01_Boulder_ClimateSignal.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Master's Thesis: Investigating Maximum Rainfall Trends in Colorado"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Institution:</b> University of Georgia <br>\n",
    "<b>Department:</b> Statistics <br>\n",
    "<b>Student:</b> Jeremy Mulcahey <br>\n",
    "<b>Advisor:</b> Dr. Lynne Seymour <br>\n",
    "<b>Last Edit:</b> 9/27/2016"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Section 0: Preparing data <br>\n",
    "Section 1: Mean<br>\n",
    "Section 2: Variance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Section 0: Preparing data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: fitdistrplus\n",
      "Loading required package: MASS\n",
      "Loading required package: survival\n",
      "Loading required package: caTools\n",
      "Loading required package: repr\n",
      "Loading required package: IRdisplay\n"
     ]
    }
   ],
   "source": [
    "require(fitdistrplus); # required for parameter estimation\n",
    "require(caTools);      # required for smoothing\n",
    "require(repr);         # required for resizing plots in IRKernel\n",
    "require(\"IRdisplay\");  # graphic embedding\n",
    "require(MASS);         # testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# establish working directorys\n",
    "setwd(\"C:/Users/jerem/Desktop/UGA/Master'sThesis/\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Data files for individual station names."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = read.csv(file = \"data/BOULDER_MonMax_GHCN.csv\", head=T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Adjust the data for later use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "165"
      ],
      "text/latex": [
       "165"
      ],
      "text/markdown": [
       "165"
      ],
      "text/plain": [
       "[1] 165"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create an index as x - used as needed\n",
    "month = seq(1,nrow(data),by=1)\n",
    "data = cbind(data,month)\n",
    "\n",
    "# first year of the data (changes by station name)\n",
    "firstYear = data$YEAR[1]\n",
    "\n",
    "# station name for plotting\n",
    "stationName = as.character(data$STATION_NAME[1])\n",
    "\n",
    "# -999 messed with the plotting - change to NA\n",
    "data[data==-999] = NA\n",
    "\n",
    "sum(is.na(data)) #print number of missing values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check number of years in the data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "116"
      ],
      "text/latex": [
       "116"
      ],
      "text/markdown": [
       "116"
      ],
      "text/plain": [
       "[1] 116"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data$YEAR[nrow(data)]-firstYear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "  1   2   3   4   5   6   7   8   9  10  11  12 \n",
       "117 117 117 117 117 117 117 117 117 117 117 117 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "table(data$MONTH)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make a data frame of all the 10 year periods following the first year for data collected at the station."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#create the first decade (first year and the following 9 years)\n",
    "max_PRCP = data.frame(data[which(data$YEAR < (firstYear + 10)),6])\n",
    "\n",
    "# add all the subsequent decades to the data frame incrementing by 1 year at a time\n",
    "for(year in c((data$YEAR[1] + 1):2005)){\n",
    "    max_PRCP = cbind(max_PRCP,data[which(data$YEAR >= year & data$YEAR < year+10),6])\n",
    "}\n",
    "\n",
    "# name the columns as the first year of the observed 10 year periods\n",
    "colnames(max_PRCP) = as.character(c(firstYear:2005))\n",
    "\n",
    "# set the missing values to NA\n",
    "max_PRCP[max_PRCP==-999] = NA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Section 1: Mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "options(repr.plot.width=9, repr.plot.height=5) #reduces the plot sizes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data2012 = data[which(data$YEAR<2013),]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# create for maximum rainfall\n",
    "maxTS = ts(data$Max.PRCP, start = firstYear, freq=12)\n",
    "\n",
    "# create regression line\n",
    "reg = lm(Max.PRCP. ~ month, data=data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "maxTS2012 = ts(data2012$Max.PRCP, start = firstYear, freq=12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "maxTSNoEvent = maxTS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "maxTSNoEvent[1389] = NA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "maxObs = max(na.omit(data2012$Max.PRCP.))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "smooth = runmean(data2012$Max.PRCP., 120)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "smoothTS = ts(smooth, start=firstYear, freq=12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1060"
      ],
      "text/latex": [
       "1060"
      ],
      "text/markdown": [
       "1060"
      ],
      "text/plain": [
       "[1] 1060"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "which(data2012$Max.PRCP.==maxObs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>STATION</th><th scope=col>STATION_NAME</th><th scope=col>YEAR</th><th scope=col>MONTH</th><th scope=col>Obs</th><th scope=col>Max.PRCP.</th><th scope=col>month</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1060</th><td>GHCND:USC00050848</td><td>BOULDER CO US    </td><td>1986             </td><td>4                </td><td>30               </td><td>904              </td><td>1060             </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllll}\n",
       "  & STATION & STATION\\_NAME & YEAR & MONTH & Obs & Max.PRCP. & month\\\\\n",
       "\\hline\n",
       "\t1060 & GHCND:USC00050848 & BOULDER CO US     & 1986              & 4                 & 30                & 904               & 1060             \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "     STATION           STATION_NAME  YEAR MONTH Obs Max.PRCP. month\n",
       "1060 GHCND:USC00050848 BOULDER CO US 1986 4     30  904       1060 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data2012[1060,]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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nGo0UccOrn3v4ijncdXlh2vf41Mcgcwd4B3LA7ZBcSBONT2QJ26+TK0e1PieLz+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\n4gAAM/8AjplyTupY09wAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(maxTS2012, xlab = \"Time (years)\", col = \"darkgrey\", lwd=1.75, ylab = \"Precipitation (1/10mm)\", \n",
    "     #main=sprintf(\"%s \\nObserved 24 Hour Max Rainfall \\nfrom %i to 2012 by Monthly Max\", stationName,firstYear),\n",
