ConiferColdHardinessModelExample.ipynb

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    "# Adapting a process based cold hardiness model to conifers\n",
    "#### Miro Stuke - Stuke@uw.edu\n",
    "\n",
    "This notebooks shows an example of the conifer cold hardiness model presented by Miro Stuke at the 2023 WFNCA grower's meeting. The model and example used here were also used for the related paper (in review; Stuke 2023).\n",
    "\n",
    "The cold hardiness observations used in this modeling example were derived from Douglas-fir nursery grown seedling data published in Timmis et al., 1994. Two seedlots (high elevation and low elevation) were tested over four dormancy seasons from 1973 to 1978.\n",
    "\n",
    "This notebook shows an example using one year of data and modeling both seed sources. \n",
    "\n",
    "All seedlings were grown at Mima nursery in south Olympia, WA as bareroot 2+0 nursery stock.\n",
    "\n",
    "The cold hardiness model used here was modified and adapted from Ferguson et al. 2014 - a model used for grapes.\n",
    "\n",
    "The data is split into training data - which will be used to calibrate the model and derive the best set of parameters for each seed lot, and testing data - will will be used to measure model performance and predictive accuarcy. \n"
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       "<p>The WebIO Jupyter extension was not detected. See the\n",
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       "    WebIO Jupyter integration documentation\n",
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   "source": [
    "#some packages need to be added to run the moedl\n",
    "using Cropbox"
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   "source": [
    "using CSV\n",
    "using DataFrames\n",
    "using TimeZones\n",
    "using Dates"
   ]
  },
  {
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   "id": "7ac40890",
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   "source": [
    "# Temperature Data\n",
    "Once the model is calibrated, it will run with just the input of daily minimum and maximum temperature for the period to be modeled. Each year has one temperature csv file and a unique configuration. The files will be and conifugrations will be added in the next section of script. "
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text-align: right;\">missing</td><td style = \"font-style: italic; text-align: right;\">missing</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">205</td><td style = \"text-align: left;\">USW00024227</td><td style = \"text-align: left;\">OLYMPIA AIRPORT, WA US</td><td style = \"text-align: right;\">46.9737</td><td style = \"text-align: right;\">-122.905</td><td style = \"text-align: right;\">60.9</td><td style = \"text-align: left;\">1975-04-23</td><td style = \"text-align: right;\">8.05556 °C</td><td style = \"text-align: right;\">46.5</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">54</td><td style = \"text-align: left;\">,,0</td><td style = \"text-align: right;\">39</td><td style = \"text-align: left;\">,,0</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"font-style: italic; text-align: right;\">missing</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">206</td><td style = \"text-align: left;\">USW00024227</td><td style = \"text-align: left;\">OLYMPIA AIRPORT, WA US</td><td style = \"text-align: right;\">46.9737</td><td style = \"text-align: right;\">-122.905</td><td style = \"text-align: right;\">60.9</td><td style = \"text-align: left;\">1975-04-24</td><td style = \"text-align: right;\">7.77778 °C</td><td style = \"text-align: right;\">46.0</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">51</td><td style = \"text-align: left;\">,,0</td><td style = \"text-align: right;\">41</td><td style = \"text-align: left;\">,,0</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"font-style: italic; text-align: right;\">missing</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">207</td><td style = \"text-align: left;\">USW00024227</td><td style = \"text-align: left;\">OLYMPIA AIRPORT, WA US</td><td style = \"text-align: right;\">46.9737</td><td style = \"text-align: right;\">-122.905</td><td style = \"text-align: right;\">60.9</td><td style = \"text-align: left;\">1975-04-25</td><td style = \"text-align: right;\">7.5 °C</td><td style = \"text-align: right;\">45.5</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">55</td><td style = \"text-align: left;\">,,0</td><td style = \"text-align: right;\">36</td><td style = \"text-align: left;\">,,0</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"font-style: italic; text-align: right;\">missing</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">208</td><td style = \"text-align: left;\">USW00024227</td><td style = \"text-align: left;\">OLYMPIA AIRPORT, WA US</td><td style = \"text-align: right;\">46.9737</td><td style = \"text-align: right;\">-122.905</td><td style = \"text-align: right;\">60.9</td><td style = \"text-align: left;\">1975-04-26</td><td style = \"text-align: right;\">6.38889 °C</td><td style = \"text-align: right;\">43.5</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">56</td><td style = \"text-align: left;\">,,0</td><td style = \"text-align: right;\">31</td><td style = \"text-align: left;\">,,0</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"font-style: italic; text-align: right;\">missing</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">209</td><td style = \"text-align: left;\">USW00024227</td><td style = \"text-align: left;\">OLYMPIA AIRPORT, WA US</td><td style = \"text-align: right;\">46.9737</td><td style = \"text-align: right;\">-122.905</td><td style = \"text-align: right;\">60.9</td><td style = \"text-align: left;\">1975-04-27</td><td style = \"text-align: right;\">7.5 °C</td><td style = \"text-align: right;\">45.5</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">53</td><td style = \"text-align: left;\">,,0</td><td style = \"text-align: right;\">38</td><td style = \"text-align: left;\">,,0</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"font-style: italic; text-align: right;\">missing</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">210</td><td style = \"text-align: left;\">USW00024227</td><td style = \"text-align: left;\">OLYMPIA AIRPORT, WA US</td><td style = \"text-align: right;\">46.9737</td><td style = \"text-align: right;\">-122.905</td><td style = \"text-align: right;\">60.9</td><td style = \"text-align: left;\">1975-04-28</td><td style = \"text-align: right;\">6.11111 °C</td><td style = \"text-align: right;\">43.0</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">52</td><td style = \"text-align: left;\">,,0</td><td style = \"text-align: right;\">34</td><td style = \"text-align: left;\">,,0</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"font-style: italic; text-align: right;\">missing</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">211</td><td style = \"text-align: left;\">USW00024227</td><td style = \"text-align: left;\">OLYMPIA AIRPORT, WA US</td><td style = \"text-align: right;\">46.9737</td><td style = \"text-align: right;\">-122.905</td><td style = \"text-align: right;\">60.9</td><td style = \"text-align: left;\">1975-04-29</td><td style = \"text-align: right;\">7.22222 °C</td><td style = \"text-align: right;\">45.0</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">61</td><td style = \"text-align: left;\">,,0</td><td style = \"text-align: right;\">29</td><td style = \"text-align: left;\">,,0</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"font-style: italic; text-align: right;\">missing</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">212</td><td style = \"text-align: left;\">USW00024227</td><td style = \"text-align: left;\">OLYMPIA AIRPORT, WA US</td><td style = \"text-align: right;\">46.9737</td><td style = \"text-align: right;\">-122.905</td><td style = \"text-align: right;\">60.9</td><td style = \"text-align: left;\">1975-04-30</td><td style = \"text-align: right;\">10.0 °C</td><td style = \"text-align: right;\">50.0</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">69</td><td style = \"text-align: left;\">,,0</td><td style = \"text-align: right;\">31</td><td style = \"text-align: left;\">,,0</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"font-style: italic; text-align: right;\">missing</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">213</td><td style = \"text-align: left;\">USW00024227</td><td style = \"text-align: left;\">OLYMPIA AIRPORT, WA US</td><td style = \"text-align: right;\">46.9737</td><td style = \"text-align: right;\">-122.905</td><td style = \"text-align: right;\">60.9</td><td style = \"text-align: left;\">1975-05-01</td><td style = \"text-align: right;\">10.5556 °C</td><td style = \"text-align: right;\">51.0</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">70</td><td style = \"text-align: left;\">,,0</td><td style = \"text-align: right;\">32</td><td style = \"text-align: left;\">,,0</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"font-style: italic; text-align: right;\">missing</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccccc}\n",
       "\t& STATION & NAME & LATITUDE & LONGITUDE & ELEVATION & date & \\\\\n",
       "\t\\hline\n",
       "\t& String15 & String31 & Float64 & Float64 & Float64 & Date & \\\\\n",
       "\t\\hline\n",
       "\t1 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-01 & $\\dots$ \\\\\n",
       "\t2 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-02 & $\\dots$ \\\\\n",
       "\t3 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-03 & $\\dots$ \\\\\n",
       "\t4 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-04 & $\\dots$ \\\\\n",
       "\t5 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-05 & $\\dots$ \\\\\n",
       "\t6 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-06 & $\\dots$ \\\\\n",
       "\t7 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-07 & $\\dots$ \\\\\n",
       "\t8 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-08 & $\\dots$ \\\\\n",
       "\t9 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-09 & $\\dots$ \\\\\n",
       "\t10 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-10 & $\\dots$ \\\\\n",
       "\t11 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-11 & $\\dots$ \\\\\n",
       "\t12 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-12 & $\\dots$ \\\\\n",
       "\t13 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-13 & $\\dots$ \\\\\n",
       "\t14 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-14 & $\\dots$ \\\\\n",
       "\t15 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-15 & $\\dots$ \\\\\n",
       "\t16 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-16 & $\\dots$ \\\\\n",
       "\t17 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-17 & $\\dots$ \\\\\n",
       "\t18 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-18 & $\\dots$ \\\\\n",
       "\t19 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-19 & $\\dots$ \\\\\n",
       "\t20 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-20 & $\\dots$ \\\\\n",
       "\t21 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-21 & $\\dots$ \\\\\n",
       "\t22 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-22 & $\\dots$ \\\\\n",
       "\t23 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-23 & $\\dots$ \\\\\n",
       "\t24 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-24 & $\\dots$ \\\\\n",
       "\t25 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-25 & $\\dots$ \\\\\n",
       "\t26 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-26 & $\\dots$ \\\\\n",
       "\t27 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-27 & $\\dots$ \\\\\n",
       "\t28 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-28 & $\\dots$ \\\\\n",
       "\t29 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-29 & $\\dots$ \\\\\n",
       "\t30 & USW00024227 & OLYMPIA AIRPORT, WA US & 46.9737 & -122.905 & 60.9 & 1974-10-30 & $\\dots$ \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ &  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m213×15 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m STATION     \u001b[0m\u001b[1m NAME                   \u001b[0m\u001b[1m LATITUDE \u001b[0m\u001b[1m LONGITUDE \u001b[0m\u001b[1m ELEVATION \u001b[0m\u001b[1m da\u001b[0m ⋯\n",
       "     │\u001b[90m String15    \u001b[0m\u001b[90m String31               \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Da\u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │ USW00024227  OLYMPIA AIRPORT, WA US   46.9737   -122.905       60.9  19 ⋯\n",
       "   2 │ USW00024227  OLYMPIA AIRPORT, WA US   46.9737   -122.905       60.9  19\n",
       "   3 │ USW00024227  OLYMPIA AIRPORT, WA US   46.9737   -122.905       60.9  19\n",
       "   4 │ USW00024227  OLYMPIA AIRPORT, WA US   46.9737   -122.905       60.9  19\n",
       "   5 │ USW00024227  OLYMPIA AIRPORT, WA US   46.9737   -122.905       60.9  19 ⋯\n",
       "   6 │ USW00024227  OLYMPIA AIRPORT, WA US   46.9737   -122.905       60.9  19\n",
       "   7 │ USW00024227  OLYMPIA AIRPORT, WA US   46.9737   -122.905       60.9  19\n",
       "   8 │ USW00024227  OLYMPIA AIRPORT, WA US   46.9737   -122.905       60.9  19\n",
       "   9 │ USW00024227  OLYMPIA AIRPORT, WA US   46.9737   -122.905       60.9  19 ⋯\n",
       "  10 │ USW00024227  OLYMPIA AIRPORT, WA US   46.9737   -122.905       60.9  19\n",
       "  11 │ USW00024227  OLYMPIA AIRPORT, WA US   46.9737   -122.905       60.9  19\n",
