO7kpyR5FRgH3BwuEGSc4A/AfZU1dH+y5QkLcfEcK+qY8AVwO3Ag8DNVXV/kmuS7Bk0ezfwDOAvknwuycElnk6StA463aFaVYeAQyP7rhp6/NKe69JJyg9XpX54h6okNchwl6QGGe6S1CBXhdSG5fy7tHKG+zK55ICkzcBpGUlqkCN3bQpO0UjL48hdkhpkuEtSg5yW0abjFI00mSN3SWqQI/cOvPxx43IUL43nyF2SGuTIXc1wFC99lyN3SWqQI3c1yVG8TnaG+xL8ELUdBr1ORoa7Tiqjb9qGvVrVKdyT7Ab+ENgCfLCq3jFy/GnAh4GfBB4HXllVj/RbqtQ/R/Vq1cRwT7IFuBZ4GTAPHE5ysKoeGGp2OfDVqvqRJPuAdwKvXIuC15JTMSe3pf7/DX1tRl1G7ucBR6rqYYAkNwF7geFw3wu8bfD4FuB9SVJV1WOta8JA1yRdfkd8A9BG0yXcTwceHdqeB16wVJuqOpbkCeA5wJf7KLJvBrr6tha/U75haDW6hHvG7BsdkXdpQ5L9wP7B5jeSPNTh/Cu1lQ365sLGrc26lmdN68o7V/xPT8r+WoXNVtdzu/zjLuE+D2wf2t4GPLZEm/kkTwWeBXxl9Imq6gBwoEthq5Vkrqpm1+Ncy7VRa7Ou5bGu5bGu5VltXV3uUD0M7EpyRpJTgX3AwZE2B4FfHDy+BPjUZphvl6RWTRy5D+bQrwBuZ/FSyOur6v4k1wBzVXUQ+FPgI0mOsDhi37eWRUuSTqzTde5VdQg4NLLvqqHH/w38XL+lrdq6TP+s0EatzbqWx7qWx7qWZ1V1xdkTSWqPq0JKUoM2fbgn2Z3koSRHklw55vhlSRaSfG7w87p1quv6JEeT3LfE8SR576Due5Ocu0HqujDJE0P9ddW4dmtQ1/YkdyR5MMn9SX51TJt177OOda17nyV5epJ/TvL5QV2/N6bN05J8bNBfdyfZuUHqmsprcnDuLUk+m+TWMcfWvb861rWy/qqqTfvD4ge8/wb8MHAq8HngzJE2lwHvm0JtPw2cC9y3xPGLgdtYvEfgfODuDVLXhcCtU+iv04BzB4+fCXxhzP/luvdZx7rWvc8GffCMweNTgLuB80fa/DJw3eDxPuBjG6SuqbwmB+d+E/DRcf9f0+ivjnWtqL82+8j9yaURqurbwPGlEaauqu5kzLX+Q/YCH65FdwHPTnLaBqhrKqrqS1X1mcHj/wQeZPHO52Hr3mcd61p3gz74xmDzlMHP6Adoe4EPDR7fArwkybgbDte7rqlIsg14OfDBJZqse391rGtFNnu4j1saYdwL72cHf8bfkmT7mOPT0LX2afipwZ/VtyX5sfU++eDP4XNYHPUNm2qfnaAumEKfDf6U/xxwFPibqlqyv6rqGHB8WZBp1wXTeU2+B/gt4H+XOD6V/upQF6ygvzZ7uHdZ9uAvgZ1VdTbwt3z3nXnaOi3ZMAWfAZ5bVT8O/BHwyfU8eZJnAB8Hfq2qvj56eMw/WZc+m1DXVPqsqr5TVT/B4l3j5yU5a6TJVPqrQ13r/ppM8grgaFXdc6JmY/ataX91rGtF/bXZw33i0ghV9XhVfWuw+QEW15zfCLos67Duqurrx/+srsX7G05JsnU9zp3kFBYD9M+r6hNjmkylzybVNc0+G5zza8Cngd0jh57sr5xgWZD1rmtKr8kLgD1JHmFx+vbFSf5spM00+mtiXSvtr80e7hOXRhiZk93D4pzpRnAQeM3gCpDzgSeq6kvTLirJDx2fZ0xyHou/I4+vw3nD4p3OD1bV7y/RbN37rEtd0+izJDNJnj14/H3AS4F/HWm27suCdKlrGq/JqnprVW2rqp0s5sSnqupVI83Wvb+61LXS/trUX7NX3ZZGeGOSPcAxFt+FL1uP2pLcyOJVFFuTzANXs/jhElV1HYt3/F4MHAG+Cbx2g9R1CfD6JMeA/wL2rfUv+MAFwKuBfxnM1wL8NrBjqLZp9FmXuqbRZ6cBH8ril+k8Bbi5qm7N9JcF6VLXVF6T42yA/upS14r6yztUJalBm31aRpI0huEuSQ0y3CWpQYa7JDXIcJekBhnuktQgw12SGmS4S1KD/g+KZPuwDp8M4AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "count, bins, ignored = plt.hist(DeltaT_TCR, 100, density=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.3545411341526896,\n",
       " 0.2913272059544135,\n",
       " 0.38170190208336513,\n",
       " 4.376450277829174)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(DeltaT_TCR),np.std(DeltaT_TCR), np.min(DeltaT_TCR),np.max(DeltaT_TCR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9407891225749152,\n",
       " 1.0154510821290672,\n",
       " 1.8778815726365852,\n",
       " 1.7326820139309325)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.percentile(DeltaT_TCR, 5), np.percentile(DeltaT_TCR, 10),np.percentile(DeltaT_TCR, 95), np.percentile(DeltaT_TCR, 90) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.135333651731879, 0.7652167067887492, 0.5350272726405247, 19.38074173813852)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(DeltaT_ECS),np.std(DeltaT_ECS), np.min(DeltaT_ECS),np.max(DeltaT_ECS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.290183164254417, 1.4130173419545313, 3.45603782381162, 2.9948177138278815)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.percentile(DeltaT_ECS, 5), np.percentile(DeltaT_ECS, 10),np.percentile(DeltaT_ECS, 95), np.percentile(DeltaT_ECS, 90)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.2837636367419236,\n",
       " 0.9214575648860129,\n",
       " 0.5350272726405247,\n",
       " 33.691244870596286)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(DeltaT_ECS_with_GHF),np.std(DeltaT_ECS_with_GHF), np.min(DeltaT_ECS),np.max(DeltaT_ECS_with_GHF)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.345049001654376, 1.475821446691046, 3.7896632506067176, 3.243759995377598)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.percentile(DeltaT_ECS_with_GHF, 5), np.percentile(DeltaT_ECS_with_GHF, 10),np.percentile(DeltaT_ECS_with_GHF, 95), np.percentile(DeltaT_ECS_with_GHF, 90)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}