    "     ylim=c(0,1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+Uz03zp2/1W4hi45TzyppDx4miP2kTEIae2DBeHSN3uNOKQP+Xm0g4oF4UVwU69\neWpl1mbXmbo7/SI5UcxqVXTbbUlv1/F086Vv91uJY/0zDjUNZtuni0MMir2idMtvIw49jtuL\n45+VvLOQEEcE699yrqbBbNuBONpE9bPJ4miDLSAOHWa34vhXo5N3FtKQOKxuy3b+tQEmikMM\nRLvs/Bn7WPPt2PlvObcHeEAccqTaOS83EEfzz1kz5YziaKqL2nJkEIdu0nqqV0G7aVAc//79\ns9VhxqHa7ojjX1EVLkvPCChx/Gub+DRxzH/LuT3A7yoOvcgRh8PbiONlDGWOpimllCbOP4um\nDaGG6v9637ONpinTb3WCs0dxzBpCrBDEgThkZN2k3KwWhpr3YXG8HnSKQ51pyJOOpqn62G8E\nUVZqsK1hK+SvTiHqNPYo9XmNfX4j+y66VMVrxOaKw2pvYAl/sDj0AfFx4vj7faWv4C0oDjX6\nexCHPFKbGXBeobyeiaPwn36x0VSozh3aZPs0YpoyJQvnokqHODxt/RNl7HADS3hdcTy+sux4\nfTUyyzeAOetqv+KQXZguDmeZIw5Vtlsc4jzBPsrtpPWR2B6OsmbRpub0X9a1cjJDKdo25zdt\ndzyJ6tdGLwe2qTQNDSzgijVvOX/+HZbTsxHEoZbKKuLw/EJrXpU3S2+COOzjVI/cRHGoprcV\nR3vA9VqjwiorhuN1jLZhO/qvl6YeUSOOViBtHSc7cYZUNs9La79cOMOs+nbs9589vvP6YyqJ\niOP1knEBcfSMfrg4xOqRXRgrDnudeFaXFEd9/a1u7t/zt9qS4uhnlDgKd3Mdt/3drJp0IshV\n0GyTB+Hzp5mB7uTL9mVKacULEEfp5qSG8vXzqZDCek3ymnarySZiXeSfmeZExZE/K97zw31j\ncbxGqv01oPe+eI6njPdPzO6gOHrMIcVh/9pfTBzil57Y+a89j30tsGcTZuFZYrHeDnTE0S7f\nbcQhC7ej2xzq9YyX4rdvpDj+qbdTC9VIf/LOwjVJziYO1xhNw9ZvKCdiUyZZcTSueByPK4jD\nnlwzgGqA20eWONqt1eNng2rRhIija/yFOJzf+c0543hxFIUlDn3gO4VMmH+vt/h8OdnX9vvE\nIce1Gj4Vbx1x+IdVeaTQt0+U4v9/z9FoJ0sMijNu6YhDXPAoXHGUhSr8TuI4ZM1NX4fjJuL4\nZ784LQopjtd6+vfPvcb8T71d1Y72ZHE4GYnjTa2edj6t7jbLtjk7UouyPaloD+V+cdQX/krx\n+u3fv+fTJtizoeceM6LNsn0V7Ri4Jo3lxWHNsO0R+cwrDmsqnrk2vUlZHDKZaeIIMMeK4vhu\n/8rsPTsuIURZarYAABbNSURBVA6zkEqfOMxiNiPVlvUcuoV9+cisxfnE0ab4yksmqTvXRnDE\n0WbsEYc4PPQq9ImjEC2JSKJL7bDJkapLykOxOd58V1GaV0R94nC3DYrjdWG31YJdt4kuc22z\nFBG8K6G5kNmuGqv1WHHI3wrN/1PE4UlG/Pf24ijPrS2uAx+AHSmOojTDYE9ue+irkfKIo327\n3AxfuxYXFEfbnjwqVecccbweiAXuiOPVhgjqFJJjKA7+IHG4p2YyyVeDbSBZSK9qO5WOLSZ3\nSxyvRpXJvK214pD5FOa8qR32drLkVLSrxnusduKdfjvF5cShC72jOMrbqXl0/1pZHP/kVQyP\nOF775JvYrhqaEk0bU8Xxr0Mc7THwDNi8hmo7Zo6PUhwFJslmwQj3hInD/D8kjrZVYwN9UJuD\nWwYaEIcZXDs51XT7Xmb5kqN216A42idaefpNzRdGJUoc6sStXxz+6bdTRBxzECWOf2oI66PO\nWTr/AsUhB20pcbS/5oQ3bHG0x71vVdsby+dGM/F1bHEUeMVhEyUOKWh5CLXD0CGOxpdNcvZB\nb4Rgz2Dx/JSX7P/zvm0xnH4l9oijTk/Gdo+cZjCs2dHi8I+o3ZRaV3aKiGMOYsTRTHhzymkW\n0msQmt9DkeIQ89Y8b1pr2hgjDusYkUvHOgK7Dqt/1vv14mhq70os/pXWYTAsDrGu2lJibEwb\nahCniMPtnOyRlZxVRlTqPpCcpz5xyKGOF4cnoJ27s3ATEIfc8nni8C2jriU5lzjkdZIOcZhX\nDW7WzZHxz3op7hVHO9VNF6Qq7OPG0+cp4hDLbG5xvB50OMLMmE5Oq8LIUhxAw+Jwd+hKPnGo\n0VteHKphxDF/iMKcvavfRMXz9FOuQGuup4mjKHrEYRa3XxyvQ8X7K7VHHGaHUEWTdrt+mlEo\nVL/bvqcmDt/eCjNv+ue/1wjLttXAva04zKhajY0Wh20PxGEo1DXwV3+tc4vXpcPZxSHx3PXR\nLPR/zqcMX3dojBeH2GIvhVItktJaB5uJw+qOmgXfSLQnks4NFTItxOEMfCEmHnF00v4ykqNR\nFmJBF3LbcuJwZFEUpZGJydb8WEIcauInisM+FseJw1mynh77xVFvbH4nvNQvTzTWFkcbpF01\niONtxdGebKjRmFkcRac42qXUyKENYBo16lDnJx3iKFV+epcz1ZuKQw9ijzj83dF7OsUh36tW\nKYgHqYijH3vpIo7lCHypoga4GYM5xSGH0JprcSA2TVjiKJ5eeV0EFCcgM4uj2Kc4vMltKw4z\nqJ2j6O2NvXB94nDSFRJYXBztSHbl7LJncZRi29riaCrL1yum7DbiaNK1Y8vGEUcbQQxWnzh6\nDNJmPTD9neJo5szKaX5x6PWDOJpxfI2FGalyLXGUjjZCxVHax4NeCH3iUP1u24oRh9qqxCGH\n2hKHlbeTpy9kpDhkf4w4rGrzi6Mpt4g4rCmxdSCGXDbhKanE0RboFofcgzhK87Q9hrcSR2fm\nM4hDJuxO/OriMJ3yDVUH84nD44Dh+IhDDMPHiEPP0ARx6Ekwg2YPoQr4HuIwhaeIQwrBVA8X\nRzcziaPNAXE0OZq16IhDxJXDgDjM01Bx6PHcrTjahOzYOuoocchOjRGHfzp9ycn+dIjDU9e7\n593F4WaAOIaL6BkaLQ67BTNo3mdyivYujqY7ZXOU2gdaaWKoTi0vDnHQK6sNRPE1ijjaef5A\ncYjRmSwOK4A/3szisEI225zUPAuhCfmu4mjTl9uHxWEl6x1VEaVbHHo80xWHXGyIY0II3xS1\nfR8Qx6uBkeJoIiCOeHGU9rP1xOHuFKtkqjh6zTQw/daUxItD10UcvfgnyTp2ignisIfQE8kR\nRyuPTcShNpariMOE30Qc4oAfEkfnktFemUkcpWxtaPqt3KaKoykpnqqe2UkijkL3faI4Sv9T\nNTuIow0fKw4xXRPFYZKLFkezCpIQhyMMZ7dqoqurTpOIQ+Efs1KN+wrikIe8EYcI7s99KXGo\nFmXhUrSpuu08HBCHyWqMONyuLCQO3/g6+9pVgDheJRDHxuIwR5k/903EUcrR0CHEgMlKuqnm\nDMsUVy2p/D3rulTxfOLQB6ld2bddikP3zCqnJlRunVEc7riOEYejX7NbNWGPUEcdO1854YjD\njE+fOAo9KrsVh1wpm4hDpyPbf3txFGYcdE/kyjPt6qY6pv8VZaQ4dFOeJhGHonCG3+r7tuJQ\nO93c48Vh2nZ0EiwOp9vqaWk3nZ44/G028ZcWh1pRQ+IQ+QxNf7OcrfSCxFFaTXmabMfHOgpc\ncejeDvDW4vAezub5CHGI6XGWgRNpsjjseVLTbzW1kDhkz6yVNCgONXztpHj2OqOTtDj01InC\nW4tDJlXKfU63ZZOIQ+GMmjPeI8RRmuNrr+LwDoQcA/Oz1D/bNmSSTktd4ijV6KgpiROHvWu8\nOMzGbnHYHejsyfLiEEszShwmBWtgEIceM/NzmjhKWdgTqbQXWLug7NXn5t70wJonFaBUE7uw\nONoOiJ+l/ikT1wFlS5Y45FE6RRwijneLPaEd2akWzEZbHGYVmHTEzCKO8nPEoSVRlqWzrS0s\nQqghtCKZJMo1xGHC6OkuAsWhxs0eCNMB8dMqLxPXAWV6jjgsdekkdfpbicOum7w41BSpprxN\nIg6BM2r7FocMo6e7eEtxiOzMSCAO2fdR4tAOQBwuzqgtIQ598FuRTBLl0uJQKWwnDnGsRYhD\n9EZ2SWTaPlKTYSO7pSO3caaIw1TSq0CNwmzikOMtF4OzChDHzCGs5TBWHHqtlvaSUUNoRVK7\nm+2lWV7dwx8gDusokynMIQ6phnBxqCzfURyiN3IcSp20swo2FYccWNlCYRVXA+dfX9bA9Ilj\n2BwfIw5nUBIWR1nKjHU+uxKHGSnVZIQ41IAuLg63J4uIw5m6JoJoQVQVuXjF4Vk9urCqpOt0\ngjjE6HVH8URSu5vtTbvJiMM66IU4SjEQi4pDOVl0UHZ7UXGYYVctyPGQldoG7VHTu628zDSU\nKl68OOx5NgMrWxBVZxCHGgdf0g4fJQ77F22sONz19bbiaNOQLacsDtUfK7C16K3h0POnh3lm\ncdjjqxOQ426Ns2nHnWczsLIFUdVafqKOMwIecciRsRdkDzsQh7VUzU9rKK1DIFocpWd99Yqj\nO/dSrY13FofKsa2rD85FxCEPSs/BLyua/uoWxHjo7i8pDjUrcjT84lADK2dONd2Ul+OqOqQH\nWo2yHBk9bb28vThK+3ecGZVwcdgt+qLYkdRuMXMdTalWmkLW4i5kNqUz7zOIQ682u+U+cViD\nUNhV2sIquVI1UoqWdbejxaHS7xKH3ffZxSEO+FBxqEUpRwNxzMBgCHs8bHGUIeIQ66x8B3E4\nHRRY4hBj5DSh01BdtVdUqDjUcImW+sUhQ6spDBKHb0BtcajE5xdHm3rTuj31bqpzikPHCRKH\n0ZmQ3SeJQyFXjFxgw+KQQ+sbL88CWlMc1lEvw5vShep+UUwWR2l+domjXZV2i4X83xqPIXFY\nk+FcRSnchu0BtUb2/cWhJ0f2156SwgrtE4cZhSY84ijlcAyIo3BqvZ4HRfJeQ9MzN9DUouIw\n4UUxa6hkGmKPSdxastPF0f7vG+527Kw6uoNLiUOMi2diZcfk0lpBHPYsII65Q8hZX1UcVgpi\n0Y8Th8pGJOkJ3xZuWhBNiUVgN6GDWT1YTBwinm+427GTdbQ4rP54xVHKps1akKXUwFm99x9n\nsmPLi8NJRw+d7K+zMGYUh2cEHBCHZyX3RppPHObYt/vyFuJw98mBdAcJcegRjRCH08Si4vAH\ntUAcnpXcG2kucZSlmUW7L/JYsOMgjqJ0RsUauzXE0R6+Yrn5J8zXlgiohsBKx5OLiKzT9wy3\nv0Nt/xGHTxylnqNOcYgxC4rUKQ47bk8r4pHVlEq2Yx2aI8jk0y0OJ083DdmyFdYzNu2Rq6LJ\nwmZEnG6rQ0U1KI8jMzR6VOPEYSXe1it8uY0VhxmGkeLQQ2Cl48lFRNbp+4a7cxHInEWeXQPg\ngji2F4fblwhxlGbZiOddWcjEg8Th6VB75DrHplXKd3gXnhDtqrey04MquxUkDjtx1VC3OEoP\njrusjU2+YeKQAcXGOHHYUeYRh7e8l/2Iox2PxcVRulM3mzhKHWBuccitveLoqlR6xOHpWOcR\nY2ug2eGIo7QHdW5xeHoYIA7xo0McnnY9bVnisIo6I+tPR9ftmm/PJrlUdfBPFYd4Wi4pDneH\nbCENcXR2wUlDtuzZ1S8Ob8eixGF3TGxbTBw2c4nD2663xWFxdBIjjo7YPeIIa+TDxSGOlmTE\noX+kKA67v27H5hSH1WKvOEpTYqQ4nD2y6nri8Fbq3j2DOPrzddiDOIwgmmfB4jClJonDaiFG\nHB2LZAVxeLYHiaMtECkOXcQnDk9K6sBvp7Gr7cKu582iTxy+dlcThz94dzo6zChx+BoKYlfi\nUE9LsdQGxKFr9QfqKbWWOGRXjBlXFYd/68zisA7Gwd/IhTtoM4nDiutLfbo4wkEcM4XoFod8\nbs1vxzE5FCglcbQdN+IYDD9SHEFNxYkjKC1/kf62P1IcEcc84mjoEod+7teJKBUUKB1xlKbj\njTgCwo8SR2BTMeIITMtfZGh8R4tjMAVP+PXF0ZtcSMHu0UYczu4hcQQG6j0mOxLoKpeWOMTO\nLcQREC6w9JBhOsURmkKHOAZysbdvKY5R+xSriuP3csoqTuffWUMMvF52dntLBQYKW18R4ugt\nEyGOwBOeoJ3ri2NOhiZpsjh8VRHHElVqHofMcJwzxKA4fE/fRBzelh1xqKhhp0X+nfsQx9B+\nnzhGtzwgjs4cNhRH3770xHHO8p9b/eh+zbPzjCEGxOGUDinVFWglcfS3bItDRx3TM13zvcUx\nxJTx6Wwuss0txdHfSHriyLNb+/iW5TOG+Dhx6KeuOCJbdZqfRRxjk1ic8eLoaM78H5PD3AM0\nkzgCC64ojizrevLaIohruf+lSUfpMeMcONuh3hgjDs/TCR3qaH6ObqZLEnknkcQEdnHGAQDr\nsu41juu9fjT3NQ4AWJc13449itcih8ciIQBgDda9j+Nc38eRny7z3scBAOuyiztHAWBdEAcA\nRIM4ACAaxAEA0SAOAIgGcQBANIgDAKJBHAAQDeIAgGgSFQcAJM2Io3p+UUwmxZxSzSrRtMgq\nnDSzGiLFrFPMKdWsEk2LrMJJM6shUsw6xZxSzSrRtMgqnDSzGiLFrFPMKdWsEk2LrMJJM6sh\nUsw6xZxSzSrRtMgqnDSzGiLFrFPMKdWsEk2LrMJJM6shUsw6xZxSzSrRtMgqnDSzGiLFrFPM\nKdWsEk2LrMJJM6shUsw6xZxSzSrRtMgqnDSzGiLFrFPMKdWsEk2LrMJJM6shUsw6xZxSzSrR\ntMgqnDSzGiLFrFPMKdWsEk2LrMJJM6sh3jNrANgUxAEA0SAOAIgGcQBANIgDAKJBHAAQDeIA\ngGgQBwBEgzgAIBrEAQDRIA4AiAZxAEA0iAMAokEcABAN4gCAaBAHAESTgDi+mxzOeXa8tg/z\n88N+uHVW34ets/Km9cdv1m5NZbBuX1n2dU8sq8fWC8u/hLbOagTbi+PW/K3sY/13sy/m4cF6\nuHVW5/ph/tguK29afzzyTGxNYrCumw+WJ6t7/szqvlVW/iW0/XKPZ3Nx3PLX/H5nx0f5+Mpu\n1e/P/Fbt+FUPt87qln09qg1fm2XlTavi9Nyc0GCV+V8qj1N2Tiqrryqfv6N3qyn0L6Htl/sI\nthbH36xmzW/LarTu1dSes+rE8qf6JSEebp3V6bml2rFNVv606kSemxMarJ86tUeWJ5VVtvEU\n+pfQ5st9DFuL4286xWxWP47V+FbnkrfspB5unVWzL9sqq6607s0xktBgtSdDSWX1ekVX6Wyj\nKWwz8q/xLbOKY2tx3Ep7frOuh1tn9eRRLcBtsupK65jdnw8SGqxDVl7y+sQ8pawur5cql82m\nsMJeQpsv9zEkkOFrlA61bH9TGUk3qyff1cnkdvPrSeuS/ZRbisObVZad6suAaWVVfldXR/Pv\nLbNyl1AKyz2aBDJ8jdIlOz3K2zGVkXSzqrnnpzIBcYi06vPaNMShprC6OPq16e92zxRe2jdY\ntptCZwmlsNyjSSDDZpTqt8pOqYykm1XFIz+KnduJQ6R1qN7cS0Mcagqraxz36o3FhLL6rl6q\n/Onse8Os3CWUwnKPJoEM24PyK8sv9bPcDF++9aozWVUcn++wb5aVm9ZXfR3+uTmhwcqSnMJD\nVl10eVQ62ywrdwmlsNyjSSBDNUq3alKf15bv5jLzff3LzG5Wf2kcjs9bITfLyk0ra0lqsMQb\njwlllW2elW8JpbDco0lHHHn92+C7GrNL/Vv0Wp1XiodbZ/WXRfOm7GZZuWlJcSQ0WM9U7tWI\nJZTV8xd6fXfJNll5l1AKyz2adMTxvJ/vkP2kcSudm9Xd3Myx3Q1+blpic1KDdahv1/xJKqtz\nVn0M5LzZ/az+JZTCco8mHXE8np8jqE/SDvXDo/Vw46y+zK/2zbLyDZbYnM5gvd6/SGwKXx8F\n2SyrjiWUwHKPJh1xlPe/YT3JDzHaDzfOSrwm2Cwr32CJzekM1t/59jG9KXx9+HSzrDqWUALL\nPZoExAEA7wbiAIBoEAcARIM4ACAaxAEA0SAOAIgGcQBANIgDAKJBHAAQDeIAgGgQBwBEgzgA\nIBrEAQDRIA4AiAZxAEA0iAMAokEcABAN4gCAaBAHAESDOAAgGsQBANEgDgCIBnEAQDSIAwCi\nQRwAEA3iAIBoEAcARIM4ACAaxAEA0SAOAIgGcQBANIgDAKJBHAAQDeL4XDLB35OwStfTiEin\n64hKkDKI43MZI4579hgR6ZHdR9SChEEcH07omcaL43lUlPNxVDVIFsTx4cSJ42fUCUd1yvEz\nqh6kCuL4cBpxVD///l2y/PJ3gpBlzzOL70OWf4vSh2MlgUP9+PnTlLiesiw/P9t6HLLT35Zj\nlh2flzeOh3W6AyuBOD4cLY5Ldb2jOt6f5jjV1z/My4zf7Lve+ls9+ckussTlebHkXLd1qh58\nP7fUWvl+1oG9gDg+HC2O46M63Ov/878zhurR45i174mcs1tZbf6qnnxld1kiq16N/NTN1S2U\nZV6V/nmen9yycRdHIFEQx4ejxfFbP7q/np/qKxqPrH0H9vi8xHGof1RGcEq8xPH7fGzehX1k\nXB7dFYjjw7GucZTyf/NmrS78Xb1I+a3+UyXu18vxJY662PnvJcvtZsWBfcB0fjhjxPGoXsdc\nqhMTWeLYPmoqXPK/5/ldxYF9wHR+OP3i6Ch8/nsRcjiUqsRXdvi+3pU4yvJ6Przeg0Ec+4Lp\n/HD6xHHKrFvFX9c4ylt2vFWvVGSJupotjvYJ1zh2BuL4cPrE8ZPlt+qKRnvp89y8qXrI8voS\nqihRXRG9qWsch+f7LPUZxy/vquwLxPHh9Injddkibz9oUl8Qrbhmr1cgpsT5dbXjt23zp91Q\nXRHhPo5dgTg+nF5xVPeFZl/iA2qH1wuOR9YoxJT4yrLj7/V58vHcV985+hQGd47uDMQBEVxf\nH3O9ZnGfd73bV0vgzUEcEMPr07HH7HugoIZPx+4NxAEx1N/HoT6/EgLfx7E7EAdEcf2qPoQS\n+TVgX7xQ2RuIAwCiQRwAEA3iAIBoEAcARIM4ACAaxAEA0SAOAIgGcQBANIgDAKJBHAAQDeIA\ngGgQBwBEgzgAIBrEAQDRIA4AiAZxAEA0iAMAokEcABAN4gCAaBAHAESDOAAgGsQBANEgDgCI\nBnEAQDSIAwCiQRwAEA3iAIBo/gcscJubJVFlPwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(maxTS2012, xlab = \"Time (years)\", col = \"darkgrey\", lwd=1.75, ylab = \"Precipitation (1/10mm)\", \n",
    "     #main=sprintf(\"%s \\nObserved 24 Hour Max Rainfall \\nfrom %i to 2012 by Monthly Max\", stationName,firstYear),\n",
    "     ylim=c(0,1000))\n",
    "abline(h=maxObs, col=\"red\", lwd=.5, lty=5)\n",
    "points(smoothTS, col=4, type=\"l\", lwd=2)\n",
    "text(1986,maxObs+50,\n",
    "           sprintf(\"%i\",maxObs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "maxObs2 = max(na.omit(data$Max.PRCP.))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "smooth2 = runmean(data$Max.PRCP., 120)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "smoothTS2 = ts(smooth2, start=firstYear, freq=12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Jq8II6V5gfiWATEAWuCOJYu/BvFcc+r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\n5n96h3zNKOahXwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(maxTS, xlab = \"Time (years)\", col = \"darkgrey\", lwd=1.75, ylab = \"Precipitation (1/10mm)\", \n",
    "     #main=sprintf(\"%s \\nObserved 24 Hour Max Rainfall \\nfrom %i to 2012 by Monthly Max\", stationName,firstYear),\n",
    "     ylim=c(0,2500))\n",
    "abline(h=maxObs2, col=\"red\", lwd=.5, lty=5)\n",
    "points(smoothTS2, col=4, type=\"l\", lwd=2)\n",
    "text(2013,maxObs2+100,sprintf(\"%i\",maxObs2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "maxTSNoEvent = ts(maxTSNoEvent, start=firstYear, freq=12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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nJMJNiU80HbsbSmkM0rwPFQKHGYHYpjNO6hOMZKgBXwFcfnLudHlzuOtrohxmTB\nppz/gjhyqzjM9sVhXz6dHHFowFscAh6P2+10KodIZ+Z9+IujtdAIJncvqU+eXy6OfF4c/S+p\nfpdaIo7Pqmsv0v4t98qa4ohTxZg4YjUvxBGIZeLoHmRp/477xVsc91Ox9U7z87+WVzGTdkYc\nwX+W/EqrfzaFpdTO6BlxTBz696nF4mgvihMazBJkcLQ4SRLUHAvE0d2fYorDb58cHG9La+7u\nOBsWx9h+jzi2gKc4buZYTuG4mXOwkPKF4mibovVzplMcy2v+eXHMJ4X4eIqjmADW7ngHQiiO\n7rG/RRwhY0spjl7uMXEsP6RZFbk4GA1Vg6c46ibqsD1Nl1BR9cVhvnfba70PjE+Jnvs04tjA\n9/oJPMVx+B5xuDwC8hZLHNVoYzPY0a7hZ8TRfII4IDZhxjjcHjr9cHlskziqtjiaMw8/IY58\n5I3x6w+thf8YByTD96zK6fsz4KSEh8MVLeKoqq5J3uqy6BaHV9UTe073RJL+HQxxbBhfcZTz\nOMzpn1vWW+vRKu5VTCc1eU8cefcnd1fimNxz9i6OPMZINyzDWxxRcKyiEkVLHN929bPiaI63\n9O9gC8SxibGbn8BTHCfHvodHFVPJ6vENizjyZqw0dHR6xVEdzm9EHAsWb+B7/QQBTsdGAHGM\n558Sh/NpK80gji0Q4HRsBBaJo91Bqc+v/Jo4mmMOv3oSgji2gKc4XqfjzEPZFrFbcfhHgzjW\njAXG8O6qRDkyFoqj+h1uDYl+Ps5/TRz5DsQxspIQhyoQx4Lo5oscS4I4HEAcG2Djp2NnxGHS\niUN0xkBU+eTp2H2IwxY94lDFzsURZep1YnHM14w4IDY+4nheMiN5auyCKmaS/aA4XGqO87VX\nA3FsAA9xFM+NNU5PjV1cxVwyxDFW85b3L/uYGeJQhYc4zub4yl/HsPf+6lYxl6wnjsFvVQpx\n1CdF5VlDgDhgDTzE8Xn843P6mWzLCCeOGJ19xBEX+4Hilr/RDvEQR8SfAKk48hFxjHSXPVEu\njpUqigfi2ACIQ84WxLFlEMcG2Lk4pqY9LAZxxAVxbADEIUe1OHaAdQWy5nThJY4OCaJqi6Na\nYkkSGsQRF8SxAbYujrmKoxwPzYpjNCyavwPVnJzhQlCDhzgiEk4cMZiock6kNH9XujP5WHPa\nQBxyEMcKtNaUsY+WQkoQhxzEsQKIQzeIQw7iWIGOOOLMxwEPVhXH3/Xz/KbTZeZ+g4jj50Ec\nullRHK9Da7eafvIb4vh5EIduVhTHxWT/Pg9ye96z6YdBSsSxMBoPEMcKIA7drCiOrPX8x1FN\nGPwAAAwuSURBVMf0NbWbF8dYS6f5u9JMAvucjGXN6WJFcXQ2/cwkKtcSVYvDkozm70ojX8Sh\nkY0fcSTZExHHCjTrEHFoZN0xjvvnNoPhxjgQx16p1mElD9acLtY8HXtsDR0eJu9xvHVxjPai\naP6udMUR5WJF8GDdeRyXch5HdrqGmsehUhydF85ZoYMxjTtyxKGOjc8cVSaO9qkAxOFFJY4c\ncahky+JIddGkpc7mqBpxhME0t1pBHApJIo7ZRuAujhQM6m2N3dQtHHH4gTh0gzjkWMRR/UUc\noUAcull1AlgH/yoQx45BHLpZURx/2W+Io36NODxAHLpZs6vyOpljOQNs5DIOR6u0ciyNxI9e\nvU287cARhx+NgxGHRtYd4/hnzL98b2McTZtGHOEYiCNtONBj5cHR59GcXrsTR/OqK45hgLR/\nV5yPOyEJq59VuZrsviNxdOagDcUxNhoCcyAO3ax/OvZxmG8SiOPnQRy6STGP47x5cbRd0RFH\nNxHiWA7i0E2SCWCBqkgvDmPM2OUyiMMTxKEaxCGnN5ENcUQBcagGcchBHGuAOFSDOOTMT9eo\nP0Ici0EcqllRHKb3S+1bRbKGJRdHa4pY1Mj2BOJQzYriuO1UHBPJBnPR2RmcQRyqWbOr8sim\nn98mrAJx7BrEoZpVxzge0/c2F1WR8Dw/4lgDxKGadQdHb61Hq3hWkbBd9eZ5jSfri4NJTQJY\nV6rZ7FkVJc1qIgzE4QXrSjWIIxpWcaQMaFuwslSDOKJhE0fKeDYG4lAN4ohGVxwm30LMikAc\nqkEc0TCDG5Dqj1kRiEM1iCMmiGM5iEM1iCMmiGM5rCzVII6YtOZ9FS83ETOAA4gjJogDdspW\nxbGRHvA3SsQBO2O74ogfRQAQB+yTrYpjI7TFMXavMIDtgTiigjhgnyCOuNRzzREH7AnEEZfm\nIhXEATsCccQFccAuQRxxaWaMcjMO2BGIIy6IA3YJ4ohLRxypgwEIBeKIS1scqWMBCAbiiAvO\ngF2COOKCOGCXII64fKd+AewLxBEXZm/ALllVHH/XU3kH39PlL1YV2kAcsEtWFMfr0Hrk9PRT\nZPezqyEO2CUriuNisn+fJ0A+79n0U2T3s6shDtglK4ojaz049mGyGFXoA3HALllRHJ0daHpv\n2s+uhjhgl3DEERfEAbtk3TGO+7N8xRgHwLZZ83TssXVW5fCKUoU6EAfsknXncVzKeRzZ6co8\nDoAtw8zRyHAbDtgjiCMyiAP2SAJx3DJzuMWtQhGIA/bImuJ4nEx2y68/NeUcccAuWVEcj9IY\nF3N+5c+TmTzm2NGuhjhgj6wojnMxd+Pymfn1MocYVSgEb8AeWX3KuTm13nQ/brGwCoXs6bsA\nVKwujn+fPsqvTDlHHLBLVu2qnKvpoq/zr0w5RxywS9a8kU9W70Rm+oADcQDoZtV5HJdKF9nk\n8QbiAFAOM0cBQAziAAAxiAMAxCAOABCDOABAzKoTwJwnhyIOANWsKI4b4gDYCateVp9NX0wf\noAoAWINVxzge0xPNQ1QBACuw7uDorfVolUhVAEB8OKsCAGIQBwCIQRwAIEapOABANQv26vCi\n8EZjTFqjUhoWUbmjM6o5NEatMSatUSkNi6jc0RnVHBqj1hiT1qiUhkVU7uiMag6NUWuMSWtU\nSsMiKnd0RjWHxqg1xqQ1KqVhEZU7OqOaQ2PUGmPSGpXSsIjKHZ1RzaExao0xaY1KaVhE5Y7O\nqObQGLXGmLRGpTQsonJHZ1RzaIxaY0xao1IaFlG5ozOqOTRGrTEmrVEpDYuo3NEZ1Rwao9YY\nk9aolIZFVO7ojGoOjVFrjElrVErDIip3dEY1xzajBoCkIA4AEIM4AEAM4gAAMYgDAMQgDgAQ\ngzgAQAziAAAxiAMAxCAOABCDOABADOIAADGIAwDEIA4AEIM4AEAM4gAAMQrEcatiuGTmeK9f\nZpdX/2XqqG6H1FFZw3rzZ+qlWlbW42zM+aksqlfqhmVvQqmjWkB6cTyqZ2Ufy+dmX5uXh97L\n1FFdypfZK11U1rDevDLTWqpiZd2TryxLVM/sE9UzVVT2JpS+uctJLo5H9t2+N3N85a+zeRS/\nn9mj+OCv8zJ1VA9zfhULzsmisoZVcPosVrSy8uwdyutkLqqiOhfxvPfeVJvQ3oTSN/cFpBbH\ne6ua6teyWFvPYtNeTHFg+a/4kWi9TB3V6bOk+CBNVPawykA+ixWtrH9laC+TqYrKJN6E9iaU\nvLkvIbU43puztTWLP8di/RbHkg9z6rxMHVX1mUkV1VhYz2ofUbSy6oMhVVF9e3SFzhJtwjoi\nextPGZWM1OJ45P3ta8Zepo7qw6togGmiGgvraJ6fF4pW1sHk16w8MNcU1fXbVbkm24QF/SaU\nvLkvQUGE37V0KGX7p2VNDqP6cCsOJtNtX0tYV/MvTykOa1TGnMphQF1R5bdidDS7pYxq2IQ0\nNHcxCiL8rqWrOb3yx1HLmhxGVfLMTrkCcbTCKo9rdYijswmLwdFz0t92yya81idY0m3CQRPS\n0NzFKIiwWkvlqbKTljU5jKrglR1bH6YTRyusQ3FyT4c4OpuwGON4FicWFUV1K7oqb53dEkY1\nbEIamrsYBRHWO+XZZNfyXdasvix1q2uiKjh+zrAni2oY1rkch/8sVrSyjMpNeDDFoMur0Fmy\nqIZNSENzF6Mgws5aehQb9TO2/GyGmZ/rDzMPo3qHcTh+pkImi2oYlqlRtbJaJx4VRWWSR2Vr\nQhqauxg94sjKX4Nbsc6u5a/ovTiubL1MHdU7iuqkbLKohmG1xaFoZX1CeRZrTFFUnx/0cnZJ\nmqisTUhDcxejRxyf+XwH80/HVLphVM9mMke6CX7DsFqLVa2sQzld85+qqC6muAzkkmw+q70J\naWjuYvSI4/W5jqA8SDuUL4+9l4mjOjc/7cmisq2s1mI9K+t7/kLZJvxeCpIsqpEmpKC5i9Ej\njvz5Xq2n9kWM/ZeJo2r1CZJFZVtZrcV6Vtb7ePuobxN+Lz5NFtVIE1LQ3MUoEAcAbA3EAQBi\nEAcAiEEcACAGcQCAGMQBAGIQBwCIQRwAIAZxAIAYxAEAYhAHAIhBHAAgBnEAgBjEAQBiEAcA\niEEcACAGcQCAGMQBAGIQBwCIQRwAIAZxAIAYxAEAYhAHAIhBHAAgBnEAgBjEAQBiEAcAiEEc\nACAGcQCAGMQBAGIQBwCIQRwAIAZxAIAYxPG7mBbvN26Z7qcFNZ3uCzKBZhDH77JEHE/zWlDT\nyzwX5ALFII4fx/VI48vxsqiWy3FRNlAL4vhxZOL4t+iAozjk+LcoH2gFcfw4lTiKv+9/V5Nd\n3wcIxnyOLG4Hk91aqQ/HQgKH8vXnb5PifjImu3zKeh3M6b3kaMzxM7xxPKzzdWAlEMeP0xXH\ntRjvKPb3jzlO5fhH0834M7dy6V/x5p+5tlNcP4Mll7KsU/Hi9llSauX2yQN7AXH8OF1xHF/F\n7l7+n72PGIpXr6Opz4lczCMvFp+LN2fzbKcwRW/kX1lcWUKeZ0Xqf5/jk4dZNjgCSkEcP05X\nHH/lq+f3/akc0XiZ+gzs8TPEcSj/FEYYpPiK4+/zujkL+zIMj+4KxPHj9MY48vb/zcnabuJb\n0Un5K/7rpHjer8evOMpkl3eX5fHo1QP7gM354ywRx6vox1yLA5N2imP9qspwzd7vs2enHtgH\nbM4fZ1ocI4kv707I4ZB3UpzN4XZ/dsSR5/fL4XsOBnHsCzbnjzMljpPpTRX/jnHkD3N8FD2V\ndooyW18c9RvGOHYG4vhxpsTxz2SPYkSjHvq8VCdVDyYrh1BbKYoR0UdnjOPwOc9SHnH8cVZl\nXyCOH2dKHN9hi6y+0KQcEC24m28PpElx+Y52/NVl/qsXFCMizOPYFYjjx5kURzEv1JxbF6gd\nvh2Ol6kU0qQ4G3P8u38OPj6flTNHP8Jg5ujOQBwg4P69zPVuZNe7PvujJbBxEAdI+F4dezS3\nmYRduDp2byAOkFDej6Nz/YoL3I9jdyAOEHE/FxehCG8DdqajsjcQBwCIQRwAIAZxAIAYxAEA\nYhAHAIhBHAAgBnEAgBjEAQBiEAcAiEEcACAGcQCAGMQBAGIQBwCIQRwAIAZxAIAYxAEAYhAH\nAIhBHAAgBnEAgBjEAQBiEAcAiEEcACAGcQCAGMQBAGIQBwCIQRwAIAZxAICY/2ifvTBHk1O2\nAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#rollSmall = runmean(data$Max.PRCP., 300)\n",