       "  ⋮  │      ⋮                 ⋮                ⋮          ⋮          ⋮         ⋱\n",
       " 204 │ USW00024227  OLYMPIA AIRPORT, WA US   46.9737   -122.905       60.9  19\n",
       " 205 │ USW00024227  OLYMPIA AIRPORT, WA US   46.9737   -122.905       60.9  19 ⋯\n",
       " 206 │ USW00024227  OLYMPIA AIRPORT, WA US   46.9737   -122.905       60.9  19\n",
       " 207 │ USW00024227  OLYMPIA AIRPORT, WA US   46.9737   -122.905       60.9  19\n",
       " 208 │ USW00024227  OLYMPIA AIRPORT, WA US   46.9737   -122.905       60.9  19\n",
       " 209 │ USW00024227  OLYMPIA AIRPORT, WA US   46.9737   -122.905       60.9  19 ⋯\n",
       " 210 │ USW00024227  OLYMPIA AIRPORT, WA US   46.9737   -122.905       60.9  19\n",
       " 211 │ USW00024227  OLYMPIA AIRPORT, WA US   46.9737   -122.905       60.9  19\n",
       " 212 │ USW00024227  OLYMPIA AIRPORT, WA US   46.9737   -122.905       60.9  19\n",
       " 213 │ USW00024227  OLYMPIA AIRPORT, WA US   46.9737   -122.905       60.9  19 ⋯\n",
       "\u001b[36m                                                 10 columns and 192 rows omitted\u001b[0m"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Temp_1974 = CSV.read(\"D.6_TempData_74.CSV\", DataFrame) |> unitfy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "76f56d47",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-family: monospace\">Config for 3 systems:</p>\n",
       "<table style=\"font-family: monospace\">\n",
       "<tr style=\"background-color: transparent\">\n",
       "<td colspan=\"3\" style=\"text-align: left; padding: 2px; padding-left: 20px; color: rebeccapurple\">Calendar</th>\n",
       "</tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">init</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">ZonedDateTime&#40;1974, 10, 1, tz&quot;UTC&quot;&#41;</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">last</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">ZonedDateTime&#40;1975, 5, 1, tz&quot;UTC&quot;&#41;</td></tr>\n",
       "</table>\n",
       "\n",
       "<table style=\"font-family: monospace\">\n",
       "<tr style=\"background-color: transparent\">\n",
       "<td colspan=\"3\" style=\"text-align: left; padding: 2px; padding-left: 20px; color: rebeccapurple\">Clock</th>\n",
       "</tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">step</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">1 d</td></tr>\n",
       "</table>\n",
       "\n",
       "<table style=\"font-family: monospace\">\n",
       "<tr style=\"background-color: transparent\">\n",
       "<td colspan=\"3\" style=\"text-align: left; padding: 2px; padding-left: 20px; color: rebeccapurple\">Temperature</th>\n",
       "</tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">data</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">213×15 DataFrame…</td></tr>\n",
       "</table>\n"
      ],
      "text/plain": [
       "Config for 3 systems:\n",
       "  \u001b[95mCalendar\u001b[39m\n",
       "    \u001b[94minit\u001b[39m\u001b[90m = \u001b[39mZonedDateTime(1974, 10, 1, tz\"UTC\")\n",
       "    \u001b[94mlast\u001b[39m\u001b[90m = \u001b[39mZonedDateTime(1975, 5, 1, tz\"UTC\")\n",
       "  \u001b[95mClock\u001b[39m\n",
       "    \u001b[94mstep\u001b[39m\u001b[90m = \u001b[39m1 d\n",
       "  \u001b[95mTemperature\u001b[39m\n",
       "    \u001b[94mdata\u001b[39m\u001b[90m = \u001b[39m213×15 DataFrame…"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D6_1974_config = @config (\n",
    "    :Calendar => (;\n",
    "        init = ZonedDateTime(1974, 10, 01, tz\"UTC\"),\n",
    "        last = ZonedDateTime(1975, 05, 01, tz\"UTC\"),\n",
    "    ),\n",
    "    :Clock => (;\n",
    "        step = 1u\"d\",\n",
    "    ),\n",
    "    :Temperature => (;\n",
    "        data = Temp_1974,\n",
    "    ),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "33e1bdba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Temperature"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@system Temperature begin\n",
    "    calendar(context)             ~      ::Calendar\n",
    "    t(calendar.date): date        ~ track::date\n",
    "\n",
    "    data                          ~ provide(parameter, index = :date, init = t)\n",
    "    T:                temperature ~ drive(from = data, by = :Tavg, u\"°C\")\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14119f14",
   "metadata": {},
   "source": [
    "# Observations\n",
    "Observations will be added using csv files seed source. Seed sources are split into high and low elevation, which reflects two unique seedlots. Each file contains observations for one dormancy season, designated by the first year of that period.\n",
    "\n",
    "Additionally each is divided into training and testing ata subsets. Training data are used for model calibration and parameterization. Testing data are used to validate the model and determine goodness of fit. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e3dcb38c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>30×5 DataFrame</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">5 rows omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">Year</th><th style = \"text-align: left;\">SeedSource</th><th style = \"text-align: left;\">JD Rounded</th><th style = \"text-align: left;\">date</th><th style = \"text-align: left;\">Hc</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"String3\" style = \"text-align: left;\">String3</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Date\" style = \"text-align: left;\">Date</th><th title = \"Unitful.Quantity{Float64, 𝚯, Unitful.FreeUnits{(K,), 𝚯, nothing}}\" style = \"text-align: left;\">Quantity…</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-71</td><td style = \"text-align: left;\">1974-10-22</td><td style = \"text-align: right;\">-5.6 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-40</td><td style = \"text-align: left;\">1974-11-22</td><td style = \"text-align: right;\">-18.0 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">1975-01-02</td><td style = \"text-align: right;\">-23.5 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">20</td><td style = \"text-align: left;\">1975-01-21</td><td style = \"text-align: right;\">-23.5 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">61</td><td style = \"text-align: left;\">1975-03-03</td><td style = \"text-align: right;\">-21.4 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">77</td><td style = \"text-align: left;\">1975-03-19</td><td style = \"text-align: right;\">-15.0 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">104</td><td style = \"text-align: left;\">1975-04-15</td><td style = \"text-align: right;\">-8.8 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-100</td><td style = \"text-align: left;\">1976-09-23</td><td style = \"text-align: right;\">-5.5 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-90</td><td style = \"text-align: left;\">1976-10-03</td><td style = \"text-align: right;\">-5.2 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-86</td><td style = \"text-align: left;\">1976-10-07</td><td style = \"text-align: right;\">-5.7 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-75</td><td style = \"text-align: left;\">1976-10-18</td><td style = \"text-align: right;\">-5.7 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-60</td><td style = \"text-align: left;\">1976-11-04</td><td style = \"text-align: right;\">-8.9 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-39</td><td style = \"text-align: left;\">1976-11-23</td><td style = \"text-align: right;\">-15.4 K</td></tr><tr><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">19</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">61</td><td style = \"text-align: left;\">1977-03-02</td><td style = \"text-align: right;\">-20.2 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">20</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">75</td><td style = \"text-align: left;\">1977-03-16</td><td style = \"text-align: right;\">-19.8 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">21</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-81</td><td style = \"text-align: left;\">1977-10-12</td><td style = \"text-align: right;\">-6.1 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">22</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-67</td><td style = \"text-align: left;\">1977-10-26</td><td style = \"text-align: right;\">-9.2 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">23</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-53</td><td style = \"text-align: left;\">1977-11-09</td><td style = \"text-align: right;\">-14.0 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">24</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-26</td><td style = \"text-align: left;\">1977-12-06</td><td style = \"text-align: right;\">-24.2 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">25</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">1977-01-02</td><td style = \"text-align: right;\">-24.0 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">26</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">8</td><td style = \"text-align: left;\">1978-01-09</td><td style = \"text-align: right;\">-24.0 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">27</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">24</td><td style = \"text-align: left;\">1978-01-25</td><td style = \"text-align: right;\">-25.9 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">28</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">53</td><td style = \"text-align: left;\">1978-02-21</td><td style = \"text-align: right;\">-21.8 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">29</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">74</td><td style = \"text-align: left;\">1978-03-16</td><td style = \"text-align: right;\">-18.2 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">30</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">86</td><td style = \"text-align: left;\">1978-03-28</td><td style = \"text-align: right;\">-11.4 K</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccc}\n",
       "\t& Year & SeedSource & JD Rounded & date & Hc\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & String3 & Int64 & Date & Quantity…\\\\\n",
       "\t\\hline\n",
       "\t1 & 1974 & Low & -71 & 1974-10-22 & -5.6 K \\\\\n",
       "\t2 & 1974 & Low & -40 & 1974-11-22 & -18.0 K \\\\\n",
       "\t3 & 1974 & Low & 1 & 1975-01-02 & -23.5 K \\\\\n",
       "\t4 & 1974 & Low & 20 & 1975-01-21 & -23.5 K \\\\\n",
       "\t5 & 1974 & Low & 61 & 1975-03-03 & -21.4 K \\\\\n",
       "\t6 & 1974 & Low & 77 & 1975-03-19 & -15.0 K \\\\\n",
       "\t7 & 1974 & Low & 104 & 1975-04-15 & -8.8 K \\\\\n",
       "\t8 & 1976 & Low & -100 & 1976-09-23 & -5.5 K \\\\\n",
       "\t9 & 1976 & Low & -90 & 1976-10-03 & -5.2 K \\\\\n",
       "\t10 & 1976 & Low & -86 & 1976-10-07 & -5.7 K \\\\\n",
       "\t11 & 1976 & Low & -75 & 1976-10-18 & -5.7 K \\\\\n",
       "\t12 & 1976 & Low & -60 & 1976-11-04 & -8.9 K \\\\\n",
       "\t13 & 1976 & Low & -39 & 1976-11-23 & -15.4 K \\\\\n",
       "\t14 & 1976 & Low & -15 & 1976-12-17 & -23.6 K \\\\\n",
       "\t15 & 1976 & Low & 2 & 1977-01-03 & -24.1 K \\\\\n",
       "\t16 & 1976 & Low & 10 & 1977-01-11 & -26.2 K \\\\\n",
       "\t17 & 1976 & Low & 36 & 1977-02-06 & -24.8 K \\\\\n",
       "\t18 & 1976 & Low & 48 & 1977-02-18 & -23.6 K \\\\\n",
       "\t19 & 1976 & Low & 61 & 1977-03-02 & -20.2 K \\\\\n",
       "\t20 & 1976 & Low & 75 & 1977-03-16 & -19.8 K \\\\\n",
       "\t21 & 1977 & Low & -81 & 1977-10-12 & -6.1 K \\\\\n",
       "\t22 & 1977 & Low & -67 & 1977-10-26 & -9.2 K \\\\\n",
       "\t23 & 1977 & Low & -53 & 1977-11-09 & -14.0 K \\\\\n",
       "\t24 & 1977 & Low & -26 & 1977-12-06 & -24.2 K \\\\\n",
       "\t25 & 1977 & Low & 1 & 1977-01-02 & -24.0 K \\\\\n",
       "\t26 & 1977 & Low & 8 & 1978-01-09 & -24.0 K \\\\\n",
       "\t27 & 1977 & Low & 24 & 1978-01-25 & -25.9 K \\\\\n",
       "\t28 & 1977 & Low & 53 & 1978-02-21 & -21.8 K \\\\\n",
       "\t29 & 1977 & Low & 74 & 1978-03-16 & -18.2 K \\\\\n",
       "\t30 & 1977 & Low & 86 & 1978-03-28 & -11.4 K \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m30×5 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m Year  \u001b[0m\u001b[1m SeedSource \u001b[0m\u001b[1m JD Rounded \u001b[0m\u001b[1m date       \u001b[0m\u001b[1m Hc        \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m String3    \u001b[0m\u001b[90m Int64      \u001b[0m\u001b[90m Date       \u001b[0m\u001b[90m Quantity… \u001b[0m\n",
       "─────┼──────────────────────────────────────────────────────\n",
       "   1 │  1974  Low                -71  1974-10-22     -5.6 K\n",
       "   2 │  1974  Low                -40  1974-11-22    -18.0 K\n",
       "   3 │  1974  Low                  1  1975-01-02    -23.5 K\n",
       "   4 │  1974  Low                 20  1975-01-21    -23.5 K\n",
       "   5 │  1974  Low                 61  1975-03-03    -21.4 K\n",
       "   6 │  1974  Low                 77  1975-03-19    -15.0 K\n",
       "   7 │  1974  Low                104  1975-04-15     -8.8 K\n",
       "   8 │  1976  Low               -100  1976-09-23     -5.5 K\n",
       "   9 │  1976  Low                -90  1976-10-03     -5.2 K\n",
       "  10 │  1976  Low                -86  1976-10-07     -5.7 K\n",
       "  11 │  1976  Low                -75  1976-10-18     -5.7 K\n",
       "  ⋮  │   ⋮        ⋮           ⋮           ⋮           ⋮\n",
       "  21 │  1977  Low                -81  1977-10-12     -6.1 K\n",
       "  22 │  1977  Low                -67  1977-10-26     -9.2 K\n",
