From 458faaa66be7ebe542750d47b9480bc254aeb6b7 Mon Sep 17 00:00:00 2001
From: David Anthoff <anthoff@berkeley.edu>
Date: Mon, 13 Jan 2014 12:24:44 -0800
Subject: [PATCH] science: Update climate dynamics calibration

---
 Fund/Data/Base/lifetempconst.csv              |    2 +-
 Fund/Data/Base/lifetemplin.csv                |    2 +-
 Fund/Data/Base/lifetempqd.csv                 |    2 +-
 .../HadCRUT.4.2.0.0.annual_ns_avg_smooth.txt  |  163 +++
 .../climate/climateforcing.radforc.csv        | 1050 +++++++++++++++++
 calibration/climate/fund_cs_calibration.ipynb |  421 +++++++
 6 files changed, 1637 insertions(+), 3 deletions(-)
 create mode 100644 calibration/climate/HadCRUT.4.2.0.0.annual_ns_avg_smooth.txt
 create mode 100644 calibration/climate/climateforcing.radforc.csv
 create mode 100644 calibration/climate/fund_cs_calibration.ipynb

diff --git a/Fund/Data/Base/lifetempconst.csv b/Fund/Data/Base/lifetempconst.csv
index 728e3adb..9e04993e 100644
--- a/Fund/Data/Base/lifetempconst.csv
+++ b/Fund/Data/Base/lifetempconst.csv
@@ -1,2 +1,2 @@
 # FUND scenario
-~N(-31.8978379263215;0.12072054186561)
+-42.7421952811
diff --git a/Fund/Data/Base/lifetemplin.csv b/Fund/Data/Base/lifetemplin.csv
index 8f419268..170a0ed5 100644
--- a/Fund/Data/Base/lifetemplin.csv
+++ b/Fund/Data/Base/lifetemplin.csv
@@ -1,2 +1,2 @@
 # FUND scenario
-~N(32.7266970287432;0.0256648976380545)
+29.0603120788
diff --git a/Fund/Data/Base/lifetempqd.csv b/Fund/Data/Base/lifetempqd.csv
index c202f764..763e2b70 100644
--- a/Fund/Data/Base/lifetempqd.csv
+++ b/Fund/Data/Base/lifetempqd.csv
@@ -1,2 +1,2 @@
 # FUND scenario
-~N(-0.00993;0.001568)
+0.0014564222822
diff --git a/calibration/climate/HadCRUT.4.2.0.0.annual_ns_avg_smooth.txt b/calibration/climate/HadCRUT.4.2.0.0.annual_ns_avg_smooth.txt
new file mode 100644
index 00000000..bbdf9dc2
--- /dev/null
+++ b/calibration/climate/HadCRUT.4.2.0.0.annual_ns_avg_smooth.txt
@@ -0,0 +1,163 @@
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+1968   -0.074   -0.090   -0.055   -0.086   -0.062   -0.109   -0.039   -0.095   -0.051   -0.115   -0.032
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diff --git a/calibration/climate/climateforcing.radforc.csv b/calibration/climate/climateforcing.radforc.csv
new file mode 100644
index 00000000..6f19dd39
--- /dev/null
+++ b/calibration/climate/climateforcing.radforc.csv
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diff --git a/calibration/climate/fund_cs_calibration.ipynb b/calibration/climate/fund_cs_calibration.ipynb
new file mode 100644
index 00000000..f1ee2e5f
--- /dev/null
+++ b/calibration/climate/fund_cs_calibration.ipynb
@@ -0,0 +1,421 @@
+{
+ "metadata": {
+  "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import numpy as np\n",
+      "import pandas\n",
+      "from math import log\n",
+      "from scipy.optimize import leastsq\n",
+      "import statsmodels.api as sm"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 1
+    },
+    {
+     "cell_type": "heading",
+     "level": 1,
+     "metadata": {},
+     "source": [
+      "FUND climate dynamics calibration"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "I. Introduction"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "This file calibrates the climatedynamics component. The general strategy is to fit the FUND climate component to observed past temperature data for various values of climate sensitivity using forcing output from FUND by adjusting the lifetemp parameter of the climate component. This gives a best-fit value for lifetemp for each climate sensitivity value. In a second step a regression is run to arrive at a simple formula for lifetemp as a function of climate sensitivity that is used in the actual model."