    "plot(smoothTS, type=\"l\", xlab = \"Time (years)\", lwd=2,\n",
    "    ylab = \"Precipitation (1/10mm)\", col = 1\n",
    "     #main=\"Smoothed 24 hour max rainfall from 1898 to 2014\"\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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9JbCeGxoTjeJ+3xTZmNLCZ+3d0xkWE1poI4lqOVUuJmPB1ssKE4rir99yyXXo9U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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#rollSmall = runmean(data$Max.PRCP., 300)\n",
    "plot(smoothTS2, type=\"l\", xlab = \"Time (years)\", lwd=2,\n",
    "    ylab = \"Precipitation (1/10mm)\", col = 4, ylim=c(130,220)\n",
    "     #main=\"Smoothed 24 hour max rainfall from 1898 to 2014\"\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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U+6Fvo3rCqoejGuKDVxJJsf1Md2Y4kjzR3rHNJZOmwXMkkYlfehF4oj9nSpUdFW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\nH45g2w2tAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Smoothed 24 hour max rainfall from 1898 to 2014\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#rollSmall = runmean(data$Max.PRCP., 300)\n",
    "plot(smoothTS2, type=\"l\", xlab = \"Time (years)\", lwd=5,\n",
    "    ylab = \"Max Precipitation (1/10mm)\", col = 1, main=\"Smoothed 24 hour max rainfall from 1898 to 2014\")\n",
    "lines(smoothTS, col=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "means = apply(max_PRCP,2,mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1642"
      ],
      "text/latex": [
       "1642"
      ],
      "text/markdown": [
       "1642"
      ],
      "text/plain": [
       "[1] 1642"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sum(is.na(max_PRCP))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Can't use the apply function with all the NAs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1389"
      ],
      "text/latex": [
       "1389"
      ],
      "text/markdown": [
       "1389"
      ],
      "text/plain": [
       "[1] 1389"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "which(data$Max.PRCP.==maxObs2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data2= data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data2$Max.PRCP.[1389]=NA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "smooth3 = runmean(data2$Max.PRCP., 120)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "smoothTS3 = ts(smooth3, start = firstYear, freq=12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#create the first decade (first year and the following 9 years)\n",
    "max_PRCP2 = data.frame(data2[which(data2$YEAR < (firstYear + 10)),6])\n",
    "\n",
    "# add all the subsequent decades to the data frame incrementing by 1 year at a time\n",
    "# i.e. 1898-1907, 1898-1908, etc\n",
    "for(year in c((data2$YEAR[1] + 1):2005)){\n",
    "    max_PRCP2 = cbind(max_PRCP2,data2[which(data2$YEAR >= year & data2$YEAR < year+10),6])\n",
    "}\n",
    "\n",
    "# name the columns as the first year of the observed 10 year periods\n",
    "colnames(max_PRCP2) = as.character(c(firstYear:2005))\n",
    "\n",
    "# set the missing values to NA\n",
    "max_PRCP2[max_PRCP2==-999] = NA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "setEPS()\n",
    "postscript(\"pics/eventComp1.eps\")\n",
    "#rollSmall = runmean(data$Max.PRCP., 300)\n",
    "plot(smoothTS2, type=\"l\", xlab = \"Time (years)\", lwd=2,\n",
    "    ylab = \"Precipitation (1/10mm)\", col = 4, \n",
    "     #main=\"Smoothed 24 hour max rainfall from 1898 to 2014\"\n",
    "    )\n",
    "#lines(smoothTS3, col=2, lwd=2)\n",
    "lines(smoothTS, col=1, lwd=2)\n",
    "legend(\"topleft\",c(\"TS with event\",\"\", \"TS omitted event\"), lty = c(1,0,1),col=c(4,0,1),\n",
    "      lwd=c(2,0,2), bty=\"n\", cex = 1, pt.cex=1)\n",
    "dev.off()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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WTD4VjBzY0RB0TH6NHVP8JtxJH5EIfa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\nAIAYxAEAYhAHAIhBHAAgBnEAgJj/Ew29ldbcWsQAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#rollSmall = runmean(data$Max.PRCP., 300)\n",
    "plot(smoothTS2, type=\"l\", xlab = \"Time (years)\", lwd=2,\n",
    "    ylab = \"Precipitation (1/10mm)\", col = 4, \n",
    "     #main=\"Smoothed 24 hour max rainfall from 1898 to 2014\"\n",
    "    )\n",
    "#lines(smoothTS3, col=2, lwd=2)\n",
    "lines(smoothTS, col=1, lwd=2)\n",
    "legend(\"topleft\",c(\"TS with event\",\"\", \"TS omitted event\"), lty = c(1,0,1),col=c(4,0,1),\n",
    "      lwd=c(2,0,2), bty=\"n\", cex = 1, pt.cex=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "120"
      ],
      "text/latex": [
       "120"
      ],
      "text/markdown": [
       "120"
      ],
      "text/plain": [
       "[1] 120"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "length(smoothTS2)-1284"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "truncSmoothTS = ts(smoothTS[1284:1320], start=2004, freq=12)\n",
    "truncSmoothTS2 = ts(smoothTS2[1284:length(smoothTS2)], start=2004, freq=12)\n",
    "truncSmoothTS3 = ts(smoothTS3[1284:length(smoothTS3)], start=2004, freq=12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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v9+/CYmOI84piJj/Rc6BvnZ3qpfZM3JHovNYSGOSHRYkrvDUh2D3An/5OrERRHx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\nX/4pEAAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#rollSmall = runmean(data$Max.PRCP., 300)\n",
    "plot(truncSmoothTS2, type=\"l\", xlab = \"Time (years)\", lwd=4,\n",
    "    ylab = \"Max Precipitation (1/10mm)\", col = 4, \n",
    "     #main=\"Smoothed 24 hour max rainfall from 1898 to 2014\"\n",
    "    )\n",
    "lines(truncSmoothTS3, col=2, lwd=3)\n",
    "lines(truncSmoothTS, col=1, lwd=2)\n",
    "legend(\"topleft\",c(\"TS with event\",\"\", \"TS omitted event\",\"\", \"TS prior to event\"), lty = c(1,0,1,0,1),col=c(4,0,2,0,1),\n",
    "      lwd=c(2,0,2,0,2), bty=\"n\", cex = 1, pt.cex=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "smoothALL = runmean(data2$Max.PRCP., 1404/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "smoothAllTS = ts(smoothALL, start=firstYear, freq = 12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "smoothALLEvent = runmean(data$Max.PRCP., 1404/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "smoothAllEventTS = ts(smoothALLEvent, start = firstYear, freq = 12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1404"
      ],
      "text/latex": [
       "1404"
      ],
      "text/markdown": [
       "1404"
      ],
      "text/plain": [