       "  23 │  1977  Low                -53  1977-11-09    -14.0 K\n",
       "  24 │  1977  Low                -26  1977-12-06    -24.2 K\n",
       "  25 │  1977  Low                  1  1977-01-02    -24.0 K\n",
       "  26 │  1977  Low                  8  1978-01-09    -24.0 K\n",
       "  27 │  1977  Low                 24  1978-01-25    -25.9 K\n",
       "  28 │  1977  Low                 53  1978-02-21    -21.8 K\n",
       "  29 │  1977  Low                 74  1978-03-16    -18.2 K\n",
       "  30 │  1977  Low                 86  1978-03-28    -11.4 K\n",
       "\u001b[36m                                              9 rows omitted\u001b[0m"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hc_Obs_Low =  CSV.read(\"Hc_Obs_Low.csv\", DataFrame) |> unitfy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7a790a89",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>24×5 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">Year</th><th style = \"text-align: left;\">SeedSource</th><th style = \"text-align: left;\">JD Rounded</th><th style = \"text-align: left;\">date</th><th style = \"text-align: left;\">Hc</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"String7\" style = \"text-align: left;\">String7</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Date\" style = \"text-align: left;\">Date</th><th title = \"Unitful.Quantity{Float64, 𝚯, Unitful.FreeUnits{(K,), 𝚯, nothing}}\" style = \"text-align: left;\">Quantity…</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">-26</td><td style = \"text-align: left;\">1976-12-06</td><td style = \"text-align: right;\">-24.1 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">3</td><td style = \"text-align: left;\">1977-01-04</td><td style = \"text-align: right;\">-21.7 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">10</td><td style = \"text-align: left;\">1977-01-11</td><td style = \"text-align: right;\">-26.9 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">36</td><td style = \"text-align: left;\">1977-02-06</td><td style = \"text-align: right;\">-24.5 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">48</td><td style = \"text-align: left;\">1977-02-18</td><td style = \"text-align: right;\">-23.0 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">61</td><td style = \"text-align: left;\">1977-03-01</td><td style = \"text-align: right;\">-22.0 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">75</td><td style = \"text-align: left;\">1977-03-15</td><td style = \"text-align: right;\">-18.9 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">-81</td><td style = \"text-align: left;\">1977-10-12</td><td style = \"text-align: right;\">-7.0 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">-67</td><td style = \"text-align: left;\">1977-10-26</td><td style = \"text-align: right;\">-9.5 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">-53</td><td style = \"text-align: left;\">1977-11-09</td><td style = \"text-align: right;\">-14.2 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">-26</td><td style = \"text-align: left;\">1977-12-06</td><td style = \"text-align: right;\">-23.4 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">1977-01-01</td><td style = \"text-align: right;\">-27.0 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">8</td><td style = \"text-align: left;\">1978-01-09</td><td style = \"text-align: right;\">-27.1 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">14</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">24</td><td style = \"text-align: left;\">1978-01-25</td><td style = \"text-align: right;\">-27.9 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">15</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">53</td><td style = \"text-align: left;\">1978-02-21</td><td style = \"text-align: right;\">-20.5 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">16</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">74</td><td style = \"text-align: left;\">1978-03-16</td><td style = \"text-align: right;\">-17.7 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">17</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">86</td><td style = \"text-align: left;\">1978-03-28</td><td style = \"text-align: right;\">-9.6 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">18</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">-71</td><td style = \"text-align: left;\">1974-10-22</td><td style = \"text-align: right;\">-6.1 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">19</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">-40</td><td style = \"text-align: left;\">1974-11-22</td><td style = \"text-align: right;\">-17.0 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">20</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">1975-01-02</td><td style = \"text-align: right;\">-24.0 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">21</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">24</td><td style = \"text-align: left;\">1975-01-25</td><td style = \"text-align: right;\">-24.4 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">22</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">61</td><td style = \"text-align: left;\">1975-03-03</td><td style = \"text-align: right;\">-21.7 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">23</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">77</td><td style = \"text-align: left;\">1975-03-19</td><td style = \"text-align: right;\">-16.1 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">24</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">104</td><td style = \"text-align: left;\">1975-04-15</td><td style = \"text-align: right;\">-7.9 K</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccc}\n",
       "\t& Year & SeedSource & JD Rounded & date & Hc\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & String7 & Int64 & Date & Quantity…\\\\\n",
       "\t\\hline\n",
       "\t1 & 1976 & High & -26 & 1976-12-06 & -24.1 K \\\\\n",
       "\t2 & 1976 & High & 3 & 1977-01-04 & -21.7 K \\\\\n",
       "\t3 & 1976 & High & 10 & 1977-01-11 & -26.9 K \\\\\n",
       "\t4 & 1976 & High & 36 & 1977-02-06 & -24.5 K \\\\\n",
       "\t5 & 1976 & High & 48 & 1977-02-18 & -23.0 K \\\\\n",
       "\t6 & 1976 & High & 61 & 1977-03-01 & -22.0 K \\\\\n",
       "\t7 & 1976 & High & 75 & 1977-03-15 & -18.9 K \\\\\n",
       "\t8 & 1977 & High & -81 & 1977-10-12 & -7.0 K \\\\\n",
       "\t9 & 1977 & High & -67 & 1977-10-26 & -9.5 K \\\\\n",
       "\t10 & 1977 & High & -53 & 1977-11-09 & -14.2 K \\\\\n",
       "\t11 & 1977 & High & -26 & 1977-12-06 & -23.4 K \\\\\n",
       "\t12 & 1977 & High & 1 & 1977-01-01 & -27.0 K \\\\\n",
       "\t13 & 1977 & High & 8 & 1978-01-09 & -27.1 K \\\\\n",
       "\t14 & 1977 & High & 24 & 1978-01-25 & -27.9 K \\\\\n",
       "\t15 & 1977 & High & 53 & 1978-02-21 & -20.5 K \\\\\n",
       "\t16 & 1977 & High & 74 & 1978-03-16 & -17.7 K \\\\\n",
       "\t17 & 1977 & High & 86 & 1978-03-28 & -9.6 K \\\\\n",
       "\t18 & 1974 & High & -71 & 1974-10-22 & -6.1 K \\\\\n",
       "\t19 & 1974 & High & -40 & 1974-11-22 & -17.0 K \\\\\n",
       "\t20 & 1974 & High & 1 & 1975-01-02 & -24.0 K \\\\\n",
       "\t21 & 1974 & High & 24 & 1975-01-25 & -24.4 K \\\\\n",
       "\t22 & 1974 & High & 61 & 1975-03-03 & -21.7 K \\\\\n",
       "\t23 & 1974 & High & 77 & 1975-03-19 & -16.1 K \\\\\n",
       "\t24 & 1974 & High & 104 & 1975-04-15 & -7.9 K \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m24×5 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m Year  \u001b[0m\u001b[1m SeedSource \u001b[0m\u001b[1m JD Rounded \u001b[0m\u001b[1m date       \u001b[0m\u001b[1m Hc        \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m String7    \u001b[0m\u001b[90m Int64      \u001b[0m\u001b[90m Date       \u001b[0m\u001b[90m Quantity… \u001b[0m\n",
       "─────┼──────────────────────────────────────────────────────\n",
       "   1 │  1976  High               -26  1976-12-06    -24.1 K\n",
       "   2 │  1976  High                 3  1977-01-04    -21.7 K\n",
       "   3 │  1976  High                10  1977-01-11    -26.9 K\n",
       "   4 │  1976  High                36  1977-02-06    -24.5 K\n",
       "   5 │  1976  High                48  1977-02-18    -23.0 K\n",
       "   6 │  1976  High                61  1977-03-01    -22.0 K\n",
       "   7 │  1976  High                75  1977-03-15    -18.9 K\n",
       "   8 │  1977  High               -81  1977-10-12     -7.0 K\n",
       "   9 │  1977  High               -67  1977-10-26     -9.5 K\n",
       "  10 │  1977  High               -53  1977-11-09    -14.2 K\n",
       "  11 │  1977  High               -26  1977-12-06    -23.4 K\n",
       "  ⋮  │   ⋮        ⋮           ⋮           ⋮           ⋮\n",
       "  15 │  1977  High                53  1978-02-21    -20.5 K\n",
       "  16 │  1977  High                74  1978-03-16    -17.7 K\n",
       "  17 │  1977  High                86  1978-03-28     -9.6 K\n",
       "  18 │  1974  High               -71  1974-10-22     -6.1 K\n",
       "  19 │  1974  High               -40  1974-11-22    -17.0 K\n",
       "  20 │  1974  High                 1  1975-01-02    -24.0 K\n",
       "  21 │  1974  High                24  1975-01-25    -24.4 K\n",
       "  22 │  1974  High                61  1975-03-03    -21.7 K\n",
       "  23 │  1974  High                77  1975-03-19    -16.1 K\n",
       "  24 │  1974  High               104  1975-04-15     -7.9 K\n",
       "\u001b[36m                                              3 rows omitted\u001b[0m"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hc_Obs_High =  CSV.read(\"Hc_Obs_High.csv\", DataFrame) |> unitfy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b3cab3ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>21×6 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">Index</th><th style = \"text-align: left;\">Year</th><th style = \"text-align: left;\">SeedSource</th><th style = \"text-align: left;\">JDay</th><th style = \"text-align: left;\">date</th><th style = \"text-align: left;\">Hc</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"String3\" style = \"text-align: left;\">String3</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Date\" style = \"text-align: left;\">Date</th><th title = \"Unitful.Quantity{Float64, 𝚯, Unitful.FreeUnits{(K,), 𝚯, nothing}}\" style = \"text-align: left;\">Quantity…</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">20</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">75</td><td style = \"text-align: left;\">1977-03-16</td><td style = \"text-align: right;\">-19.8 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">25</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">1977-01-02</td><td style = \"text-align: right;\">-24.0 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-75</td><td style = \"text-align: left;\">1976-10-18</td><td style = \"text-align: right;\">-5.7 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">13</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-39</td><td style = \"text-align: left;\">1976-11-23</td><td style = \"text-align: right;\">-15.4 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">7</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">104</td><td style = \"text-align: left;\">1975-04-15</td><td style = \"text-align: right;\">-8.8 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-40</td><td style = \"text-align: left;\">1974-11-22</td><td style = \"text-align: right;\">-18.0 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-71</td><td style = \"text-align: left;\">1974-10-22</td><td style = \"text-align: right;\">-5.6 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">15</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">1977-01-03</td><td style = \"text-align: right;\">-24.1 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">21</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-81</td><td style = \"text-align: left;\">1977-10-12</td><td style = \"text-align: right;\">-6.1 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">27</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">24</td><td style = \"text-align: left;\">1978-01-25</td><td style = \"text-align: right;\">-25.9 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">30</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">86</td><td style = \"text-align: left;\">1978-03-28</td><td style = \"text-align: right;\">-11.4 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: right;\">29</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">74</td><td style = \"text-align: left;\">1978-03-16</td><td style = \"text-align: right;\">-18.2 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-100</td><td style = \"text-align: left;\">1976-09-23</td><td style = \"text-align: right;\">-5.5 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">14</td><td style = \"text-align: right;\">14</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-15</td><td style = \"text-align: left;\">1976-12-17</td><td style = \"text-align: right;\">-23.6 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">15</td><td style = \"text-align: right;\">22</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-67</td><td style = \"text-align: left;\">1977-10-26</td><td style = \"text-align: right;\">-9.2 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">16</td><td style = \"text-align: right;\">23</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-53</td><td style = \"text-align: left;\">1977-11-09</td><td style = \"text-align: right;\">-14.0 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">17</td><td style = \"text-align: right;\">17</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">36</td><td style = \"text-align: left;\">1977-02-06</td><td style = \"text-align: right;\">-24.8 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">18</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-90</td><td style = \"text-align: left;\">1976-10-03</td><td style = \"text-align: right;\">-5.2 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">19</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">77</td><td style = \"text-align: left;\">1975-03-19</td><td style = \"text-align: right;\">-15.0 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">20</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">1975-01-02</td><td style = \"text-align: right;\">-23.5 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">21</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-60</td><td style = \"text-align: left;\">1976-11-04</td><td style = \"text-align: right;\">-8.9 K</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccc}\n",