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "II. Load data"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Data obtained from http://www.metoffice.gov.uk/hadobs/hadcrut4/data/current/download.html on 12/2/2013 by Anthoff.\n",
+      "\n",
+      "Direct link http://www.metoffice.gov.uk/hadobs/hadcrut4/data/current/time_series/HadCRUT.4.2.0.0.annual_ns_avg_smooth.txt)."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "hadcrut4_file = pandas.read_csv('HadCRUT.4.2.0.0.annual_ns_avg_smooth.txt', \n",
+      "                                   header=None, delim_whitespace=True, index_col=0, \n",
+      "                                   usecols=[0,1], names=['year','temp'])"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 2
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Run FUND in default configuration and save the variable radforc in the climateforcing component to a text file."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "fundrf_file = pandas.read_csv('climateforcing.radforc.csv', names=['year','rf'], index_col=0)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 3
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "III. Prepare data"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "df_obs = pandas.DataFrame(index=range(1950,2001))\n",
+      "  \n",
+      "df_obs['temp'] = (hadcrut4_file -hadcrut4_file.loc[1850:1870].mean())\n",
+      "df_obs['rf'] = fundrf_file['rf']\n",
+      "   \n",
+      "df_obs.plot()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 4,
+       "text": [
+        "<matplotlib.axes.AxesSubplot at 0x9edfb00>"
+       ]
+      },
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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ATl4Ou87sYv3x9aw/sZ70m+n0dulNL+de9HLuRfPazWW6AiHMhKKoE5V9+qna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\nrkJggg==\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x9edf780>"
+       ]
+      }
+     ],
+     "prompt_number": 4
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "IV. Fit step"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Code for the climate dynamics component in FUND"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "def ClimateForcingModule(rf, lifetemp, t0, cs):\n",
+      "    temp = []\n",
+      "    temp.append(t0)\n",
+      "    \n",
+      "    delaytemp = 1.0/lifetemp\n",
+      "    temps = cs / 5.35 / log(2.0)\n",
+      "    \n",
+      "    for t in range(0,len(rf)):                   \n",
+      "        temp.append(temp[t] + delaytemp * temps * rf[t] - delaytemp * temp[t])\n",
+      "        \n",
+      "    return temp"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 5
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Code that computes the residuals between the climate dynamics component and observations for a given set of parameters"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "def residuals(lifetemp,temp,rf, t0, cs): \n",
+      "    calculated = ClimateForcingModule(rf[1:],lifetemp, t0, cs)\n",
+      "    rr = temp-calculated\n",
+      "    return rr"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 6
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Fit the model for all climate sensitivities between 1.5 and 15.5 (stepsize 0.1), the calibrated parameter is lifetemp."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "css = np.arange(1.5,15.5,0.1)\n",
+      "lifetemps = np.zeros(len(css))\n",
+      "\n",
+      "for ix, cs in enumerate(css):\n",
+      "    pqrs = leastsq(residuals, [66.0],args=(df_obs['temp'].values,df_obs['rf'].values, 0.2, cs))\n",
+      "    lifetemps[ix] = pqrs[0][0]    "
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 7
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "fittedvalues = pandas.DataFrame(lifetemps, index=css)\n",
+      "fittedvalues.plot()\n",
+      "xlabel('climate sensitivity')\n",
+      "ylabel('lifetemp')"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 8,
+       "text": [
+        "<matplotlib.text.Text at 0xa048c18>"
+       ]
+      },
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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oae9eePppaNxYG0aStp3CLKr63SkT0kJUQmEhxMXBW2/B22/D8OFyl7MwF5fd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\nEEIIUYoUByGEEKX8f4VOkam2uV2XAAAAAElFTkSuQmCC\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0xa047ac8>"
+       ]
+      }
+     ],
+     "prompt_number": 8
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "V. Regression step"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Run a regression lifetemp ~ cs + cs^2."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "x1 = css\n",
+      "x2 = css**2.0\n",
+      "y = lifetemps\n",
+      "\n",
+      "x = np.column_stack((x1,x2))\n",
+      "x = sm.add_constant(x, prepend=True)\n",
+      "\n",
+      "res = sm.OLS(y,x).fit()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 9
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "print res.params"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "[ -4.27421953e+01   2.90603121e+01   1.45642228e-03]\n"
+       ]
+      }
+     ],
+     "prompt_number": 10
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "print res.bse"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "[ 0.00755182  0.00201893  0.00011682]\n"
+       ]
+      }
+     ],
+     "prompt_number": 11
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "print res.summary()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "                            OLS Regression Results                            \n",
+        "==============================================================================\n",
+        "Dep. Variable:                      y   R-squared:                       1.000\n",
+        "Model:                            OLS   Adj. R-squared:                  1.000\n",
+        "Method:                 Least Squares   F-statistic:                 2.372e+09\n",
+        "Date:                Fri, 28 Feb 2014   Prob (F-statistic):               0.00\n",
+        "Time:                        17:31:07   Log-Likelihood:                 349.22\n",
+        "No. Observations:                 140   AIC:                            -692.4\n",
+        "Df Residuals:                     137   BIC:                            -683.6\n",
+        "Df Model:                           2                                         \n",
+        "==============================================================================\n",
+        "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
+        "------------------------------------------------------------------------------\n",
+        "const        -42.7422      0.008  -5659.850      0.000       -42.757   -42.727\n",
+        "x1            29.0603      0.002   1.44e+04      0.000        29.056    29.064\n",
+        "x2             0.0015      0.000     12.467      0.000         0.001     0.002\n",
+        "==============================================================================\n",
+        "Omnibus:                       42.103   Durbin-Watson:                   0.723\n",
+        "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              820.842\n",
+        "Skew:                          -0.243   Prob(JB):                    5.71e-179\n",
+        "Kurtosis:                      14.852   Cond. No.                         513.\n",
+        "==============================================================================\n"
+       ]
+      }
+     ],
+     "prompt_number": 12
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "print 'Half life CS 3:', res.params[0] + res.params[1] * 3.0 + res.params[2] * 9.0"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Half life CS 3: 44.4518487557\n"
+       ]
+      }
+     ],
+     "prompt_number": 13
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "VI. Output"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Write the input files for the model."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "with open('../../Fund/Data/Base/lifetempconst.csv','w') as f:\n",
+      "    f.write('# FUND scenario\\n')\n",
+      "    f.write(str(res.params[0]))\n",
+      "    f.write('\\n')\n",
+      "    \n",
+      "with open('../../Fund/Data/Base/lifetemplin.csv','w') as f:\n",
+      "    f.write('# FUND scenario\\n')\n",
+      "    f.write(str(res.params[1]))\n",
+      "    f.write('\\n')\n",
+      "    \n",
+      "with open('../../Fund/Data/Base/lifetempqd.csv','w') as f:\n",
+      "    f.write('# FUND scenario\\n')\n",
+      "    f.write(str(res.params[2]))\n",
+      "    f.write('\\n')    "
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 14
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}
\ No newline at end of file