       "[1] 1404"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "length(smoothAllTS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "702"
      ],
      "text/latex": [
       "702"
      ],
      "text/markdown": [
       "702"
      ],
      "text/plain": [
       "[1] 702"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "1404/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(smoothAllEventTS, type=\"l\", col=\"blue\", ylab=\"Smoothed Precipitation (1/10mm)\", xlab=\"Time (years)\")\n",
    "lines(smoothAllTS)\n",
    "legend(\"topleft\",c(\"Smoothing with Event\",\"\", \"Smoothing without Event\"), col = c(4,0,1),, lty=c(1,0,1), bty=\"n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Change point detection for mean signal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ERROR",
     "evalue": "Error in eval(expr, envir, enclos): object 'means1TS' not found\n",
     "output_type": "error",
     "traceback": [
      "Error in eval(expr, envir, enclos): object 'means1TS' not found\nTraceback:\n"
     ]
    }
   ],
   "source": [
    "means1TS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ERROR",
     "evalue": "Error in eval(expr, envir, enclos): object 'means1TS' not found\n",
     "output_type": "error",
     "traceback": [
      "Error in eval(expr, envir, enclos): object 'means1TS' not found\nTraceback:\n"
     ]
    }
   ],
   "source": [
    "means1TS[81]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data1st = data[which(data$YEAR<=1981),]\n",
    "data2nd = data[-which(data$YEAR<=1981),]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mean1sthalf = mean(na.omit(data1st$Max.PRCP.))\n",
    "v1 = var(na.omit(data1st$Max.PRCP.))\n",
    "mean2ndhalf = mean(na.omit(data2nd$Max.PRCP.))\n",
    "v2 = var(na.omit(data2nd$Max.PRCP.))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1898</li>\n",
       "\t<li>1899</li>\n",
       "\t<li>1900</li>\n",
       "\t<li>1901</li>\n",
       "\t<li>1902</li>\n",
       "\t<li>1903</li>\n",
       "\t<li>1904</li>\n",
       "\t<li>1905</li>\n",
       "\t<li>1906</li>\n",
       "\t<li>1907</li>\n",
       "\t<li>1908</li>\n",
       "\t<li>1909</li>\n",
       "\t<li>1910</li>\n",
       "\t<li>1911</li>\n",
       "\t<li>1912</li>\n",
       "\t<li>1913</li>\n",
       "\t<li>1914</li>\n",
       "\t<li>1915</li>\n",
       "\t<li>1916</li>\n",
       "\t<li>1917</li>\n",
       "\t<li>1918</li>\n",
       "\t<li>1919</li>\n",
       "\t<li>1920</li>\n",
       "\t<li>1921</li>\n",
       "\t<li>1922</li>\n",
       "\t<li>1923</li>\n",
       "\t<li>1924</li>\n",
       "\t<li>1925</li>\n",
       "\t<li>1926</li>\n",
       "\t<li>1927</li>\n",
       "\t<li>1928</li>\n",
       "\t<li>1929</li>\n",
       "\t<li>1930</li>\n",
       "\t<li>1931</li>\n",
       "\t<li>1932</li>\n",
       "\t<li>1933</li>\n",
       "\t<li>1934</li>\n",
       "\t<li>1935</li>\n",
       "\t<li>1936</li>\n",
       "\t<li>1937</li>\n",
       "\t<li>1938</li>\n",
       "\t<li>1939</li>\n",
       "\t<li>1940</li>\n",
       "\t<li>1941</li>\n",
       "\t<li>1942</li>\n",
       "\t<li>1943</li>\n",
       "\t<li>1944</li>\n",
       "\t<li>1945</li>\n",
       "\t<li>1946</li>\n",
       "\t<li>1947</li>\n",
       "\t<li>1948</li>\n",
       "\t<li>1949</li>\n",
       "\t<li>1950</li>\n",
       "\t<li>1951</li>\n",
       "\t<li>1952</li>\n",
       "\t<li>1953</li>\n",
       "\t<li>1954</li>\n",
       "\t<li>1955</li>\n",
       "\t<li>1956</li>\n",
       "\t<li>1957</li>\n",
       "\t<li>1958</li>\n",
       "\t<li>1959</li>\n",
       "\t<li>1960</li>\n",
       "\t<li>1961</li>\n",
       "\t<li>1962</li>\n",
       "\t<li>1963</li>\n",
       "\t<li>1964</li>\n",
       "\t<li>1965</li>\n",
       "\t<li>1966</li>\n",
       "\t<li>1967</li>\n",
       "\t<li>1968</li>\n",
       "\t<li>1969</li>\n",
       "\t<li>1970</li>\n",
       "\t<li>1971</li>\n",
       "\t<li>1972</li>\n",
       "\t<li>1973</li>\n",
       "\t<li>1974</li>\n",
       "\t<li>1975</li>\n",
       "\t<li>1976</li>\n",
       "\t<li>1977</li>\n",
       "\t<li>1978</li>\n",
       "\t<li>1979</li>\n",
       "\t<li>1980</li>\n",
       "\t<li>1981</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1898\n",
       "\\item 1899\n",
       "\\item 1900\n",
       "\\item 1901\n",
       "\\item 1902\n",
       "\\item 1903\n",
       "\\item 1904\n",
       "\\item 1905\n",
       "\\item 1906\n",
       "\\item 1907\n",
       "\\item 1908\n",
       "\\item 1909\n",
       "\\item 1910\n",
       "\\item 1911\n",
       "\\item 1912\n",
       "\\item 1913\n",
       "\\item 1914\n",
       "\\item 1915\n",
       "\\item 1916\n",
       "\\item 1917\n",
       "\\item 1918\n",
       "\\item 1919\n",
       "\\item 1920\n",
       "\\item 1921\n",
       "\\item 1922\n",
       "\\item 1923\n",
       "\\item 1924\n",
       "\\item 1925\n",
       "\\item 1926\n",
       "\\item 1927\n",
       "\\item 1928\n",
       "\\item 1929\n",
       "\\item 1930\n",
       "\\item 1931\n",
       "\\item 1932\n",
       "\\item 1933\n",
       "\\item 1934\n",
       "\\item 1935\n",
       "\\item 1936\n",
       "\\item 1937\n",
       "\\item 1938\n",
       "\\item 1939\n",
       "\\item 1940\n",
       "\\item 1941\n",
       "\\item 1942\n",
       "\\item 1943\n",
       "\\item 1944\n",
       "\\item 1945\n",
       "\\item 1946\n",
       "\\item 1947\n",
       "\\item 1948\n",
       "\\item 1949\n",
       "\\item 1950\n",
       "\\item 1951\n",
       "\\item 1952\n",
       "\\item 1953\n",
       "\\item 1954\n",
       "\\item 1955\n",
       "\\item 1956\n",
       "\\item 1957\n",
       "\\item 1958\n",
       "\\item 1959\n",
       "\\item 1960\n",
       "\\item 1961\n",
       "\\item 1962\n",
       "\\item 1963\n",
       "\\item 1964\n",
       "\\item 1965\n",
       "\\item 1966\n",
       "\\item 1967\n",
       "\\item 1968\n",
       "\\item 1969\n",
       "\\item 1970\n",
       "\\item 1971\n",
       "\\item 1972\n",
       "\\item 1973\n",
       "\\item 1974\n",
       "\\item 1975\n",
       "\\item 1976\n",
       "\\item 1977\n",
       "\\item 1978\n",
       "\\item 1979\n",
       "\\item 1980\n",
       "\\item 1981\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1898\n",
       "2. 1899\n",
       "3. 1900\n",
       "4. 1901\n",
       "5. 1902\n",
       "6. 1903\n",
       "7. 1904\n",
       "8. 1905\n",
       "9. 1906\n",
       "10. 1907\n",
       "11. 1908\n",
       "12. 1909\n",
       "13. 1910\n",
       "14. 1911\n",
       "15. 1912\n",
       "16. 1913\n",
       "17. 1914\n",
       "18. 1915\n",
       "19. 1916\n",
       "20. 1917\n",
       "21. 1918\n",
       "22. 1919\n",
       "23. 1920\n",
       "24. 1921\n",
       "25. 1922\n",
       "26. 1923\n",
       "27. 1924\n",
       "28. 1925\n",
       "29. 1926\n",
       "30. 1927\n",
       "31. 1928\n",
       "32. 1929\n",
       "33. 1930\n",
       "34. 1931\n",
       "35. 1932\n",
       "36. 1933\n",
       "37. 1934\n",
       "38. 1935\n",
       "39. 1936\n",
       "40. 1937\n",
       "41. 1938\n",
       "42. 1939\n",
       "43. 1940\n",
       "44. 1941\n",
       "45. 1942\n",
       "46. 1943\n",
       "47. 1944\n",
       "48. 1945\n",
       "49. 1946\n",
       "50. 1947\n",
       "51. 1948\n",
       "52. 1949\n",
       "53. 1950\n",
       "54. 1951\n",
       "55. 1952\n",
       "56. 1953\n",
       "57. 1954\n",
       "58. 1955\n",
       "59. 1956\n",
       "60. 1957\n",
       "61. 1958\n",
       "62. 1959\n",
       "63. 1960\n",
       "64. 1961\n",
       "65. 1962\n",