       "\t& Index & Year & SeedSource & JDay & date & Hc\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & String3 & Int64 & Date & Quantity…\\\\\n",
       "\t\\hline\n",
       "\t1 & 20 & 1976 & Low & 75 & 1977-03-16 & -19.8 K \\\\\n",
       "\t2 & 25 & 1977 & Low & 1 & 1977-01-02 & -24.0 K \\\\\n",
       "\t3 & 11 & 1976 & Low & -75 & 1976-10-18 & -5.7 K \\\\\n",
       "\t4 & 13 & 1976 & Low & -39 & 1976-11-23 & -15.4 K \\\\\n",
       "\t5 & 7 & 1974 & Low & 104 & 1975-04-15 & -8.8 K \\\\\n",
       "\t6 & 2 & 1974 & Low & -40 & 1974-11-22 & -18.0 K \\\\\n",
       "\t7 & 1 & 1974 & Low & -71 & 1974-10-22 & -5.6 K \\\\\n",
       "\t8 & 15 & 1976 & Low & 2 & 1977-01-03 & -24.1 K \\\\\n",
       "\t9 & 21 & 1977 & Low & -81 & 1977-10-12 & -6.1 K \\\\\n",
       "\t10 & 27 & 1977 & Low & 24 & 1978-01-25 & -25.9 K \\\\\n",
       "\t11 & 30 & 1977 & Low & 86 & 1978-03-28 & -11.4 K \\\\\n",
       "\t12 & 29 & 1977 & Low & 74 & 1978-03-16 & -18.2 K \\\\\n",
       "\t13 & 8 & 1976 & Low & -100 & 1976-09-23 & -5.5 K \\\\\n",
       "\t14 & 14 & 1976 & Low & -15 & 1976-12-17 & -23.6 K \\\\\n",
       "\t15 & 22 & 1977 & Low & -67 & 1977-10-26 & -9.2 K \\\\\n",
       "\t16 & 23 & 1977 & Low & -53 & 1977-11-09 & -14.0 K \\\\\n",
       "\t17 & 17 & 1976 & Low & 36 & 1977-02-06 & -24.8 K \\\\\n",
       "\t18 & 9 & 1976 & Low & -90 & 1976-10-03 & -5.2 K \\\\\n",
       "\t19 & 6 & 1974 & Low & 77 & 1975-03-19 & -15.0 K \\\\\n",
       "\t20 & 3 & 1974 & Low & 1 & 1975-01-02 & -23.5 K \\\\\n",
       "\t21 & 12 & 1976 & Low & -60 & 1976-11-04 & -8.9 K \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m21×6 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m Index \u001b[0m\u001b[1m Year  \u001b[0m\u001b[1m SeedSource \u001b[0m\u001b[1m JDay  \u001b[0m\u001b[1m date       \u001b[0m\u001b[1m Hc        \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m String3    \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Date       \u001b[0m\u001b[90m Quantity… \u001b[0m\n",
       "─────┼────────────────────────────────────────────────────────\n",
       "   1 │    20   1976  Low            75  1977-03-16    -19.8 K\n",
       "   2 │    25   1977  Low             1  1977-01-02    -24.0 K\n",
       "   3 │    11   1976  Low           -75  1976-10-18     -5.7 K\n",
       "   4 │    13   1976  Low           -39  1976-11-23    -15.4 K\n",
       "   5 │     7   1974  Low           104  1975-04-15     -8.8 K\n",
       "   6 │     2   1974  Low           -40  1974-11-22    -18.0 K\n",
       "   7 │     1   1974  Low           -71  1974-10-22     -5.6 K\n",
       "   8 │    15   1976  Low             2  1977-01-03    -24.1 K\n",
       "   9 │    21   1977  Low           -81  1977-10-12     -6.1 K\n",
       "  10 │    27   1977  Low            24  1978-01-25    -25.9 K\n",
       "  11 │    30   1977  Low            86  1978-03-28    -11.4 K\n",
       "  12 │    29   1977  Low            74  1978-03-16    -18.2 K\n",
       "  13 │     8   1976  Low          -100  1976-09-23     -5.5 K\n",
       "  14 │    14   1976  Low           -15  1976-12-17    -23.6 K\n",
       "  15 │    22   1977  Low           -67  1977-10-26     -9.2 K\n",
       "  16 │    23   1977  Low           -53  1977-11-09    -14.0 K\n",
       "  17 │    17   1976  Low            36  1977-02-06    -24.8 K\n",
       "  18 │     9   1976  Low           -90  1976-10-03     -5.2 K\n",
       "  19 │     6   1974  Low            77  1975-03-19    -15.0 K\n",
       "  20 │     3   1974  Low             1  1975-01-02    -23.5 K\n",
       "  21 │    12   1976  Low           -60  1976-11-04     -8.9 K"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LowTrain = CSV.read(\"LowTrain.csv\", DataFrame) |> unitfy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "94ec3550",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>17×6 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">Index</th><th style = \"text-align: left;\">Year</th><th style = \"text-align: left;\">SeedSource</th><th style = \"text-align: left;\">JDay</th><th style = \"text-align: left;\">date</th><th style = \"text-align: left;\">Hc</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"String7\" style = \"text-align: left;\">String7</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Date\" style = \"text-align: left;\">Date</th><th title = \"Unitful.Quantity{Float64, 𝚯, Unitful.FreeUnits{(K,), 𝚯, nothing}}\" style = \"text-align: left;\">Quantity…</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">21</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">24</td><td style = \"text-align: left;\">1975-01-25</td><td style = \"text-align: right;\">-24.4 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">7</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">75</td><td style = \"text-align: left;\">1977-03-15</td><td style = \"text-align: right;\">-18.9 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">-81</td><td style = \"text-align: left;\">1977-10-12</td><td style = \"text-align: right;\">-7.0 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">18</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">-71</td><td style = \"text-align: left;\">1974-10-22</td><td style = \"text-align: right;\">-6.1 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">36</td><td style = \"text-align: left;\">1977-02-06</td><td style = \"text-align: right;\">-24.5 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">13</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">8</td><td style = \"text-align: left;\">1978-01-09</td><td style = \"text-align: right;\">-27.1 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">61</td><td style = \"text-align: left;\">1977-03-01</td><td style = \"text-align: right;\">-22.0 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">17</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">86</td><td style = \"text-align: left;\">1978-03-28</td><td style = \"text-align: right;\">-9.6 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">20</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">1975-01-02</td><td style = \"text-align: right;\">-24.0 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">15</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">53</td><td style = \"text-align: left;\">1978-02-21</td><td style = \"text-align: right;\">-20.5 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">16</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">74</td><td style = \"text-align: left;\">1978-03-16</td><td style = \"text-align: right;\">-17.7 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: right;\">22</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">61</td><td style = \"text-align: left;\">1975-03-03</td><td style = \"text-align: right;\">-21.7 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">-26</td><td style = \"text-align: left;\">1976-12-06</td><td style = \"text-align: right;\">-24.1 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">14</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">-67</td><td style = \"text-align: left;\">1977-10-26</td><td style = \"text-align: right;\">-9.5 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">15</td><td style = \"text-align: right;\">24</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">104</td><td style = \"text-align: left;\">1975-04-15</td><td style = \"text-align: right;\">-7.9 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">16</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">-53</td><td style = \"text-align: left;\">1977-11-09</td><td style = \"text-align: right;\">-14.2 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">17</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">48</td><td style = \"text-align: left;\">1977-02-18</td><td style = \"text-align: right;\">-23.0 K</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccc}\n",
       "\t& Index & Year & SeedSource & JDay & date & Hc\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & String7 & Int64 & Date & Quantity…\\\\\n",
       "\t\\hline\n",
       "\t1 & 21 & 1974 & High & 24 & 1975-01-25 & -24.4 K \\\\\n",
       "\t2 & 7 & 1976 & High & 75 & 1977-03-15 & -18.9 K \\\\\n",
       "\t3 & 8 & 1977 & High & -81 & 1977-10-12 & -7.0 K \\\\\n",
       "\t4 & 18 & 1974 & High & -71 & 1974-10-22 & -6.1 K \\\\\n",
       "\t5 & 4 & 1976 & High & 36 & 1977-02-06 & -24.5 K \\\\\n",
       "\t6 & 13 & 1977 & High & 8 & 1978-01-09 & -27.1 K \\\\\n",
       "\t7 & 6 & 1976 & High & 61 & 1977-03-01 & -22.0 K \\\\\n",
       "\t8 & 17 & 1977 & High & 86 & 1978-03-28 & -9.6 K \\\\\n",
       "\t9 & 20 & 1974 & High & 1 & 1975-01-02 & -24.0 K \\\\\n",
       "\t10 & 15 & 1977 & High & 53 & 1978-02-21 & -20.5 K \\\\\n",
       "\t11 & 16 & 1977 & High & 74 & 1978-03-16 & -17.7 K \\\\\n",
       "\t12 & 22 & 1974 & High & 61 & 1975-03-03 & -21.7 K \\\\\n",
       "\t13 & 1 & 1976 & High & -26 & 1976-12-06 & -24.1 K \\\\\n",
       "\t14 & 9 & 1977 & High & -67 & 1977-10-26 & -9.5 K \\\\\n",
       "\t15 & 24 & 1974 & High & 104 & 1975-04-15 & -7.9 K \\\\\n",
       "\t16 & 10 & 1977 & High & -53 & 1977-11-09 & -14.2 K \\\\\n",
       "\t17 & 5 & 1976 & High & 48 & 1977-02-18 & -23.0 K \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m17×6 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m Index \u001b[0m\u001b[1m Year  \u001b[0m\u001b[1m SeedSource \u001b[0m\u001b[1m JDay  \u001b[0m\u001b[1m date       \u001b[0m\u001b[1m Hc        \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m String7    \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Date       \u001b[0m\u001b[90m Quantity… \u001b[0m\n",
       "─────┼────────────────────────────────────────────────────────\n",
       "   1 │    21   1974  High           24  1975-01-25    -24.4 K\n",
       "   2 │     7   1976  High           75  1977-03-15    -18.9 K\n",
       "   3 │     8   1977  High          -81  1977-10-12     -7.0 K\n",
       "   4 │    18   1974  High          -71  1974-10-22     -6.1 K\n",
       "   5 │     4   1976  High           36  1977-02-06    -24.5 K\n",
       "   6 │    13   1977  High            8  1978-01-09    -27.1 K\n",
       "   7 │     6   1976  High           61  1977-03-01    -22.0 K\n",
       "   8 │    17   1977  High           86  1978-03-28     -9.6 K\n",
       "   9 │    20   1974  High            1  1975-01-02    -24.0 K\n",
       "  10 │    15   1977  High           53  1978-02-21    -20.5 K\n",
       "  11 │    16   1977  High           74  1978-03-16    -17.7 K\n",
       "  12 │    22   1974  High           61  1975-03-03    -21.7 K\n",
       "  13 │     1   1976  High          -26  1976-12-06    -24.1 K\n",
       "  14 │     9   1977  High          -67  1977-10-26     -9.5 K\n",
       "  15 │    24   1974  High          104  1975-04-15     -7.9 K\n",
       "  16 │    10   1977  High          -53  1977-11-09    -14.2 K\n",
       "  17 │     5   1976  High           48  1977-02-18    -23.0 K"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HighTrain = CSV.read(\"HighTrain.csv\", DataFrame) |> unitfy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b656dd98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>9×6 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">Index</th><th style = \"text-align: left;\">Year</th><th style = \"text-align: left;\">SeedSource</th><th style = \"text-align: left;\">JDay</th><th style = \"text-align: left;\">date</th><th style = \"text-align: left;\">Hc</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"String3\" style = \"text-align: left;\">String3</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Date\" style = \"text-align: left;\">Date</th><th title = \"Unitful.Quantity{Float64, 𝚯, Unitful.FreeUnits{(K,), 𝚯, nothing}}\" style = \"text-align: left;\">Quantity…</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">20</td><td style = \"text-align: left;\">1975-01-21</td><td style = \"text-align: right;\">-23.5 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">61</td><td style = \"text-align: left;\">1975-03-03</td><td style = \"text-align: right;\">-21.4 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-86</td><td style = \"text-align: left;\">1976-10-07</td><td style = \"text-align: right;\">-5.7 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">16</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">10</td><td style = \"text-align: left;\">1977-01-11</td><td style = \"text-align: right;\">-26.2 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">18</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">48</td><td style = \"text-align: left;\">1977-02-18</td><td style = \"text-align: right;\">-23.6 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">19</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">61</td><td style = \"text-align: left;\">1977-03-02</td><td style = \"text-align: right;\">-20.2 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">24</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">-26</td><td style = \"text-align: left;\">1977-12-06</td><td style = \"text-align: right;\">-24.2 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">26</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">8</td><td style = \"text-align: left;\">1978-01-09</td><td style = \"text-align: right;\">-24.0 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">28</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">Low</td><td style = \"text-align: right;\">53</td><td style = \"text-align: left;\">1978-02-21</td><td style = \"text-align: right;\">-21.8 K</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccc}\n",
