error-space-diagram-single.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Error-space diagram - example for 1 input pair, 1 derived var, 1 region"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Load needed packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: oce\n",
      "Loading required package: gsw\n",
      "Loading required package: lattice\n",
      "Loading required package: survival\n",
      "Loading required package: Formula\n",
      "Loading required package: ggplot2\n",
      "\n",
      "Attaching package: ‘Hmisc’\n",
      "\n",
      "The following objects are masked from ‘package:base’:\n",
      "\n",
      "    format.pval, round.POSIXt, trunc.POSIXt, units\n",
      "\n"
     ]
    }
   ],
   "source": [
    "library(seacarb)\n",
    "library(Hmisc)   #for minor ticks in plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Get routines and specify input vars"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1 Read in new and modified functions "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The commands below read in routines that have been modified (derivnum and errors) or are completely new relative to the standard version of the seacarb distribution.  You can get these new and modified routines from github:\n",
    "\n",
    "git clone https://github.com/jamesorr/seacarb-git.git\n",
    "\n",
    "Then just change the directory in the 4 lines of the cell just below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "source(\"/homel/orr/Software/R/seacarb-git-orr/R/errhalf.R\")\n",
    "source(\"/homel/orr/Software/R/seacarb-git-orr/R/errmid.R\")\n",
    "source(\"/homel/orr/Software/R/seacarb-git-orr/R/errors.R\")\n",
    "source(\"/homel/orr/Software/R/seacarb-git-orr/R/derivnum.R\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2 Specify input variables and their corresponding uncertainties (errors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Specify flag & corresponding 2 input variables \n",
    "  flag = 15\n",
    "\n",
    "# Input variables:\n",
    "# ----------------\n",
    "# Approximate regional mean for Southern Ocean (picked off of Fig. 3.2 from Orr, 2011)\n",
    "# For ALK & DIC input pair\n",
    "  ALK  = 2295e-6  #(umol/kg)\n",
    "  DIC  = 2155e-6\n",
    "\n",
    "  temp = -0.49    #C\n",
    "  salt = 33.96    #psu\n",
    "  press = 0       #bar\n",
    "\n",
    "  Phos = 2.e-6    #(umol/kg)\n",
    "  Sil = 60.e-6    #(umol/kg)\n",
    "\n",
    "# Uncertainties in input variables\n",
    "# ---------------------------------\n",
    "  ALK_e <- seq(0., 20., 1.0) * 1e-6\n",
    "  DIC_e <- ALK_e\n",
    "  pCO2_e <- seq(0,20,1)\n",
    "  pH_e   <- seq(0,0.03,0.0015)\n",
    "\n",
    "  salt_e = 0.01   \n",
    "  temp_e = 0.01   \n",
    "\n",
    "  Pt_e = 0.1e-6\n",
    "  Sit_e = 4.0e-6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3 Default uncertainties in equilibrium constants (pK0, pK1, pK2, pKb, pKw, pKa, pKc, Bt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Estimates for errors in constants in errors.R routine (from Orr et al., 2017)\n",
    "  epKstd  <- c(0.004, 0.015,  0.03, 0.01,  0.01, 0.02, 0.02, 0.01)\n",
    "# epKstd  <- c(0.004, 0.015,  0.03, 0.01,  0.01, 0.02, 0.02)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3 Compute derived carbonate system vars with std seacarb routine `carb`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>H</th><th scope=col>pH</th><th scope=col>CO2</th><th scope=col>fCO2</th><th scope=col>pCO2</th><th scope=col>HCO3</th><th scope=col>CO3</th><th scope=col>OmegaAragonite</th><th scope=col>OmegaCalcite</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>7.729963e-09</td><td>8.111823</td><td>2.122323e-05</td><td>329.0886</td><td>330.5511</td><td>0.002029921</td><td>0.000103856</td><td>1.570135</td><td>2.504053</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllllll}\n",
       "  & H & pH & CO2 & fCO2 & pCO2 & HCO3 & CO3 & OmegaAragonite & OmegaCalcite\\\\\n",
       "\\hline\n",
       "\t1 & 7.729963e-09 & 8.111823 & 2.122323e-05 & 329.0886 & 330.5511 & 0.002029921 & 0.000103856 & 1.570135 & 2.504053\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "             H       pH          CO2     fCO2     pCO2        HCO3         CO3\n",
       "1 7.729963e-09 8.111823 2.122323e-05 329.0886 330.5511 0.002029921 0.000103856\n",
       "  OmegaAragonite OmegaCalcite\n",
       "1       1.570135     2.504053"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute derived carbonate system variables with standard seacarb routine 'carb':\n",
    "\n",
    "# Southern Ocean\n",
    "vars <- carb  (flag=15, var1=ALK, DIC, S=salt, T=temp, Patm=1, P=press, Pt=Phos, Sit=Sil, \n",
    "                    k1k2='w14', kf='dg', ks=\"d\", pHscale=\"T\", b=\"u74\", gas=\"potential\", warn='n')\n",
    "\n",
    "pH <- vars$pH\n",
    "pCO2 <- vars$pCO2\n",
    "\n",
    "# Compute H+ from pH, i.e., pH = -log10[H+], where [H+] is the hydrogen ion concentration in mol/kg\n",
    "H = 10^(-1*vars$pH)\n",
    "\n",
    "# Keep only key columns to be consistent with output from 'errors.R' routine (called below)\n",
    "vars <- data.frame(H, vars[,c('pH','CO2','fCO2','pCO2','HCO3','CO3','OmegaAragonite','OmegaCalcite')] )\n",
    "vars\n",
    "\n",
    "# Duplicate rows in *vars* until same as number of members of error vector ALK_e\n",
    "numerrs <- length(ALK_e)\n",
    "vars <- vars[rep(row.names(vars), numerrs), ]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.4 Use 1-D error vectors to build 2-D error array (to plot contours in DIC-ALK space)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "  dat <- expand.grid(DIC_e, ALK_e)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.5 Specify state-of-art (soa) errors for vars: from error-propagation manuscript (Orr et al. 2017, Table 1) \n",
    "\n",
    "These will be plotted as crosses on the error-space diagrams"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 2\n",
       "2. 2\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 2 2"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
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    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "</ol>\n"
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       "\\begin{enumerate*}\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 2\n",
       "2. 2\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 2 2"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "ALK_e_soa   <- 2 #umol/kg\n",
    "DIC_e_soa   <- 2 #umol/kg\n",
    "\n",
    "ALK_e_soa2  <- c(ALK_e_soa, ALK_e_soa)\n",
    "DIC_e_soa2  <- c(DIC_e_soa, DIC_e_soa)\n",
    "\n",
    "ALK_e_soa2\n",
    "DIC_e_soa2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Compute derived variables (with `carb`) and propagated errors (with `errors`)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1 Computations of derived vars and their errors (for At-Ct pair only) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In seacarb::Kb(S, T, P, pHscale = pHscale, kSWS2scale = kSWS2scale, : S and/or T is outside the range of validity of the formulation available for Kb in seacarb.Warning message:\n",
      "In seacarb::Kb(S, T, P, pHscale = pHscale, kSWS2scale = kSWS2scale, : S and/or T is outside the range of validity of the formulation available for Kb in seacarb.Warning message:\n",
      "In seacarb::Kw(S, T, P, pHscale = pHscale, kSWS2scale = kSWS2scale): S and/or T is outside the range of validity of the formulation available for Kw in seacarb.Warning message:\n",
      "In seacarb::Kw(S, T, P, pHscale = pHscale, kSWS2scale = kSWS2scale): S and/or T is outside the range of validity of the formulation available for Kw in seacarb.Warning message:\n",
      "In seacarb::Kspa(S, T, P): S and/or T is outside the range of validity of the formulation available for Kspa in seacarb.Warning message:\n",
      "In seacarb::Kspa(S, T, P): S and/or T is outside the range of validity of the formulation available for Kspa in seacarb.Warning message:\n",
      "In seacarb::Kspc(S, T, P): S and/or T is outside the range of validity of the formulation available for Kspc in seacarb.Warning message:\n",
      "In seacarb::Kspc(S, T, P): S and/or T is outside the range of validity of the formulation available for Kspc in seacarb.Warning message:\n",
      "In seacarb::Kb(S, T, P, pHscale = pHscale, kSWS2scale = kSWS2scale, : S and/or T is outside the range of validity of the formulation available for Kb in seacarb.Warning message:\n",
      "In seacarb::Kb(S, T, P, pHscale = pHscale, kSWS2scale = kSWS2scale, : S and/or T is outside the range of validity of the formulation available for Kb in seacarb.Warning message:\n",
      "In seacarb::Kw(S, T, P, pHscale = pHscale, kSWS2scale = kSWS2scale): S and/or T is outside the range of validity of the formulation available for Kw in seacarb.Warning message:\n",
      "In seacarb::Kw(S, T, P, pHscale = pHscale, kSWS2scale = kSWS2scale): S and/or T is outside the range of validity of the formulation available for Kw in seacarb.Warning message:\n",
      "In seacarb::Kspa(S, T, P): S and/or T is outside the range of validity of the formulation available for Kspa in seacarb.Warning message:\n",
      "In seacarb::Kspa(S, T, P): S and/or T is outside the range of validity of the formulation available for Kspa in seacarb.Warning message:\n",
      "In seacarb::Kspc(S, T, P): S and/or T is outside the range of validity of the formulation available for Kspc in seacarb.Warning message:\n",
      "In seacarb::Kspc(S, T, P): S and/or T is outside the range of validity of the formulation available for Kspc in seacarb."