       "66. 1963\n",
       "67. 1964\n",
       "68. 1965\n",
       "69. 1966\n",
       "70. 1967\n",
       "71. 1968\n",
       "72. 1969\n",
       "73. 1970\n",
       "74. 1971\n",
       "75. 1972\n",
       "76. 1973\n",
       "77. 1974\n",
       "78. 1975\n",
       "79. 1976\n",
       "80. 1977\n",
       "81. 1978\n",
       "82. 1979\n",
       "83. 1980\n",
       "84. 1981\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912\n",
       "[16] 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927\n",
       "[31] 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942\n",
       "[46] 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957\n",
       "[61] 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972\n",
       "[76] 1973 1974 1975 1976 1977 1978 1979 1980 1981"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "unique(data1st$YEAR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "anotherTS = smoothTS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: changepoint\n",
      "Loading required package: zoo\n",
      "\n",
      "Attaching package: 'zoo'\n",
      "\n",
      "The following objects are masked from 'package:base':\n",
      "\n",
      "    as.Date, as.Date.numeric\n",
      "\n",
      "Successfully loaded changepoint package version 2.2.1\n",
      " NOTE: Predefined penalty values have changed.  Previous penalty values with a postfix 1 i.e. SIC1 are now without i.e. SIC and previous penalties without a postfix i.e. SIC are now with a postfix 0 i.e. SIC0. See NEWS and help files for further details.\n"
     ]
    }
   ],
   "source": [
    "require(changepoint)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Class 'cpt' : Changepoint Object\n",
       "       ~~   : S4 class containing 12 slots with names\n",
       "              date version data.set cpttype method test.stat pen.type pen.value minseglen cpts ncpts.max param.est \n",
       "\n",
       "Created on  : Tue Sep 13 17:22:34 2016 \n",
       "\n",
       "summary(.)  :\n",
       "----------\n",
       "Created Using changepoint version 2.2.1 \n",
       "Changepoint type      : Change in mean \n",
       "Method of analysis    : AMOC \n",
       "Test Statistic  : Normal \n",
       "Type of penalty       : MBIC with value, 21.68952 \n",
       "Minimum Segment Length : 1 \n",
       "Maximum no. of cpts   : 1 \n",
       "Changepoint Locations : 1007 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cpt.mean(anotherTS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>STATION</th><th scope=col>STATION_NAME</th><th scope=col>YEAR</th><th scope=col>MONTH</th><th scope=col>Obs</th><th scope=col>Max.PRCP.</th><th scope=col>month</th><th scope=col>box</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1007</th><td>GHCND:USC00050848</td><td>BOULDER CO US    </td><td>1981             </td><td>11               </td><td>30               </td><td>53               </td><td>1007             </td><td>1                </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllllll}\n",
       "  & STATION & STATION\\_NAME & YEAR & MONTH & Obs & Max.PRCP. & month & box\\\\\n",
       "\\hline\n",
       "\t1007 & GHCND:USC00050848 & BOULDER CO US     & 1981              & 11                & 30                & 53                & 1007              & 1                \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "     STATION           STATION_NAME  YEAR MONTH Obs Max.PRCP. month box\n",
       "1007 GHCND:USC00050848 BOULDER CO US 1981 11    30  53        1007  1  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data[1007,]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1380"
      ],
      "text/latex": [
       "1380"
      ],
      "text/markdown": [
       "1380"
      ],
      "text/plain": [
       "[1] 1380"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "1404"
      ],
      "text/latex": [
       "1404"
      ],
      "text/markdown": [
       "1404"
      ],
      "text/plain": [
       "[1] 1404"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "length(smoothTS)\n",
    "nrow(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tShapiro-Wilk normality test\n",
       "\n",
       "data:  smoothTS\n",
       "W = 0.98121, p-value = 1.981e-12\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "shapiro.test(smoothTS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0cL6dIqBxXhlVjeBzDBWZUDRfI2gC8Ex2EYpiBeBMdRYngPwAJPgwOA1344qs0H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\nEQ2QbJP2AAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Normal Q-Q Plot\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qqnorm(smoothTS);qqline(smoothTS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#setEPS()\n",
    "#postscript(\"pics/tri.eps\")\n",
    "#hist(smoothTS,breaks=40,xlab=\"Precipitation (1/10mm)\", main=\"\")\n",
    "#dev.off()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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O2pal+lVH7/XL2tAR0Fcfhq4jEW4pjL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\ngg==",
      "text/plain": [
       "Plot with title \"Histogram of smoothTS\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(smoothTS,breaks=40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>159.644230769231</li>\n",
       "\t<li>159.5</li>\n",
       "\t<li>166.038461538462</li>\n",
       "\t<li>166.971153846154</li>\n",
       "\t<li>166</li>\n",
       "\t<li>166.855769230769</li>\n",
       "\t<li>165.490384615385</li>\n",
       "\t<li>165.173076923077</li>\n",
       "\t<li>166.201923076923</li>\n",
       "\t<li>168.105769230769</li>\n",
       "\t<li>168.788461538462</li>\n",
       "\t<li>169.663461538462</li>\n",
       "\t<li>170.769230769231</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 159.644230769231\n",
       "\\item 159.5\n",
       "\\item 166.038461538462\n",
       "\\item 166.971153846154\n",
       "\\item 166\n",
       "\\item 166.855769230769\n",
       "\\item 165.490384615385\n",
       "\\item 165.173076923077\n",
       "\\item 166.201923076923\n",
       "\\item 168.105769230769\n",
       "\\item 168.788461538462\n",
       "\\item 169.663461538462\n",
       "\\item 170.769230769231\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 159.644230769231\n",
       "2. 159.5\n",
       "3. 166.038461538462\n",
       "4. 166.971153846154\n",
       "5. 166\n",
       "6. 166.855769230769\n",
       "7. 165.490384615385\n",
       "8. 165.173076923077\n",
       "9. 166.201923076923\n",
       "10. 168.105769230769\n",
       "11. 168.788461538462\n",
       "12. 169.663461538462\n",
       "13. 170.769230769231\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] 159.6442 159.5000 166.0385 166.9712 166.0000 166.8558 165.4904 165.1731\n",
       " [9] 166.2019 168.1058 168.7885 169.6635 170.7692"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "smoothTS[998:1010]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>159.644230769231</li>\n",
       "\t<li>159.5</li>\n",
       "\t<li>166.038461538462</li>\n",
       "\t<li>166.971153846154</li>\n",
       "\t<li>166</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 159.644230769231\n",
       "\\item 159.5\n",
       "\\item 166.038461538462\n",
       "\\item 166.971153846154\n",
       "\\item 166\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 159.644230769231\n",
       "2. 159.5\n",
       "3. 166.038461538462\n",
       "4. 166.971153846154\n",