       "\t& Index & Year & SeedSource & JDay & date & Hc\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & String3 & Int64 & Date & Quantity…\\\\\n",
       "\t\\hline\n",
       "\t1 & 4 & 1974 & Low & 20 & 1975-01-21 & -23.5 K \\\\\n",
       "\t2 & 5 & 1974 & Low & 61 & 1975-03-03 & -21.4 K \\\\\n",
       "\t3 & 10 & 1976 & Low & -86 & 1976-10-07 & -5.7 K \\\\\n",
       "\t4 & 16 & 1976 & Low & 10 & 1977-01-11 & -26.2 K \\\\\n",
       "\t5 & 18 & 1976 & Low & 48 & 1977-02-18 & -23.6 K \\\\\n",
       "\t6 & 19 & 1976 & Low & 61 & 1977-03-02 & -20.2 K \\\\\n",
       "\t7 & 24 & 1977 & Low & -26 & 1977-12-06 & -24.2 K \\\\\n",
       "\t8 & 26 & 1977 & Low & 8 & 1978-01-09 & -24.0 K \\\\\n",
       "\t9 & 28 & 1977 & Low & 53 & 1978-02-21 & -21.8 K \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m9×6 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m Index \u001b[0m\u001b[1m Year  \u001b[0m\u001b[1m SeedSource \u001b[0m\u001b[1m JDay  \u001b[0m\u001b[1m date       \u001b[0m\u001b[1m Hc        \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m String3    \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Date       \u001b[0m\u001b[90m Quantity… \u001b[0m\n",
       "─────┼────────────────────────────────────────────────────────\n",
       "   1 │     4   1974  Low            20  1975-01-21    -23.5 K\n",
       "   2 │     5   1974  Low            61  1975-03-03    -21.4 K\n",
       "   3 │    10   1976  Low           -86  1976-10-07     -5.7 K\n",
       "   4 │    16   1976  Low            10  1977-01-11    -26.2 K\n",
       "   5 │    18   1976  Low            48  1977-02-18    -23.6 K\n",
       "   6 │    19   1976  Low            61  1977-03-02    -20.2 K\n",
       "   7 │    24   1977  Low           -26  1977-12-06    -24.2 K\n",
       "   8 │    26   1977  Low             8  1978-01-09    -24.0 K\n",
       "   9 │    28   1977  Low            53  1978-02-21    -21.8 K"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LowTest = CSV.read(\"LowTest.csv\", DataFrame) |> unitfy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "901c2846",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>7×6 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">Index</th><th style = \"text-align: left;\">Year</th><th style = \"text-align: left;\">SeedSource</th><th style = \"text-align: left;\">JDay</th><th style = \"text-align: left;\">date</th><th style = \"text-align: left;\">Hc</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"String7\" style = \"text-align: left;\">String7</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Date\" style = \"text-align: left;\">Date</th><th title = \"Unitful.Quantity{Float64, 𝚯, Unitful.FreeUnits{(K,), 𝚯, nothing}}\" style = \"text-align: left;\">Quantity…</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">3</td><td style = \"text-align: left;\">1977-01-04</td><td style = \"text-align: right;\">-21.7 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">1976</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">10</td><td style = \"text-align: left;\">1977-01-11</td><td style = \"text-align: right;\">-26.9 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">-26</td><td style = \"text-align: left;\">1977-12-06</td><td style = \"text-align: right;\">-23.4 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">1977-01-01</td><td style = \"text-align: right;\">-27.0 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">14</td><td style = \"text-align: right;\">1977</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">24</td><td style = \"text-align: left;\">1978-01-25</td><td style = \"text-align: right;\">-27.9 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">19</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">-40</td><td style = \"text-align: left;\">1974-11-22</td><td style = \"text-align: right;\">-17.0 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">23</td><td style = \"text-align: right;\">1974</td><td style = \"text-align: left;\">High</td><td style = \"text-align: right;\">77</td><td style = \"text-align: left;\">1975-03-19</td><td style = \"text-align: right;\">-16.1 K</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccc}\n",
       "\t& Index & Year & SeedSource & JDay & date & Hc\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & String7 & Int64 & Date & Quantity…\\\\\n",
       "\t\\hline\n",
       "\t1 & 2 & 1976 & High & 3 & 1977-01-04 & -21.7 K \\\\\n",
       "\t2 & 3 & 1976 & High & 10 & 1977-01-11 & -26.9 K \\\\\n",
       "\t3 & 11 & 1977 & High & -26 & 1977-12-06 & -23.4 K \\\\\n",
       "\t4 & 12 & 1977 & High & 1 & 1977-01-01 & -27.0 K \\\\\n",
       "\t5 & 14 & 1977 & High & 24 & 1978-01-25 & -27.9 K \\\\\n",
       "\t6 & 19 & 1974 & High & -40 & 1974-11-22 & -17.0 K \\\\\n",
       "\t7 & 23 & 1974 & High & 77 & 1975-03-19 & -16.1 K \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m7×6 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m Index \u001b[0m\u001b[1m Year  \u001b[0m\u001b[1m SeedSource \u001b[0m\u001b[1m JDay  \u001b[0m\u001b[1m date       \u001b[0m\u001b[1m Hc        \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m String7    \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Date       \u001b[0m\u001b[90m Quantity… \u001b[0m\n",
       "─────┼────────────────────────────────────────────────────────\n",
       "   1 │     2   1976  High            3  1977-01-04    -21.7 K\n",
       "   2 │     3   1976  High           10  1977-01-11    -26.9 K\n",
       "   3 │    11   1977  High          -26  1977-12-06    -23.4 K\n",
       "   4 │    12   1977  High            1  1977-01-01    -27.0 K\n",
       "   5 │    14   1977  High           24  1978-01-25    -27.9 K\n",
       "   6 │    19   1974  High          -40  1974-11-22    -17.0 K\n",
       "   7 │    23   1974  High           77  1975-03-19    -16.1 K"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " HighTest = CSV.read(\"HighTest.csv\", DataFrame) |> unitfy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7876aa33",
   "metadata": {},
   "source": [
    "# Cold hardienss model\n",
    "The cold hardiness model used here divides cold hardiness during dormancy into two phases, acclimation (fall into winter) and deacclimation (winter into spring). These two phases are switched between based on a required chilling accumulation. Model formulas are shown below and model implementation is the code chunk at the bottom of this section.  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92603747",
   "metadata": {},
   "source": [
    "- Cold Hardiness Model Parameters\n",
    "\n",
    "| Symbol | Example Parameter Value | Units | Description |\n",
    "|:-------|:------|:------|:------------|\n",
    "| $H_{\\mathrm{c}}$ | - | °$\\mathrm{C}$ | Cold Hardiness |\n",
    "| $H_{\\mathrm{c, i}}$ | -2.40 | °$\\mathrm{C}$ | Initial Cold Hardiness Value |\n",
    "| $H_{\\mathrm{c, ll}}$ | -17.4 / -22.0 | °$\\mathrm{C}$ |Lower Limit of Cold Hardiness Temperature (Most Hardy) |\n",
    "| $H_{\\mathrm{c, ul}}$ | -2.33 |°$\\mathrm{C}$ | Upper Limit of Cold Hardiness Temperature (Least Hardy) |\n",
    "| $T_{\\mathrm{th,a}}$ | 9.43 | °$\\mathrm{C}$ | Threshold temperature for degree-days during acclimation | \n",
    "| $T_{\\mathrm{th,d}}$ | 8.63 | °$\\mathrm{C}$ | Threshold temperature for degree-days during deacclimation | \n",
    "| $R_{\\mathrm{c}}$ | -252 | °$\\mathrm{C}$ | Chilling requirement |\n",
    "| $R_{\\mathrm{f}}$ | 395 | °$\\mathrm{C}$ | Forcing requirement |\n",
    "| $k_{\\mathrm{a}}$ | 0.12 |°$\\mathrm{C}$ °$\\mathrm{C^{-1}}$| Acclimation rate during acclimation |\n",
    "| $k_{\\mathrm{d}}$ | 1.81 |°$\\mathrm{C}$ °$\\mathrm{C^{-1}}$| Deacclimation rate during deacclimation || $T_{\\mathrm{max}}$ | - | °$\\mathrm{C}$ | Maximum Daily Temperature |\n",
    "| $T_{\\mathrm{mean}}$ | - | °$\\mathrm{C}$ | Mean Daily Temperature |\n",
    "| $T_{\\mathrm{min}}$ | - | °$\\mathrm{C}$ | Minimum Daily Temperature |\n",
    "| $DD_{\\mathrm{c}}$ | - |°$\\mathrm{C}$ |Chilling degree-days |\n",
    "| $DD_{\\mathrm{f}}$ | - |°$\\mathrm{C}$ | Forcing degree-days |\n",
    "\n",
    "- $H_{\\mathrm{c}}$ values are always negative"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dabc1c29",
   "metadata": {},
   "source": [
    "- Equation 1: Average Daily Temperature \n",
    "$$\n",
    "\\begin{align}\n",
    "T_{\\mathrm{mean}} &= \\frac{(T_{\\mathrm{max}} + T_{\\mathrm{min}})}{2}\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "- Equation 2: Degree Day\n",
    "$$\n",
    "DD = T_{\\mathrm{mean}} - T_{\\mathrm{th}}\n",
    "$$\n",
    "\n",
    "- Equation 3: Changes in acclimation or deacclimation\n",
    "\n",
    "                                                    If forcing requirement has not been met. \n",
    "$$\n",
    "ΔH_{\\mathrm{c}} = (DD_{\\mathrm{c}} * k_{\\mathrm{a}} *  c_{\\mathrm{log, a}}) \n",
    "$$\n",
    "                                                    If forcing requirement has been met.\n",
    "$$\n",
    "ΔH_{\\mathrm{c}} = (DD_{\\mathrm{f}} * k_{\\mathrm{d}} *  c_{\\mathrm{log, d}})\n",
    "$$\n",
    "\n",
    "- Equation 4: Acclimation logistic fuction\n",
    "$$\n",
    "\\begin{align}\n",
    "c_{\\mathrm{log, a}} &= \\frac{ H_{\\mathrm{c, ll}} - H_{\\mathrm{c, i-1}}}{ H_{\\mathrm{c, ll}} - H_{\\mathrm{c, ul}}} \\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "- Equation 5: Deacclimation logistic fuction\n",
    "$$\n",
    "\\begin{align}\n",
    "c_{\\mathrm{log, d}} &= \\frac{ H_{\\mathrm{c, i-1}} - H_{\\mathrm{c, ul}}}{ H_{\\mathrm{c, ll}} - H_{\\mathrm{c, ul}}} \\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "- Equation 6: Cold Hardiness on a given day\n",
    "$$\n",
    "H_{\\mathrm{c,i}} = H_{\\mathrm{c,i-1}} + ΔH_{\\mathrm{c}}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "bba32a34",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ColdHardinessEstimator"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#This is the implementation of the cold hardiness model\n",
    "#Here and throughout the rest of the script Hc_min=Hc_ll and Hc_max=Hc_ul\n",
    "@system ColdHardinessEstimator(Temperature, Controller) begin\n",
    "    Tc_a: temperature_threshold_acclimation ~ preserve(u\"°C\", parameter)\n",
    "    Tc_d: temperature_threshold_deacclimation ~ preserve(u\"°C\", parameter)\n",
    "    Rc: chilling_requirement ~ preserve(u\"K\", parameter)\n",
    "    #Rf: forcing_requirement ~ preserve(u\"K\", parameter)\n",
    "\n",
    "    year(t=calendar.last) => Dates.year(t) ~ preserve::Int\n",
    "    \n",
    "    doy(t): day_of_year => Dates.dayofyear(t) ~ track::Int(u\"d\")\n",
    "\n",
    "    Ta(T) ~ track(u\"°C\", min=0)\n",
    "    Δt(context.clock.step) ~ preserve(u\"d\")\n",
    "    ΔT_a(Ta, Tc_a, Δt) => (Ta - Tc_a) / Δt ~ track(u\"K/d\")\n",
    "    ΔT_d(Ta, Tc_d, Δt) => (Ta - Tc_d) / Δt ~ track(u\"K/d\")\n",
    "\n",
    "    c(ΔT_a): chilling ~ track(u\"K/d\", max=0)\n",
    "    C(c): chilling_accumulated ~ accumulate(when=!d, u\"K\")\n",
    "\n",
    "    d(C, Rc): chilling_done => (C <= Rc) ~ flag\n",
    "\n",
    "    f(ΔT_d): forcing ~ track(u\"K/d\", min=0)\n",
    "    F(f): forcing_accumulated ~ accumulate(when=d, u\"K\")\n",
    "\n",
    "    #match(F, Rf) => (F >= Rf) ~ flag\n",
    "    match(Hc, Hc_max) => (Hc >= Hc_max) ~ flag\n",
    "    stop(m=match, s=calendar.stop) => (m || s) ~ flag\n",
    "    \n",
    "    Hc_min: minimum_cold_hardiness ~ preserve(u\"K\", parameter) #changed from K\n",
    "    Hc_max: maximum_cold_hardiness ~ preserve(u\"K\", parameter) #changed from K\n",
    "    Hc0: initial_cold_hardiness ~ preserve(u\"K\", parameter) #changed from K\n",
    "    ka: acclimation_constant ~ preserve(parameter)\n",
    "    kd: deacclimation_constant ~ preserve(parameter)\n",
    "    \n",
    "    ΔHc_a(c, ka, Hc_min, Hc_max, Hc): change_cold_hardiness_acclimation => c * ka * ((Hc_min - Hc) / (Hc_min - Hc_max)) ~ track(when=!d, u\"K/d\")\n",
    "    ΔHc_d(f, kd, Hc_min, Hc_max, Hc): change_cold_hardiness_deacclimation => f * kd * ((Hc - Hc_max) / (Hc_min - Hc_max)) ~ track(when=d, u\"K/d\")\n",
    "    \n",
    "    Hc(ΔHc_a, ΔHc_d) => ΔHc_a + ΔHc_d ~ accumulate(u\"K \", init=Hc0, min = -40, max=0) \n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8becc1c",
   "metadata": {},
   "source": [
    "# Model Calibration\n",