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>H</th><th scope=col>pH</th><th scope=col>CO2</th><th scope=col>fCO2</th><th scope=col>pCO2</th><th scope=col>HCO3</th><th scope=col>CO3</th><th scope=col>OmegaAragonite</th><th scope=col>OmegaCalcite</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>7.729963e-09</td><td>8.111823</td><td>2.122323e-05</td><td>329.0886</td><td>330.5511</td><td>0.002029921</td><td>0.000103856</td><td>1.570135</td><td>2.504053</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllllll}\n",
       "  & H & pH & CO2 & fCO2 & pCO2 & HCO3 & CO3 & OmegaAragonite & OmegaCalcite\\\\\n",
       "\\hline\n",
       "\t1 & 7.729963e-09 & 8.111823 & 2.122323e-05 & 329.0886 & 330.5511 & 0.002029921 & 0.000103856 & 1.570135 & 2.504053\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "             H       pH          CO2     fCO2     pCO2        HCO3         CO3\n",
       "1 7.729963e-09 8.111823 2.122323e-05 329.0886 330.5511 0.002029921 0.000103856\n",
       "  OmegaAragonite OmegaCalcite\n",
       "1       1.570135     2.504053"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>H</th><th scope=col>pH</th><th scope=col>CO2</th><th scope=col>fCO2</th><th scope=col>pCO2</th><th scope=col>HCO3</th><th scope=col>CO3</th><th scope=col>OmegaAragonite</th><th scope=col>OmegaCalcite</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>4.139159</td><td>0.2216044</td><td>4.929374</td><td>5.014682</td><td>5.014689</td><td>0.1866465</td><td>2.7889</td><td>5.383828</td><td>5.383828</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllllll}\n",
       "  & H & pH & CO2 & fCO2 & pCO2 & HCO3 & CO3 & OmegaAragonite & OmegaCalcite\\\\\n",
       "\\hline\n",
       "\t1 & 4.139159 & 0.2216044 & 4.929374 & 5.014682 & 5.014689 & 0.1866465 & 2.7889 & 5.383828 & 5.383828\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "         H        pH      CO2     fCO2     pCO2      HCO3    CO3 OmegaAragonite\n",
       "1 4.139159 0.2216044 4.929374 5.014682 5.014689 0.1866465 2.7889       5.383828\n",
       "  OmegaCalcite\n",
       "1     5.383828"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute variables\n",
    "vars <- carb  (flag=15, var1=ALK, var2=DIC, S=salt, T=temp, Patm=1, P=press, Pt=Phos, Sit=Sil, \n",
    "                    k1k2='w14', kf='dg', ks=\"d\", pHscale=\"T\", b=\"u74\", gas=\"potential\", warn='n')\n",
    "\n",
    "H = 10^(-1*vars$pH)         # H+ concentration (mol/kg)\n",
    "vars <- data.frame(H, vars) # Add H+ as new column to vars data frame\n",
    "\n",
    "# Absolute errors: propagated uncertainties \n",
    "absEt <- errors (flag=15, var1=ALK, var2=DIC, S=salt, T=temp, \n",
    "                      Patm=1, P=press, Pt=Phos, Sit=Sil, \n",
    "                      evar1=dat$Var2, evar2=dat$Var1, eS=0, eT=0, ePt=0, eSit=0, epK=epKstd,\n",
    "                      k1k2='w14', kf='dg', ks=\"d\", pHscale=\"T\", b=\"u74\", gas=\"potential\", warn='no')\n",
    "\n",
    "# Aboslute error from constants only (all other input errors assumed to be zero)\n",
    "absEk <- errors  (flag=15, var1=ALK, var2=DIC, S=salt, T=temp, \n",
    "                       Patm=1, P=press, Pt=Phos, Sit=Sil, \n",
    "                       evar1=0, evar2=0, \n",
    "                       eS=0, eT=0, ePt=0, eSit=0, epK=epKstd,\n",
    "                       k1k2='w14', kf='dg', ks=\"d\", pHscale=\"T\", b=\"u74\", gas=\"potential\", warn='n')\n",
    "\n",
    "# Keep only key columns in vars for consistency with columns in absEt\n",
    "vars <- vars[,colnames(absEt)] \n",
    "vars\n",
    "\n",