       "5. 166\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 159.6442 159.5000 166.0385 166.9712 166.0000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "anotherTS[998:1002]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "83"
      ],
      "text/latex": [
       "83"
      ],
      "text/markdown": [
       "83"
      ],
      "text/plain": [
       "[1] 83"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "996/12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1980"
      ],
      "text/latex": [
       "1980"
      ],
      "text/markdown": [
       "1980"
      ],
      "text/plain": [
       "[1] 1980"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "1897+83"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "115"
      ],
      "text/latex": [
       "115"
      ],
      "text/markdown": [
       "115"
      ],
      "text/plain": [
       "[1] 115"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "length(smoothTS)/12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "anotherTS[1:1007] = mean1sthalf\n",
    "anotherTS[1008:length(smoothTS)] = mean2ndhalf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ywBkxHLpO7J0e3lLW5TLgFTEcvEVRXI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\nFAdQ7D9hS7OFRwr2twAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(anotherTS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vA85PAljrH0q4lDmw7KmoYdFjf2zCOdiRTL1DYDPcQxi6M4mk8bi/12UefP95/L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",
      "text/plain": [
       "Plot with title \"Smoothed 24 hour max rainfall from 1898 to 2012\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#rollSmall = runmean(data$Max.PRCP., 300)\n",
    "plot(smoothTS2, type=\"l\", xlab = \"Time (years)\", lwd=2,\n",
    "    ylab = \"Max Precipitation (1/10mm)\", col = 1, main=\"Smoothed 24 hour max rainfall from 1898 to 2012\")\n",
    "    #points(rollLarge, type=\"l\", col=4)\n",
    "    #egend(0,200, c(\"300 window\",\"\", \"900 window\"), col=c(2,0,4), lty=c(1,0,1), bty=\"n\")\n",
    "    lines(anotherTS,col=2,lwd=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data1st2 = data2[which(data2$YEAR<=1981),]\n",
    "data2nd2 = data2[-which(data2$YEAR<=1981),]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mean1sthalf2 = mean(na.omit(data1st2$Max.PRCP.))\n",
    "mean2ndhalf2 = mean(na.omit(data2nd2$Max.PRCP.))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "188.402266288952"
      ],
      "text/latex": [
       "188.402266288952"
      ],
      "text/markdown": [
       "188.402266288952"
      ],
      "text/plain": [
       "[1] 188.4023"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean2ndhalf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "182.386363636364"
      ],
      "text/latex": [
       "182.386363636364"
      ],
      "text/markdown": [
       "182.386363636364"
      ],
      "text/plain": [
       "[1] 182.3864"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean2ndhalf2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "anotherTS2 = anotherTS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "anotherTS2[1:1007] = mean1sthalf2\n",
    "anotherTS2[1008:length(smoothTS)] = mean2ndhalf2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "155.953724604966"
      ],
      "text/latex": [
       "155.953724604966"
      ],
      "text/markdown": [
       "155.953724604966"
      ],
      "text/plain": [
       "[1] 155.9537"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean1sthalf2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "182.386363636364"
      ],
      "text/latex": [
       "182.386363636364"
      ],
      "text/markdown": [
       "182.386363636364"
      ],
      "text/plain": [
       "[1] 182.3864"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean2ndhalf2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "177.623762376238"
      ],
      "text/latex": [
       "177.623762376238"
      ],
      "text/markdown": [
       "177.623762376238"
      ],
      "text/plain": [
       "[1] 177.6238"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "smoothTS[1048]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AFxrIyjOOoBfot1nmj3f3yrxHNW40QmjqGjC1NJxNGvH0ocXpo6Bo7iOJU9Dptb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\nAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#rollSmall = runmean(data$Max.PRCP., 300)\n",
    "plot(smoothTS, type=\"l\", xlab = \"Time (years)\", lwd=2,\n",
    "    ylab = \"Max Precipitation (1/10mm)\", col = 1, \n",
    "     #main=\"Smoothed 24 hour max rainfall from 1898 to 2012\"\n",
    "    )\n",
    "    #points(rollLarge, type=\"l\", col=4)\n",
    "    #egend(0,200, c(\"300 window\",\"\", \"900 window\"), col=c(2,0,4), lty=c(1,0,1), bty=\"n\")\n",
    "    lines(anotherTS2,col=2,lwd=3)\n",
    "    legend(\"topleft\",c(\"Trend Line\",\"\",\"Mean prior and post change point\"), lty=c(1,0,1), lwd=c(2,0,2), col=c(1,0,2),\n",
    "    bty=\"n\", cex = .8, pt.cex=.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1380"
      ],
      "text/latex": [
       "1380"
      ],
      "text/markdown": [
       "1380"
      ],
      "text/plain": [
       "[1] 1380"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "length(smoothTS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1404"
      ],
      "text/latex": [
       "1404"
      ],
      "text/markdown": [
       "1404"
      ],
      "text/plain": [
       "[1] 1404"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "length(smoothTS2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data[\"box\"] = as.numeric(data$YEAR>=1981)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data2[\"box\"] = as.numeric(data2$YEAR>=1981)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "156.339816933638"
      ],
      "text/latex": [
       "156.339816933638"
      ],
      "text/markdown": [
       "156.339816933638"
      ],
      "text/plain": [
       "[1] 156.3398"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(na.omit(data2[which(data2$box == 0),\"Max.PRCP.\"]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "180.587912087912"
      ],
      "text/latex": [
       "180.587912087912"
      ],
      "text/markdown": [
       "180.587912087912"
      ],
      "text/plain": [
       "[1] 180.5879"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(na.omit(data2[which(data2$box == 1),\"Max.PRCP.\"]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In is.na(object): is.na() applied to non-(list or vector) of type 'NULL'"
     ]
    },
    {
     "ename": "ERROR",
     "evalue": "Error in var(na.omit(data2[which(data2$box == 0), \"M`ax.PRCP.\"])): 'x' is NULL\n",
     "output_type": "error",
     "traceback": [
      "Error in var(na.omit(data2[which(data2$box == 0), \"M`ax.PRCP.\"])): 'x' is NULL\nTraceback:\n",
      "1. var(na.omit(data2[which(data2$box == 0), \"M`ax.PRCP.\"]))"
     ]
    }
   ],
   "source": [
    "var(na.omit(data2[which(data2$box == 0),\"M`ax.PRCP.\"]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "21874.0941785487"
      ],
      "text/latex": [
       "21874.0941785487"
      ],
      "text/markdown": [
       "21874.0941785487"
      ],
      "text/plain": [
       "[1] 21874.09"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "var(na.omit(data2[which(data2$box == 1),\"Max.PRCP.\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Box plots with noise from the event"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fmngN9t/WHwUcdrfmb7upysPp7b7vjt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\nTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "boxplot(data$Max.PRCP.~data$box)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A little less noise in the box plots by removing the event"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "setEPS()\n",