    "Model calibration is an optimization method that selects the best set of the parameters for the given training data set and model. Calibration here is set to run 5000 steps to select the best model parameters. Parameter value thresholds can be mannualy controlled or fixed in the script below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "1bd8946a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Starting optimization with optimizer BlackBoxOptim.DiffEvoOpt{BlackBoxOptim.FitPopulation{Float64}, BlackBoxOptim.RadiusLimitedSelector, BlackBoxOptim.AdaptiveDiffEvoRandBin{3}, BlackBoxOptim.RandomBound{BlackBoxOptim.ContinuousRectSearchSpace}}\n",
      "0.00 secs, 0 evals, 0 steps\n",
      "\n",
      "Optimization stopped after 5001 steps and 5.68 seconds\n",
      "Termination reason: Max number of steps (5000) reached\n",
      "Steps per second = 880.30\n",
      "Function evals per second = 893.86\n",
      "Improvements/step = 0.16600\n",
      "Total function evaluations = 5078\n",
      "\n",
      "\n",
      "Best candidate found: [8.68023, 3.28032, -494.642, -23.8273, -0.0290756, -3.79958, 0.598756, 0.25087]\n",
      "\n",
      "Fitness: "
     ]
    },
    {
     "data": {
      "text/html": [
       "<p style=\"font-family: monospace\">Config for 1 system:</p>\n",
       "<table style=\"font-family: monospace\">\n",
       "<tr style=\"background-color: transparent\">\n",
       "<td colspan=\"3\" style=\"text-align: left; padding: 2px; padding-left: 20px; color: rebeccapurple\">ColdHardinessEstimator</th>\n",
       "</tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">Tc_a</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">8.68023 °C</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">Tc_d</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">3.28032 °C</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">Rc</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">-494.642 K</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">Hc_min</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">-23.8273 K</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">Hc_max</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">-0.0290756 K</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">Hc0</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">-3.79958 K</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">ka</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">0.598756</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">kd</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">0.25087</td></tr>\n",
       "</table>\n"
      ],
      "text/plain": [
       "Config for 1 system:\n",
       "  \u001b[95mColdHardinessEstimator\u001b[39m\n",
       "    \u001b[94mTc_a  \u001b[39m\u001b[90m = \u001b[39m8.68023 °C\n",
       "    \u001b[94mTc_d  \u001b[39m\u001b[90m = \u001b[39m3.28032 °C\n",
       "    \u001b[94mRc    \u001b[39m\u001b[90m = \u001b[39m-494.642 K\n",
       "    \u001b[94mHc_min\u001b[39m\u001b[90m = \u001b[39m-23.8273 K\n",
       "    \u001b[94mHc_max\u001b[39m\u001b[90m = \u001b[39m-0.0290756 K\n",
       "    \u001b[94mHc0   \u001b[39m\u001b[90m = \u001b[39m-3.79958 K\n",
       "    \u001b[94mka    \u001b[39m\u001b[90m = \u001b[39m0.598756\n",
       "    \u001b[94mkd    \u001b[39m\u001b[90m = \u001b[39m0.25087"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.403492468\n",
      "\n"
     ]
    }
   ],
   "source": [
    "calib_config_Low = calibrate(ColdHardinessEstimator, LowTrain;\n",
    "    config = @config(D6_1974_config),\n",
    "    index = :date,\n",
    "    target = :Hc,\n",
    "    parameters = :ColdHardinessEstimator => (;   \n",
    "        Tc_a = (0, 10),\n",
    "        Tc_d = (0, 10),\n",
    "        Rc = (-1000, -100), \n",
    "        Hc_min = (-40, -15), #-40 is the chemical limit of supercooling, the mechanism responsible for Hc\n",
    "        Hc_max = (-5, 0),\n",
    "        Hc0 = (-7, 0),\n",
    "        ka = (0,1),\n",
    "        kd = (0,1),\n",
    "    ),\n",
    "    stop = :stop,\n",
    "    optim = (;\n",
    "        MaxSteps=5000,\n",
    "    ),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "975ac82c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Starting optimization with optimizer BlackBoxOptim.DiffEvoOpt{BlackBoxOptim.FitPopulation{Float64}, BlackBoxOptim.RadiusLimitedSelector, BlackBoxOptim.AdaptiveDiffEvoRandBin{3}, BlackBoxOptim.RandomBound{BlackBoxOptim.ContinuousRectSearchSpace}}\n",
      "0.00 secs, 0 evals, 0 steps\n",
      "\n",
      "Optimization stopped after 5001 steps and 5.20 seconds\n",
      "Termination reason: Max number of steps (5000) reached\n",
      "Steps per second = 961.55\n",
      "Function evals per second = 982.89\n",
      "Improvements/step = 0.15140\n",
      "Total function evaluations = 5112\n",
      "\n",
      "\n",
      "Best candidate found: [9.67082, 0.666556, -630.037, -24.453, -0.82516, -4.6808, 0.289712, 0.133168]\n",
      "\n",
      "Fitness: 0.466501485\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<p style=\"font-family: monospace\">Config for 1 system:</p>\n",
       "<table style=\"font-family: monospace\">\n",
       "<tr style=\"background-color: transparent\">\n",
       "<td colspan=\"3\" style=\"text-align: left; padding: 2px; padding-left: 20px; color: rebeccapurple\">ColdHardinessEstimator</th>\n",
       "</tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">Tc_a</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">9.67082 °C</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">Tc_d</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">0.666556 °C</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">Rc</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">-630.037 K</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">Hc_min</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">-24.453 K</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">Hc_max</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">-0.82516 K</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">Hc0</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">-4.6808 K</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">ka</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">0.289712</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">kd</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">0.133168</td></tr>\n",
       "</table>\n"
      ],
      "text/plain": [
       "Config for 1 system:\n",
       "  \u001b[95mColdHardinessEstimator\u001b[39m\n",
       "    \u001b[94mTc_a  \u001b[39m\u001b[90m = \u001b[39m9.67082 °C\n",
       "    \u001b[94mTc_d  \u001b[39m\u001b[90m = \u001b[39m0.666556 °C\n",
       "    \u001b[94mRc    \u001b[39m\u001b[90m = \u001b[39m-630.037 K\n",
       "    \u001b[94mHc_min\u001b[39m\u001b[90m = \u001b[39m-24.453 K\n",
       "    \u001b[94mHc_max\u001b[39m\u001b[90m = \u001b[39m-0.82516 K\n",
       "    \u001b[94mHc0   \u001b[39m\u001b[90m = \u001b[39m-4.6808 K\n",
       "    \u001b[94mka    \u001b[39m\u001b[90m = \u001b[39m0.289712\n",
       "    \u001b[94mkd    \u001b[39m\u001b[90m = \u001b[39m0.133168"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calib_config_High = calibrate(ColdHardinessEstimator, HighTrain;\n",
    "    config = @config(D6_1974_config),\n",
    "    index = :date,\n",
    "    target = :Hc,\n",
    "    parameters = :ColdHardinessEstimator => (;   \n",
    "        Tc_a = (0, 10),\n",
    "        Tc_d = (0, 10),\n",
    "        Rc = (-1000, -100), \n",
    "        Hc_min = (-40, -15), #-40 is the chemical limit of supercooling, the mechanism responsible for Hc\n",
    "        Hc_max = (-5, 0),\n",
    "        Hc0 = (-7, 0),\n",
    "        ka = (0,1),\n",
    "        kd = (0,1),\n",
    "    ),\n",
    "    stop = :stop,\n",
    "    optim = (;\n",
    "        MaxSteps=5000,\n",
    "    ),\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "531bcf93",
   "metadata": {},
   "source": [
    "# Model Predictions\n",
    "Once parameters are determined via calibration the model can be run to predict cold hardiness at daily intervals. These predictions are estimated from daily temperature inputs, and controlled by model parameters. So in the case where there is high confidence in model parameters cold hardiness can be predicted with just daily average temperature. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "de029cd3",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>213×5 DataFrame</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">188 rows omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">t</th><th style = \"text-align: left;\">T</th><th style = \"text-align: left;\">C</th><th style = \"text-align: left;\">F</th><th style = \"text-align: left;\">Hc</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Date\" style = \"text-align: left;\">Date</th><th title = \"Unitful.Quantity{Float64, 𝚯, Unitful.FreeUnits{(K,), 𝚯, Unitful.Affine{-5463//20}}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝚯, Unitful.FreeUnits{(K,), 𝚯, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝚯, Unitful.FreeUnits{(K,), 𝚯, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝚯, Unitful.FreeUnits{(K,), 𝚯, nothing}}\" style = \"text-align: left;\">Quantity…</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">1974-10-01</td><td style = \"text-align: right;\">16.3889 °C</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.6808 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">1974-10-02</td><td style = \"text-align: right;\">14.4444 °C</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.6808 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">1974-10-03</td><td style = \"text-align: right;\">11.1111 °C</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.6808 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">1974-10-04</td><td style = \"text-align: right;\">10.0 °C</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.6808 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">1974-10-05</td><td style = \"text-align: right;\">9.16667 °C</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.6808 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: left;\">1974-10-06</td><td style = \"text-align: right;\">9.16667 °C</td><td style = \"text-align: right;\">-0.504156 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.80303 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: left;\">1974-10-07</td><td style = \"text-align: right;\">11.9444 °C</td><td style = \"text-align: right;\">-1.00831 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.9245 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: left;\">1974-10-08</td><td style = \"text-align: right;\">13.3333 °C</td><td style = \"text-align: right;\">-1.00831 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.9245 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: left;\">1974-10-09</td><td style = \"text-align: right;\">10.5556 °C</td><td style = \"text-align: right;\">-1.00831 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.9245 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: left;\">1974-10-10</td><td style = \"text-align: right;\">11.3889 °C</td><td style = \"text-align: right;\">-1.00831 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.9245 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: left;\">1974-10-11</td><td style = \"text-align: right;\">12.7778 °C</td><td style = \"text-align: right;\">-1.00831 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.9245 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: left;\">1974-10-12</td><td style = \"text-align: right;\">12.2222 °C</td><td style = \"text-align: right;\">-1.00831 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.9245 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: left;\">1974-10-13</td><td style = \"text-align: right;\">10.0 °C</td><td style = \"text-align: right;\">-1.00831 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.9245 K</td></tr><tr><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">202</td><td style = \"text-align: left;\">1975-04-20</td><td style = \"text-align: right;\">6.11111 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">242.395 K</td><td style = \"text-align: right;\">-6.71335 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">203</td><td style = \"text-align: left;\">1975-04-21</td><td style = \"text-align: right;\">7.5 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">247.839 K</td><td style = \"text-align: right;\">-6.53267 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">204</td><td style = \"text-align: left;\">1975-04-22</td><td style = \"text-align: right;\">7.22222 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">254.673 K</td><td style = \"text-align: right;\">-6.31285 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">205</td><td style = \"text-align: left;\">1975-04-23</td><td style = \"text-align: right;\">8.05556 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">261.228 K</td><td style = \"text-align: right;\">-6.11009 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">206</td><td style = \"text-align: left;\">1975-04-24</td><td style = \"text-align: right;\">7.77778 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">268.617 K</td><td style = \"text-align: right;\">-5.89 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">207</td><td style = \"text-align: left;\">1975-04-25</td><td style = \"text-align: right;\">7.5 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">275.728 K</td><td style = \"text-align: right;\">-5.68701 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">208</td><td style = \"text-align: left;\">1975-04-26</td><td style = \"text-align: right;\">6.38889 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">282.562 K</td><td style = \"text-align: right;\">-5.49976 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">209</td><td style = \"text-align: left;\">1975-04-27</td><td style = \"text-align: right;\">7.5 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">288.284 K</td><td style = \"text-align: right;\">-5.349 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">210</td><td style = \"text-align: left;\">1975-04-28</td><td style = \"text-align: right;\">6.11111 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">295.118 K</td><td style = \"text-align: right;\">-5.17477 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">211</td><td style = \"text-align: left;\">1975-04-29</td><td style = \"text-align: right;\">7.22222 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">300.562 K</td><td style = \"text-align: right;\">-5.0413 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">212</td><td style = \"text-align: left;\">1975-04-30</td><td style = \"text-align: right;\">10.0 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">307.118 K</td><td style = \"text-align: right;\">-4.88552 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">213</td><td style = \"text-align: left;\">1975-05-01</td><td style = \"text-align: right;\">10.5556 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">316.451 K</td><td style = \"text-align: right;\">-4.67193 K</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccc}\n",