    "# Duplicate rows in *vars* until same as number of members of error vector ALK_e\n",
    "numerrs <- length(dat$Var1)\n",
    "vars <- vars[rep(row.names(vars), numerrs), ]\n",
    "\n",
    "#Relative errors (in percent)\n",
    "relEk <- 100* absEk / vars[1,]        #Relative error from constants only\n",
    "relEt <- 100* absEt / vars            #Total relative error (from constants and other input variables)\n",
    "relEk"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Define simpler names of variables to be plotted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#   Absolute changes:\n",
    "    pH       <- absEt$pH\n",
    "    pCO2     <- absEt$pCO2\n",
    "    CO3      <- absEt$CO3\n",
    "    CO2      <- absEt$CO2\n",
    "    pCO2socn <- absEt$pCO2\n",
    "    OmegaA   <- absEt$OmegaAragonite\n",
    "    HCO3     <- absEt$HCO3\n",
    "    H        <- absEt$H\n",
    "\n",
    "#   Relative changes:\n",
    "    rCO3  <- relEt$CO3\n",
    "    rH    <- relEt$H\n",
    "#     rpCO2 <- relEt$pCO2\n",
    "    rCO2  <- relEt$CO2\n",
    "    rpCO2   <- relEt$pCO2\n",
    "    rOmegaA <- relEt$OmegaAragonite\n",
    "    rHCO3   <- relEt$HCO3\n",
    "    \n",
    "    rHCO3H <- sqrt(rHCO3^2 + rH^2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Compute other parts of error-space diagrams"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1 Constants-pair CURVE (along which propagated error from constants equals that from the input pair)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In seacarb::K1(S, T, P, k1k2 = k1k2, pHscale = pHscale, kSWS2scale = kSWS2scale, : S and/or T is outside the range of validity of the formulation chosen for K1.Warning message:\n",
      "In seacarb::K1(S, T, P, k1k2 = k1k2, pHscale = pHscale, kSWS2scale = kSWS2scale, : S and/or T is outside the range of validity of the formulation chosen for K1.Warning message:\n",
      "In seacarb::K2(S, T, P, k1k2 = k1k2, pHscale = pHscale, kSWS2scale = kSWS2scale, : S and/or T is outside the range of validity of the formulation chosen for K2.Warning message:\n",
      "In seacarb::K2(S, T, P, k1k2 = k1k2, pHscale = pHscale, kSWS2scale = kSWS2scale, : S and/or T is outside the range of validity of the formulation chosen for K2.Warning message:\n",
      "In seacarb::Kb(S, T, P, pHscale = pHscale, kSWS2scale = kSWS2scale, : S and/or T is outside the range of validity of the formulation available for Kb in seacarb.Warning message:\n",
      "In seacarb::Kb(S, T, P, pHscale = pHscale, kSWS2scale = kSWS2scale, : S and/or T is outside the range of validity of the formulation available for Kb in seacarb.Warning message:\n",
      "In seacarb::Kw(S, T, P, pHscale = pHscale, kSWS2scale = kSWS2scale): S and/or T is outside the range of validity of the formulation available for Kw in seacarb.Warning message:\n",
      "In seacarb::Kw(S, T, P, pHscale = pHscale, kSWS2scale = kSWS2scale): S and/or T is outside the range of validity of the formulation available for Kw in seacarb.Warning message:\n",
      "In seacarb::Kspa(S, T, P): S and/or T is outside the range of validity of the formulation available for Kspa in seacarb.Warning message:\n",
      "In seacarb::Kspa(S, T, P): S and/or T is outside the range of validity of the formulation available for Kspa in seacarb.Warning message:\n",
      "In seacarb::Kspc(S, T, P): S and/or T is outside the range of validity of the formulation available for Kspc in seacarb.Warning message:\n",
      "In seacarb::Kspc(S, T, P): S and/or T is outside the range of validity of the formulation available for Kspc in seacarb."