    "postscript(\"pics/fullBBox.eps\")\n",
    "boxplot(data2$Max.PRCP. ~ data2$box, xlab = \"Group (0=pre change point, 1=post change point)\",\n",
    "       col = c(\"blue\",\"green\"), ylab = \"Precipitation (1/10mm)\")\n",
    "dev.off()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KR5PzqwH+M4ZZJvRxBWYYrdNVfJbnd5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\nYv8BGVLK0LZG58YAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "boxplot(data2$Max.PRCP. ~ data2$box, xlab = \"Group (0=pre change point, 1=post change point)\",\n",
    "       col = c(\"blue\",\"green\"), ylab = \"Precipitation (1/10mm)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "indicator = c(rep(0,1007),rep(1,373))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1380"
      ],
      "text/latex": [
       "1380"
      ],
      "text/markdown": [
       "1380"
      ],
      "text/plain": [
       "[1] 1380"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "length(indicator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "115"
      ],
      "text/latex": [
       "115"
      ],
      "text/markdown": [
       "115"
      ],
      "text/plain": [
       "[1] 115"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "1380/12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "meansBox = as.data.frame(cbind(smoothTS,indicator))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "meansBoxSea = as.data.frame(cbind(smoothTS, rep(c(1,2,3,4,5,6,7,8,9,10,11,12),115)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "names(meansBoxSea) = c(\"precipitation\",\"month\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, can see the difference in the mean of the smoothed signals, however, given the actual variance of the data, the significance here is debatable - not to mention the independence assumption is not valid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABDgAAAJYCAMAAACw6qbdAAAANlBMVEUAAAAAAP8A/wBNTU1o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\nRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "boxplot(meansBox$smoothTS ~ meansBox$indicator, xlab = \"Group (0=pre change point, 1=post change point)\",\n",
    "       col = c(\"blue\",\"green\"), ylab = \"Precipitation (1/10mm)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  Variances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "vars1 = NULL\n",
    "for(i in 1:(length(max_PRCP))){\n",
    "    vars1 = c(vars1,var(na.omit(max_PRCP2[,i])))\n",
    "}\n",
    "vars1TS = ts(vars1, start = firstYear)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Time Series:\n",
       "Start = 1898 \n",
       "End = 2005 \n",
       "Frequency = 1 \n",
       "  [1] 15735.445 16735.987 21717.573 21413.277 20911.507 20214.089 19024.025\n",
       "  [8] 19370.459 19138.029 20172.380 20669.951 19906.785 11160.880 11160.880\n",
       " [15] 12257.411 12257.411 12403.928 10693.007  9738.124  9159.137 10643.624\n",
       " [22] 12057.087 16897.540 16811.445 16855.751 15592.587 15460.528 15301.591\n",
       " [29] 16331.526 17620.114 16467.833 19074.140 15891.415 14795.405 14265.135\n",
       " [36] 17592.027 17560.073 20464.765 19856.686 18820.315 19267.625 15618.359\n",
       " [43] 19993.306 21174.749 24261.373 23429.325 23363.168 19541.288 18462.987\n",
       " [50] 19181.076 24157.529 24284.032 20359.226 20334.972 17473.730 15668.663\n",
       " [57] 17485.983 17917.805 18603.220 17700.123 12800.595 12895.826 18311.969\n",
       " [64] 19158.864 19788.176 19715.589 18549.150 19624.154 19825.643 19614.951\n",
       " [71] 20238.990 23020.257 18520.727 16617.942 15134.727 17396.821 20128.606\n",
       " [78] 20188.919 19639.970 25445.023 26833.222 24427.260 24427.260 26299.775\n",
       " [85] 28620.467 28642.189 25127.827 24689.448 29739.018 24828.903 26272.644\n",
       " [92] 27680.726 27680.726 26108.475 24263.847 22971.381 25218.301 24873.447\n",
       " [99] 20995.786 20001.355 15441.223 14739.436 16434.138 16519.090 16812.487\n",
       "[106] 17456.845 15148.631 16444.685"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vars1TS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rollSmall = ts(runmean(vars1TS,15),start=firstYear)\n",
    "rollSmall2 = ts(runmean(vars1TS,30),start=firstYear)\n",
    "rollSmall3 = ts(runmean(vars1TS,50),start=firstYear)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>png:</strong> 2"
      ],
      "text/latex": [
       "\\textbf{png:} 2"
      ],
      "text/markdown": [
       "**png:** 2"
      ],
      "text/plain": [
       "png \n",
       "  2 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "setEPS()\n",
    "postscript(\"pics/var1.eps\")\n",
    "plot(vars1TS, type=\"l\", xlab = \"Time (years)\", lwd=2,\n",
    "    ylab = \"Precipitation (1/10mm)^2\", col = 1)\n",
    "lines(rollSmall, col=3,lwd=2)\n",
    "lines(rollSmall2, col=2,lwd=2)\n",
    "lines(rollSmall3, col=4,lwd=2)\n",
    "legend(\"topleft\",c(\"Variance, of Intervals\",\"\",\"Small Smoothing\", \"\",\"Medium Smoothing\",\"\",\"Large Smoothing\"),\n",
    "      col = c(1,0,3,0,2,0,4), lty = c(1,0,1,0,1,0,1), lwd=c(2,2,2,2), bty=\"n\")\n",
    "dev.off()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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sLCe8S/4tfLGz7iUK7DgIO6wIAWs6tCCsvpjaEWLG1MSxFW5KCZI0IcV7VFtb5Z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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(vars1TS, type=\"l\", xlab = \"Time (years)\", lwd=2,\n",
    "    ylab = \"Precipitation (1/10mm)^2\", col = 1)\n",
    "lines(rollSmall, col=3,lwd=2)\n",
    "lines(rollSmall2, col=2,lwd=2)\n",
    "lines(rollSmall3, col=4,lwd=2)\n",
    "legend(\"topleft\",c(\"Variance, of Intervals\",\"\",\"Small Smoothing\", \"\",\"Medium Smoothing\",\"\",\"Large Smoothing\"),\n",
    "      col = c(1,0,3,0,2,0,4), lty = c(1,0,1,0,1,0,1), lwd=c(2,2,2,2), bty=\"n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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yFzy0UbLMQhZmFJgn4731Fwd/zaWVccHd+/fkrX7c/vrfXfitW/VcSh+sI9BYny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\nZCAOAAAZiAMAQAbiAACQgTgAAGT+D7HigcTQRuiMAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(sqrt(vars1TS), type=\"l\", xlab = \"Time (years)\", lwd=2,\n",
    "    ylab = \"Precipitation (1/10mm)^2\", col = 1)\n",
    "lines(sqrt(rollSmall), col=3,lwd=2)\n",
    "lines(sqrt(rollSmall2), col=2,lwd=2)\n",
    "lines(sqrt(rollSmall3), col=4,lwd=2)\n",
    "legend(\"topleft\",c(\"Standard Deviation, of Intervals\",\"\",\"Small Smoothing\", \"\",\"Medium Smoothing\",\"\",\"Large Smoothing\"),\n",
    "      col = c(1,0,3,0,2,0,4), lty = c(1,0,1,0,1,0,1), lwd=c(2,2,2,2), bty=\"n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "setEPS()\n",
    "postscript(\"pics/stdBoulder1.eps\")\n",
    "plot(sqrt(vars1TS), type=\"l\", xlab = \"Time (years)\", lwd=2,\n",
    "    ylab = \"Precipitation (1/10mm)^2\", col = 1)\n",
    "lines(sqrt(rollSmall), col=3,lwd=2)\n",
    "lines(sqrt(rollSmall2), col=2,lwd=2)\n",
    "lines(sqrt(rollSmall3), col=4,lwd=2)\n",
    "legend(\"topleft\",c(\"Standard Deviation, of Intervals\",\"\",\"Small Smoothing\", \"\",\"Medium Smoothing\",\"\",\"Large Smoothing\"),\n",
    "      col = c(1,0,3,0,2,0,4), lty = c(1,0,1,0,1,0,1), lwd=c(2,2,2,2), bty=\"n\")\n",
    "dev.off()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": []
  }
 ],
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