       "\t& t & T & C & F & Hc\\\\\n",
       "\t\\hline\n",
       "\t& Date & Quantity… & Quantity… & Quantity… & Quantity…\\\\\n",
       "\t\\hline\n",
       "\t1 & 1974-10-01 & 16.3889 °C & 0.0 K & 0.0 K & -4.6808 K \\\\\n",
       "\t2 & 1974-10-02 & 14.4444 °C & 0.0 K & 0.0 K & -4.6808 K \\\\\n",
       "\t3 & 1974-10-03 & 11.1111 °C & 0.0 K & 0.0 K & -4.6808 K \\\\\n",
       "\t4 & 1974-10-04 & 10.0 °C & 0.0 K & 0.0 K & -4.6808 K \\\\\n",
       "\t5 & 1974-10-05 & 9.16667 °C & 0.0 K & 0.0 K & -4.6808 K \\\\\n",
       "\t6 & 1974-10-06 & 9.16667 °C & -0.504156 K & 0.0 K & -4.80303 K \\\\\n",
       "\t7 & 1974-10-07 & 11.9444 °C & -1.00831 K & 0.0 K & -4.9245 K \\\\\n",
       "\t8 & 1974-10-08 & 13.3333 °C & -1.00831 K & 0.0 K & -4.9245 K \\\\\n",
       "\t9 & 1974-10-09 & 10.5556 °C & -1.00831 K & 0.0 K & -4.9245 K \\\\\n",
       "\t10 & 1974-10-10 & 11.3889 °C & -1.00831 K & 0.0 K & -4.9245 K \\\\\n",
       "\t11 & 1974-10-11 & 12.7778 °C & -1.00831 K & 0.0 K & -4.9245 K \\\\\n",
       "\t12 & 1974-10-12 & 12.2222 °C & -1.00831 K & 0.0 K & -4.9245 K \\\\\n",
       "\t13 & 1974-10-13 & 10.0 °C & -1.00831 K & 0.0 K & -4.9245 K \\\\\n",
       "\t14 & 1974-10-14 & 9.16667 °C & -1.00831 K & 0.0 K & -4.9245 K \\\\\n",
       "\t15 & 1974-10-15 & 10.5556 °C & -1.51247 K & 0.0 K & -5.04522 K \\\\\n",
       "\t16 & 1974-10-16 & 10.5556 °C & -1.51247 K & 0.0 K & -5.04522 K \\\\\n",
       "\t17 & 1974-10-17 & 10.0 °C & -1.51247 K & 0.0 K & -5.04522 K \\\\\n",
       "\t18 & 1974-10-18 & 9.16667 °C & -1.51247 K & 0.0 K & -5.04522 K \\\\\n",
       "\t19 & 1974-10-19 & 7.5 °C & -2.01662 K & 0.0 K & -5.16519 K \\\\\n",
       "\t20 & 1974-10-20 & 8.88889 °C & -4.18745 K & 0.0 K & -5.67858 K \\\\\n",
       "\t21 & 1974-10-21 & 5.83333 °C & -4.96938 K & 0.0 K & -5.85859 K \\\\\n",
       "\t22 & 1974-10-22 & 6.38889 °C & -8.80687 K & 0.0 K & -6.73352 K \\\\\n",
       "\t23 & 1974-10-23 & 6.94444 °C & -12.0888 K & 0.0 K & -7.44657 K \\\\\n",
       "\t24 & 1974-10-24 & 6.94444 °C & -14.8152 K & 0.0 K & -8.01509 K \\\\\n",
       "\t25 & 1974-10-25 & 8.05556 °C & -17.5416 K & 0.0 K & -8.5646 K \\\\\n",
       "\t26 & 1974-10-26 & 9.44444 °C & -19.1568 K & 0.0 K & -8.87928 K \\\\\n",
       "\t27 & 1974-10-27 & 7.77778 °C & -19.3832 K & 0.0 K & -8.9225 K \\\\\n",
       "\t28 & 1974-10-28 & 7.77778 °C & -21.2763 K & 0.0 K & -9.28299 K \\\\\n",
       "\t29 & 1974-10-29 & 6.38889 °C & -23.1693 K & 0.0 K & -9.63511 K \\\\\n",
       "\t30 & 1974-10-30 & 7.77778 °C & -26.4512 K & 0.0 K & -10.2314 K \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m213×5 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m t          \u001b[0m\u001b[1m T          \u001b[0m\u001b[1m C           \u001b[0m\u001b[1m F         \u001b[0m\u001b[1m Hc         \u001b[0m\n",
       "     │\u001b[90m Date       \u001b[0m\u001b[90m Quantity…  \u001b[0m\u001b[90m Quantity…   \u001b[0m\u001b[90m Quantity… \u001b[0m\u001b[90m Quantity…  \u001b[0m\n",
       "─────┼────────────────────────────────────────────────────────────\n",
       "   1 │ 1974-10-01  16.3889 °C        0.0 K      0.0 K   -4.6808 K\n",
       "   2 │ 1974-10-02  14.4444 °C        0.0 K      0.0 K   -4.6808 K\n",
       "   3 │ 1974-10-03  11.1111 °C        0.0 K      0.0 K   -4.6808 K\n",
       "   4 │ 1974-10-04     10.0 °C        0.0 K      0.0 K   -4.6808 K\n",
       "   5 │ 1974-10-05  9.16667 °C        0.0 K      0.0 K   -4.6808 K\n",
       "   6 │ 1974-10-06  9.16667 °C  -0.504156 K      0.0 K  -4.80303 K\n",
       "   7 │ 1974-10-07  11.9444 °C   -1.00831 K      0.0 K   -4.9245 K\n",
       "   8 │ 1974-10-08  13.3333 °C   -1.00831 K      0.0 K   -4.9245 K\n",
       "   9 │ 1974-10-09  10.5556 °C   -1.00831 K      0.0 K   -4.9245 K\n",
       "  10 │ 1974-10-10  11.3889 °C   -1.00831 K      0.0 K   -4.9245 K\n",
       "  11 │ 1974-10-11  12.7778 °C   -1.00831 K      0.0 K   -4.9245 K\n",
       "  ⋮  │     ⋮           ⋮            ⋮           ⋮          ⋮\n",
       " 204 │ 1975-04-22  7.22222 °C   -630.088 K  254.673 K  -6.31285 K\n",
       " 205 │ 1975-04-23  8.05556 °C   -630.088 K  261.228 K  -6.11009 K\n",
       " 206 │ 1975-04-24  7.77778 °C   -630.088 K  268.617 K     -5.89 K\n",
       " 207 │ 1975-04-25      7.5 °C   -630.088 K  275.728 K  -5.68701 K\n",
       " 208 │ 1975-04-26  6.38889 °C   -630.088 K  282.562 K  -5.49976 K\n",
       " 209 │ 1975-04-27      7.5 °C   -630.088 K  288.284 K    -5.349 K\n",
       " 210 │ 1975-04-28  6.11111 °C   -630.088 K  295.118 K  -5.17477 K\n",
       " 211 │ 1975-04-29  7.22222 °C   -630.088 K  300.562 K   -5.0413 K\n",
       " 212 │ 1975-04-30     10.0 °C   -630.088 K  307.118 K  -4.88552 K\n",
       " 213 │ 1975-05-01  10.5556 °C   -630.088 K  316.451 K  -4.67193 K\n",
       "\u001b[36m                                                  192 rows omitted\u001b[0m"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "High_pred_1974 = simulate(ColdHardinessEstimator;\n",
    "    config = @config(calib_config_High, D6_1974_config),\n",
    "    index = :t,\n",
    "    target = [:T, :C, :F, :Hc],\n",
    "    stop = :stop,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b2176755",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>213×5 DataFrame</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">188 rows omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">t</th><th style = \"text-align: left;\">T</th><th style = \"text-align: left;\">C</th><th style = \"text-align: left;\">F</th><th style = \"text-align: left;\">Hc</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Date\" style = \"text-align: left;\">Date</th><th title = \"Unitful.Quantity{Float64, 𝚯, Unitful.FreeUnits{(K,), 𝚯, Unitful.Affine{-5463//20}}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝚯, Unitful.FreeUnits{(K,), 𝚯, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝚯, Unitful.FreeUnits{(K,), 𝚯, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝚯, Unitful.FreeUnits{(K,), 𝚯, nothing}}\" style = \"text-align: left;\">Quantity…</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">1974-10-01</td><td style = \"text-align: right;\">16.3889 °C</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.6808 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">1974-10-02</td><td style = \"text-align: right;\">14.4444 °C</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.6808 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">1974-10-03</td><td style = \"text-align: right;\">11.1111 °C</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.6808 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">1974-10-04</td><td style = \"text-align: right;\">10.0 °C</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.6808 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">1974-10-05</td><td style = \"text-align: right;\">9.16667 °C</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.6808 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: left;\">1974-10-06</td><td style = \"text-align: right;\">9.16667 °C</td><td style = \"text-align: right;\">-0.504156 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.80303 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: left;\">1974-10-07</td><td style = \"text-align: right;\">11.9444 °C</td><td style = \"text-align: right;\">-1.00831 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.9245 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: left;\">1974-10-08</td><td style = \"text-align: right;\">13.3333 °C</td><td style = \"text-align: right;\">-1.00831 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.9245 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: left;\">1974-10-09</td><td style = \"text-align: right;\">10.5556 °C</td><td style = \"text-align: right;\">-1.00831 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.9245 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: left;\">1974-10-10</td><td style = \"text-align: right;\">11.3889 °C</td><td style = \"text-align: right;\">-1.00831 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.9245 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: left;\">1974-10-11</td><td style = \"text-align: right;\">12.7778 °C</td><td style = \"text-align: right;\">-1.00831 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.9245 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: left;\">1974-10-12</td><td style = \"text-align: right;\">12.2222 °C</td><td style = \"text-align: right;\">-1.00831 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.9245 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: left;\">1974-10-13</td><td style = \"text-align: right;\">10.0 °C</td><td style = \"text-align: right;\">-1.00831 K</td><td style = \"text-align: right;\">0.0 K</td><td style = \"text-align: right;\">-4.9245 K</td></tr><tr><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">202</td><td style = \"text-align: left;\">1975-04-20</td><td style = \"text-align: right;\">6.11111 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">242.395 K</td><td style = \"text-align: right;\">-6.71335 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">203</td><td style = \"text-align: left;\">1975-04-21</td><td style = \"text-align: right;\">7.5 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">247.839 K</td><td style = \"text-align: right;\">-6.53267 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">204</td><td style = \"text-align: left;\">1975-04-22</td><td style = \"text-align: right;\">7.22222 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">254.673 K</td><td style = \"text-align: right;\">-6.31285 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">205</td><td style = \"text-align: left;\">1975-04-23</td><td style = \"text-align: right;\">8.05556 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">261.228 K</td><td style = \"text-align: right;\">-6.11009 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">206</td><td style = \"text-align: left;\">1975-04-24</td><td style = \"text-align: right;\">7.77778 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">268.617 K</td><td style = \"text-align: right;\">-5.89 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">207</td><td style = \"text-align: left;\">1975-04-25</td><td style = \"text-align: right;\">7.5 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">275.728 K</td><td style = \"text-align: right;\">-5.68701 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">208</td><td style = \"text-align: left;\">1975-04-26</td><td style = \"text-align: right;\">6.38889 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">282.562 K</td><td style = \"text-align: right;\">-5.49976 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">209</td><td style = \"text-align: left;\">1975-04-27</td><td style = \"text-align: right;\">7.5 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">288.284 K</td><td style = \"text-align: right;\">-5.349 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">210</td><td style = \"text-align: left;\">1975-04-28</td><td style = \"text-align: right;\">6.11111 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">295.118 K</td><td style = \"text-align: right;\">-5.17477 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">211</td><td style = \"text-align: left;\">1975-04-29</td><td style = \"text-align: right;\">7.22222 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">300.562 K</td><td style = \"text-align: right;\">-5.0413 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">212</td><td style = \"text-align: left;\">1975-04-30</td><td style = \"text-align: right;\">10.0 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">307.118 K</td><td style = \"text-align: right;\">-4.88552 K</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">213</td><td style = \"text-align: left;\">1975-05-01</td><td style = \"text-align: right;\">10.5556 °C</td><td style = \"text-align: right;\">-630.088 K</td><td style = \"text-align: right;\">316.451 K</td><td style = \"text-align: right;\">-4.67193 K</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccc}\n",
       "\t& t & T & C & F & Hc\\\\\n",
       "\t\\hline\n",