     ]
    }
   ],
   "source": [
    "# Critical curves (Constants-Pairs curve)\n",
    "# ===============\n",
    "# Southern Ocean\n",
    "errcirc <- errhalf(flag=15, var1=ALK, var2=DIC, S=salt, T=temp, \n",
    "                   Patm=1, P=press, Pt=Phos, Sit=Sil,\n",
    "                   epK=epKstd,\n",
    "                   k1k2='l', kf='dg', ks=\"d\", pHscale=\"T\", b=\"u74\", gas=\"potential\", warn=\"n\")  \n",
    "sig1_AtCt   <- data.frame(errcirc[1]) * 1e+6\n",
    "sig2_AtCt   <- data.frame(errcirc[2]) * 1e+6\n",
    "sigy_AtCt   <- data.frame(errcirc[3]) \n",
    "sig1hp_AtCt <- data.frame(errcirc[4]) * 1e+6\n",
    "sig2hp_AtCt <- data.frame(errcirc[5]) * 1e+6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 Balanced-pair LINE (along which both members of input pair contrbute equally to propagated error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In seacarb::K1(S, T, P, k1k2 = k1k2, pHscale = pHscale, kSWS2scale = kSWS2scale, : S and/or T is outside the range of validity of the formulation chosen for K1.Warning message:\n",
      "In seacarb::K1(S, T, P, k1k2 = k1k2, pHscale = pHscale, kSWS2scale = kSWS2scale, : S and/or T is outside the range of validity of the formulation chosen for K1.Warning message:\n",
      "In seacarb::K2(S, T, P, k1k2 = k1k2, pHscale = pHscale, kSWS2scale = kSWS2scale, : S and/or T is outside the range of validity of the formulation chosen for K2.Warning message:\n",
      "In seacarb::K2(S, T, P, k1k2 = k1k2, pHscale = pHscale, kSWS2scale = kSWS2scale, : S and/or T is outside the range of validity of the formulation chosen for K2.Warning message:\n",
      "In seacarb::Kb(S, T, P, pHscale = pHscale, kSWS2scale = kSWS2scale, : S and/or T is outside the range of validity of the formulation available for Kb in seacarb.Warning message:\n",
      "In seacarb::Kb(S, T, P, pHscale = pHscale, kSWS2scale = kSWS2scale, : S and/or T is outside the range of validity of the formulation available for Kb in seacarb.Warning message:\n",
      "In seacarb::Kw(S, T, P, pHscale = pHscale, kSWS2scale = kSWS2scale): S and/or T is outside the range of validity of the formulation available for Kw in seacarb.Warning message:\n",
      "In seacarb::Kw(S, T, P, pHscale = pHscale, kSWS2scale = kSWS2scale): S and/or T is outside the range of validity of the formulation available for Kw in seacarb.Warning message:\n",
      "In seacarb::Kspa(S, T, P): S and/or T is outside the range of validity of the formulation available for Kspa in seacarb.Warning message:\n",
      "In seacarb::Kspa(S, T, P): S and/or T is outside the range of validity of the formulation available for Kspa in seacarb.Warning message:\n",
      "In seacarb::Kspc(S, T, P): S and/or T is outside the range of validity of the formulation available for Kspc in seacarb.Warning message:\n",
      "In seacarb::Kspc(S, T, P): S and/or T is outside the range of validity of the formulation available for Kspc in seacarb.Warning message:\n",
      "In sqrt(0.5 * (sigmay^2 - eKall^2)/dd1^2): NaNs producedWarning message:\n",
      "In sqrt(0.5 * (sigmay^2 - eKall^2)/dd2^2): NaNs produced"
     ]
    }
   ],
   "source": [
    "sigyspct <- seq(0,20,by=0.1) # in percent\n",
    "\n",
    "# At-Ct pair\n",
    "# ----------\n",
    "# Southern Ocean\n",
    "errm <- errmid(flag=15, var1=ALK, var2=DIC, S=salt, T=temp, \n",
    "                   Patm=1, P=press, Pt=Phos, Sit=Sil,\n",
    "                   sigyspct, epK=epKstd,\n",
    "                   k1k2='l', kf='dg', ks=\"d\", pHscale=\"T\", b=\"u74\", gas=\"potential\", warn=\"n\")  \n",
    "sigm1_AtCt   <- data.frame(errm[1]) * 1e+6\n",
    "sigm2_AtCt   <- data.frame(errm[2]) * 1e+6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Plot results: contours of calculated errors from input errors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1 Create file 'prettyaxes.R' to beautify subsequent plots (call it in cell below)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "cat(' box()\\n',\n",
    "    'axis(1,labels=FALSE, tcl=-0.35) ; axis(1, lwd=0, line=-0.4, labels=TRUE)\\n',\n",
    "    'axis(2,labels=FALSE,tcl=-0.35)  ; axis(2, lwd=0, line=-0.4, las=2, labels=TRUE)\\n',\n",
    "    'axis(3,labels=FALSE,tcl=-0.35) ; axis(4,labels=FALSE,tcl=-0.25)\\n',\n",
    "   file='prettyaxes.R')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2 Function to strip NaNs and add a 0 at beginning of a vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "zenon <- function(x){\n",
    "       # Get rid of NaN's\n",
    "       x <- c(0.0, x[!is.na(x)]) \n",
    "       return(x)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3 Function to make plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plterrcontour <- function(sigcritXa, sigcritYa, xlab, ylab, subtitle, xlim, ylim,\n",
    "                           sighpXa, sighpYa,\n",
    "                           sigmidXa, sigmidYa,\n",
    "                           sigsoaX, sigsoaY,\n",
    "                           x, y, za, levels1,\n",
    "                           methoda='flattest'){\n",
    "    \n",
    "#   Region 'a' is Southern Ocean  ;  Region 'b' is Tropics:\n",
    "    # 'contour' command must come after any 'plot', 'lines', or 'points' commands \n",
    "    plot (sigcritXa, sigcritYa, xlab=xlab, ylab=ylab, plot.title=title(main=subtitle),\n",
    "          xlim=xlim, ylim=ylim, col=\"black\", type='l', lwd=4, lty='solid',xaxt='n',yaxt='n',\n",
    "          cex.lab=1.4, ann=F, xaxs='r', yaxs='r')\n",
    "#   Plot critical point\n",
    "    if ( is.null(sighpXa) ) {\n",
    "        points(sigcritXa[11], sigcritYa[11], col=\"black\", cex=1.7, pch=19)\n",
    "    } else {\n",
    "        points(sighpXa, sighpYa, col=\"black\", cex=1.7, pch=19)\n",
    "    }    \n",
    "#   Plot mid-line (where e1 = e2 on each isoline [and between isolines])\n",
    "    lines(sigmidXa, sigmidYa, col=\"black\", lwd=1, lty='solid')\n",
    "#   symbols(x=sigcritXb[11], y=sigcritYb[11], circles=1, inches=1/3, ann=F, bg=\"steelblue2\", fg=NULL, add=TRUE)\n",
    "#   Plot point(s) at state-of-the-art (soa) for absolute error in each member of the input pair\n",
    "#   - pH has 2 points (random & overall error); other 3 input variables only have 1 point\n",
    "    points(sigsoaX, sigsoaY, col=\"black\", cex=1.7, pch=4)\n",
    "    axis(1,labels=TRUE, tcl=-0.35, cex.axis=1.3) \n",
    "    axis(2, tcl=-0.35, labels=FALSE, las=0) \n",
    "    title(xlab = xlab, cex.lab = 1.4, line = 2.9)\n",
    "    title(ylab = ylab, cex.lab = 1.4, line = 1.9)\n",
    "\n",
    "#   Add 2 colored text strings near origin to indicate the propagated error at the origin (from constants only)\n",
    "    a0 <- za[1,1]\n",
    "    if (a0 < 1) {ndiga <- 2} else {ndiga <- 3}\n",
    "    mtext( format(a0, digits=ndiga), side=1, line=2.5, at=0, srt=0,  cex=1.05, col='blue')\n",
    "\n",
    "#  'contour' command MUST come after any 'plot', 'lines', or 'points' commands \n",
    "#   For 'method', use 'simple, edge or flattest (flattest looks best but seems to fail often when lines are vertical)\n",
    "    contour(x, y , za, levels=levels1, method=methoda, col=\"blue\", lty=1, lwd=2, \n",
    "            yaxt='n', , labcex=1.0, add=TRUE)\n",
    "    axis(2, tcl=-0.35, labels=FALSE) \n",
    "\n",
    "    axis(2, tcl=-0.35, labels=FALSE, las=0) ; \n",
    "    axis(2, lwd=0, line=-0.4, las=2, labels=TRUE, cex.axis=1.4)\n",
    "    axis(3,labels=FALSE,tcl=-0.35) ; axis(4,labels=FALSE,tcl=-0.25)\n",
    "    done <- c('error contour plot')\n",
    "#return(NULL)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.4 Error-space diagram of relative error in CO3  for At-Ct input pair\n",
    "\n",
    "Combine (1) contour plot of CO3 with (2) constants-pair curve, (3) balanced-pair line, ane (4) symbol indicating current state-of-the-art uncertainty."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "plot without title"
      ]
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   "source": [
    "### Start PDF device driver to save output to figure.pdf\n",
    "# Comment out line below & last line of this script to display resulting graph on computer screen\n",
    "# pdf(file=\"halfway_CO3.pdf\",  width=10.0, height=7.0)\n",
    "\n",
    "  options(repr.plot.width=7.0, repr.plot.height=7)\n",
    "\n",
    "\n",
    "    dim(rCO3) <- c(length(DIC_e), length(ALK_e))\n",
    "\n",
    "#   pdf(file=\"Fig_AbsErrContours2_trop_socn.pdf\")\n",
    "    par(mfrow=c(1,1), mar=c(4,3.7,1,1.5)+0.1, oma=c(2,0,0,0.5), mgp=c(2,1,0), font.main=1) \n",
    "\n",
    "    subtitle <- NULL\n",
    "\n",
    "#   At-Ct\n",
    "#   -------------------\n",
    "    xlabel <- expression(paste(sigma[italic(\"C\")[T]],\" (\",mu,\"mol kg\"^{-1},\")\",sep=\"\"))\n",
    "    ylabel <- expression(paste(sigma[italic(\"A\")[T]],\" (\",mu,\"mol kg\"^{-1},\")\",sep=\"\"))\n",
    "\n",
    "    sigcritXa <- sig2_AtCt$CO3  ;  sigcritYa <- sig1_AtCt$CO3  #sig2_ is x axis; sig1_ is y axis\n",
    "    x <- DIC_e*1e+6  ;  y <- ALK_e*1e+6\n",
    "    za <- rCO3  \n",
    "    xlim <- c(0,20)  ; ylim <- xlim\n",
    "    levels1 <- c(1,seq(2,20,by=2))  \n",
    "\n",
    "    plterrcontour (sigcritXa, sigcritYa, xlabel, ylabel, subtitle, xlim, ylim,\n",
    "                   sig1hp_AtCt$CO3, sig2hp_AtCt$CO3,\n",
    "                   zenon(sigm2_AtCt$CO3), zenon(sigm1_AtCt$CO3),\n",
    "                   DIC_e_soa2, ALK_e_soa2,\n",
    "                   x, y, za, levels1,\n",
    "                   'flattest')\n",
    "\n",
    "# Turn off device driver (to flush output to PDF)\n",
    "# dev.off()"
   ]
  },
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   "source": [
    "***Figure:*** Percent relative uncertainty in computed $[\\text{CO}_3^{2-}]$ from the $A_\\text{T}-C_\\text{T}$ input pair as a function of uncertainties in each member of that input pair. Each of those members is indicated by the x- and y-axis labels. Propagated relative error (in percent) is shown for the Southern Ocean (blue solid lines). Sublots without pH as an input member also include the Constants-Pair curve (thick black line), where the total propagated error from the constants is equal to that from the input pair. The balanced-pair line (thin black line) indicates where each member of the input pair contributes equally to total propagated error. "
   ]
  }
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