       "\t& Date & Quantity… & Quantity… & Quantity… & Quantity…\\\\\n",
       "\t\\hline\n",
       "\t1 & 1974-10-01 & 16.3889 °C & 0.0 K & 0.0 K & -4.6808 K \\\\\n",
       "\t2 & 1974-10-02 & 14.4444 °C & 0.0 K & 0.0 K & -4.6808 K \\\\\n",
       "\t3 & 1974-10-03 & 11.1111 °C & 0.0 K & 0.0 K & -4.6808 K \\\\\n",
       "\t4 & 1974-10-04 & 10.0 °C & 0.0 K & 0.0 K & -4.6808 K \\\\\n",
       "\t5 & 1974-10-05 & 9.16667 °C & 0.0 K & 0.0 K & -4.6808 K \\\\\n",
       "\t6 & 1974-10-06 & 9.16667 °C & -0.504156 K & 0.0 K & -4.80303 K \\\\\n",
       "\t7 & 1974-10-07 & 11.9444 °C & -1.00831 K & 0.0 K & -4.9245 K \\\\\n",
       "\t8 & 1974-10-08 & 13.3333 °C & -1.00831 K & 0.0 K & -4.9245 K \\\\\n",
       "\t9 & 1974-10-09 & 10.5556 °C & -1.00831 K & 0.0 K & -4.9245 K \\\\\n",
       "\t10 & 1974-10-10 & 11.3889 °C & -1.00831 K & 0.0 K & -4.9245 K \\\\\n",
       "\t11 & 1974-10-11 & 12.7778 °C & -1.00831 K & 0.0 K & -4.9245 K \\\\\n",
       "\t12 & 1974-10-12 & 12.2222 °C & -1.00831 K & 0.0 K & -4.9245 K \\\\\n",
       "\t13 & 1974-10-13 & 10.0 °C & -1.00831 K & 0.0 K & -4.9245 K \\\\\n",
       "\t14 & 1974-10-14 & 9.16667 °C & -1.00831 K & 0.0 K & -4.9245 K \\\\\n",
       "\t15 & 1974-10-15 & 10.5556 °C & -1.51247 K & 0.0 K & -5.04522 K \\\\\n",
       "\t16 & 1974-10-16 & 10.5556 °C & -1.51247 K & 0.0 K & -5.04522 K \\\\\n",
       "\t17 & 1974-10-17 & 10.0 °C & -1.51247 K & 0.0 K & -5.04522 K \\\\\n",
       "\t18 & 1974-10-18 & 9.16667 °C & -1.51247 K & 0.0 K & -5.04522 K \\\\\n",
       "\t19 & 1974-10-19 & 7.5 °C & -2.01662 K & 0.0 K & -5.16519 K \\\\\n",
       "\t20 & 1974-10-20 & 8.88889 °C & -4.18745 K & 0.0 K & -5.67858 K \\\\\n",
       "\t21 & 1974-10-21 & 5.83333 °C & -4.96938 K & 0.0 K & -5.85859 K \\\\\n",
       "\t22 & 1974-10-22 & 6.38889 °C & -8.80687 K & 0.0 K & -6.73352 K \\\\\n",
       "\t23 & 1974-10-23 & 6.94444 °C & -12.0888 K & 0.0 K & -7.44657 K \\\\\n",
       "\t24 & 1974-10-24 & 6.94444 °C & -14.8152 K & 0.0 K & -8.01509 K \\\\\n",
       "\t25 & 1974-10-25 & 8.05556 °C & -17.5416 K & 0.0 K & -8.5646 K \\\\\n",
       "\t26 & 1974-10-26 & 9.44444 °C & -19.1568 K & 0.0 K & -8.87928 K \\\\\n",
       "\t27 & 1974-10-27 & 7.77778 °C & -19.3832 K & 0.0 K & -8.9225 K \\\\\n",
       "\t28 & 1974-10-28 & 7.77778 °C & -21.2763 K & 0.0 K & -9.28299 K \\\\\n",
       "\t29 & 1974-10-29 & 6.38889 °C & -23.1693 K & 0.0 K & -9.63511 K \\\\\n",
       "\t30 & 1974-10-30 & 7.77778 °C & -26.4512 K & 0.0 K & -10.2314 K \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m213×5 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m t          \u001b[0m\u001b[1m T          \u001b[0m\u001b[1m C           \u001b[0m\u001b[1m F         \u001b[0m\u001b[1m Hc         \u001b[0m\n",
       "     │\u001b[90m Date       \u001b[0m\u001b[90m Quantity…  \u001b[0m\u001b[90m Quantity…   \u001b[0m\u001b[90m Quantity… \u001b[0m\u001b[90m Quantity…  \u001b[0m\n",
       "─────┼────────────────────────────────────────────────────────────\n",
       "   1 │ 1974-10-01  16.3889 °C        0.0 K      0.0 K   -4.6808 K\n",
       "   2 │ 1974-10-02  14.4444 °C        0.0 K      0.0 K   -4.6808 K\n",
       "   3 │ 1974-10-03  11.1111 °C        0.0 K      0.0 K   -4.6808 K\n",
       "   4 │ 1974-10-04     10.0 °C        0.0 K      0.0 K   -4.6808 K\n",
       "   5 │ 1974-10-05  9.16667 °C        0.0 K      0.0 K   -4.6808 K\n",
       "   6 │ 1974-10-06  9.16667 °C  -0.504156 K      0.0 K  -4.80303 K\n",
       "   7 │ 1974-10-07  11.9444 °C   -1.00831 K      0.0 K   -4.9245 K\n",
       "   8 │ 1974-10-08  13.3333 °C   -1.00831 K      0.0 K   -4.9245 K\n",
       "   9 │ 1974-10-09  10.5556 °C   -1.00831 K      0.0 K   -4.9245 K\n",
       "  10 │ 1974-10-10  11.3889 °C   -1.00831 K      0.0 K   -4.9245 K\n",
       "  11 │ 1974-10-11  12.7778 °C   -1.00831 K      0.0 K   -4.9245 K\n",
       "  ⋮  │     ⋮           ⋮            ⋮           ⋮          ⋮\n",
       " 204 │ 1975-04-22  7.22222 °C   -630.088 K  254.673 K  -6.31285 K\n",
       " 205 │ 1975-04-23  8.05556 °C   -630.088 K  261.228 K  -6.11009 K\n",
       " 206 │ 1975-04-24  7.77778 °C   -630.088 K  268.617 K     -5.89 K\n",
       " 207 │ 1975-04-25      7.5 °C   -630.088 K  275.728 K  -5.68701 K\n",
       " 208 │ 1975-04-26  6.38889 °C   -630.088 K  282.562 K  -5.49976 K\n",
       " 209 │ 1975-04-27      7.5 °C   -630.088 K  288.284 K    -5.349 K\n",
       " 210 │ 1975-04-28  6.11111 °C   -630.088 K  295.118 K  -5.17477 K\n",
       " 211 │ 1975-04-29  7.22222 °C   -630.088 K  300.562 K   -5.0413 K\n",
       " 212 │ 1975-04-30     10.0 °C   -630.088 K  307.118 K  -4.88552 K\n",
       " 213 │ 1975-05-01  10.5556 °C   -630.088 K  316.451 K  -4.67193 K\n",
       "\u001b[36m                                                  192 rows omitted\u001b[0m"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Low_pred_1974 = simulate(ColdHardinessEstimator;\n",
    "    config = @config(calib_config_High, D6_1974_config),\n",
    "    index = :t,\n",
    "    target = [:T, :C, :F, :Hc],\n",
    "    stop = :stop,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94479d33",
   "metadata": {},
   "source": [
    "# Visualization\n",
    "The blue line in the plots below shows the model estimated cold hardiness based on daily average temperature and parameters derived from calibration for each seed source. The points show the observed cold hardiness values. All y axes are in LT50 in C and x axes are date based."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "ab275b47",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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      "text/plain": [
       "\"<Cropbox.Plot{Gadfly.Plot}>\""
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#High Elevation Seed Source Model\n",
    "init = Date(1974, 10, 01)\n",
    "last = Date(1975, 05, 01)\n",
    "p74H = visualize(ColdHardinessEstimator, :t, :Hc;\n",
    "    config = (calib_config_High, D6_1974_config),\n",
    "    stop = :stop,\n",
    "    kind = :line,\n",
    "    xlim = ((init, last)),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "fcfe993c",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
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       "      <g class=\"primitive\">\n",
       "        <text text-anchor=\"middle\" dy=\"0.35em\" transform=\"rotate(-90,0, 2)\">Hc (K)</text>\n",
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       "  </g>\n",
       "</g>\n",
       "<defs>\n",
       "  <clipPath id=\"img-19f79c36-13\">\n",
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       "  </clipPath>\n",
       "</defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "\"<Cropbox.Plot{Gadfly.Plot}>\""
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#High Elevation Seed Source Model Fit\n",
    "plot!(p74H, Hc_Obs_High, :date, :Hc, kind=:scatter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "bc9a21e8",
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "\"<Cropbox.Plot{Gadfly.Plot}>\""
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     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Low Elevation Seed Source Model\n",
    "init = Date(1974, 10, 01)\n",
    "last = Date(1975, 05, 01)\n",
    "p74L = visualize(ColdHardinessEstimator, :t, :Hc;\n",
    "    config = (calib_config_Low, D6_1974_config),\n",
    "    stop = :stop,\n",
    "    kind = :line,\n",
    "    xlim = ((init, last)),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "0f5ee790",
   "metadata": {},
   "outputs": [
    {
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       "                  <text dy=\"-1.2em\">1977-11-09<tspan x=\"0\" dy=\"1.1000em\">-14.0</tspan></text>\n",
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       "                  <text dy=\"-1.2em\">1977-10-26<tspan x=\"0\" dy=\"1.1000em\">-9.2</tspan></text>\n",
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       "            <g fill-opacity=\"0\" ilabel=\"21RGBA{Float32}(0.83092886f0,0.7934697f0,0.22566332f0,1.0f0)\" class=\"datatip\" id=\"img-466669ba-88\">\n",
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       "          <g class=\"color_RGBA{Float32}(0.83092886f0,0.7934697f0,0.22566332f0,1.0f0)\" id=\"img-466669ba-90\">\n",
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       "            <g fill-opacity=\"0\" ilabel=\"20RGBA{Float32}(0.83092886f0,0.7934697f0,0.22566332f0,1.0f0)\" class=\"datatip\" id=\"img-466669ba-93\">\n",
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       "          </g>\n",
       "          <g class=\"color_RGBA{Float32}(0.83092886f0,0.7934697f0,0.22566332f0,1.0f0)\" id=\"img-466669ba-95\">\n",
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       "            <g fill-opacity=\"0\" ilabel=\"19RGBA{Float32}(0.83092886f0,0.7934697f0,0.22566332f0,1.0f0)\" class=\"datatip\" id=\"img-466669ba-98\">\n",
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       "            <g fill-opacity=\"0\" ilabel=\"17RGBA{Float32}(0.83092886f0,0.7934697f0,0.22566332f0,1.0f0)\" class=\"datatip\" id=\"img-466669ba-108\">\n",
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       "          <g class=\"color_RGBA{Float32}(0.83092886f0,0.7934697f0,0.22566332f0,1.0f0)\" id=\"img-466669ba-110\">\n",
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       "            <g fill-opacity=\"0\" ilabel=\"16RGBA{Float32}(0.83092886f0,0.7934697f0,0.22566332f0,1.0f0)\" class=\"datatip\" id=\"img-466669ba-113\">\n",
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       "          </g>\n",
       "          <g class=\"color_RGBA{Float32}(0.83092886f0,0.7934697f0,0.22566332f0,1.0f0)\" id=\"img-466669ba-115\">\n",
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       "            <g fill-opacity=\"0\" ilabel=\"15RGBA{Float32}(0.83092886f0,0.7934697f0,0.22566332f0,1.0f0)\" class=\"datatip\" id=\"img-466669ba-118\">\n",
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       "          </g>\n",
       "          <g class=\"color_RGBA{Float32}(0.83092886f0,0.7934697f0,0.22566332f0,1.0f0)\" id=\"img-466669ba-120\">\n",
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       "            <g fill-opacity=\"0\" ilabel=\"14RGBA{Float32}(0.83092886f0,0.7934697f0,0.22566332f0,1.0f0)\" class=\"datatip\" id=\"img-466669ba-123\">\n",
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       "          </g>\n",
       "          <g class=\"color_RGBA{Float32}(0.83092886f0,0.7934697f0,0.22566332f0,1.0f0)\" id=\"img-466669ba-125\">\n",
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       "            <g fill-opacity=\"0\" ilabel=\"13RGBA{Float32}(0.83092886f0,0.7934697f0,0.22566332f0,1.0f0)\" class=\"datatip\" id=\"img-466669ba-128\">\n",
       "              <g transform=\"translate(412.31,52.49)\" id=\"img-466669ba-129\">\n",
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       "                  <text dy=\"-1.2em\">1976-11-23<tspan x=\"0\" dy=\"1.1000em\">-15.4</tspan></text>\n",
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       "          </g>\n",
       "          <g class=\"color_RGBA{Float32}(0.83092886f0,0.7934697f0,0.22566332f0,1.0f0)\" id=\"img-466669ba-130\">\n",
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       "            <g fill-opacity=\"0\" ilabel=\"12RGBA{Float32}(0.83092886f0,0.7934697f0,0.22566332f0,1.0f0)\" class=\"datatip\" id=\"img-466669ba-133\">\n",
       "              <g transform=\"translate(402.82,28.65)\" id=\"img-466669ba-134\">\n",
       "                <g class=\"primitive\">\n",
       "                  <text dy=\"-1.2em\">1976-11-04<tspan x=\"0\" dy=\"1.1000em\">-8.9</tspan></text>\n",
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       "              </g>\n",
       "            </g>\n",
       "          </g>\n",
       "          <g class=\"color_RGBA{Float32}(0.83092886f0,0.7934697f0,0.22566332f0,1.0f0)\" id=\"img-466669ba-135\">\n",
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       "            <g fill-opacity=\"0\" ilabel=\"11RGBA{Float32}(0.83092886f0,0.7934697f0,0.22566332f0,1.0f0)\" class=\"datatip\" id=\"img-466669ba-138\">\n",
       "              <g transform=\"translate(394.33,16.91)\" id=\"img-466669ba-139\">\n",
       "                <g class=\"primitive\">\n",
       "                  <text dy=\"-1.2em\">1976-10-18<tspan x=\"0\" dy=\"1.1000em\">-5.7</tspan></text>\n",
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       "          </g>\n",
       "          <g class=\"color_RGBA{Float32}(0.83092886f0,0.7934697f0,0.22566332f0,1.0f0)\" id=\"img-466669ba-140\">\n",
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       "            <g fill-opacity=\"0\" ilabel=\"10RGBA{Float32}(0.83092886f0,0.7934697f0,0.22566332f0,1.0f0)\" class=\"datatip\" id=\"img-466669ba-143\">\n",
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       "                  <text dy=\"-1.2em\">1976-10-07<tspan x=\"0\" dy=\"1.1000em\">-5.7</tspan></text>\n",
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       "          </g>\n",
       "          <g class=\"color_RGBA{Float32}(0.83092886f0,0.7934697f0,0.22566332f0,1.0f0)\" id=\"img-466669ba-145\">\n",
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       "            <g fill-opacity=\"0\" ilabel=\"9RGBA{Float32}(0.83092886f0,0.7934697f0,0.22566332f0,1.0f0)\" class=\"datatip\" id=\"img-466669ba-148\">\n",
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       "          </g>\n",
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       "          </g>\n",
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       "                  <text dy=\"-1.2em\">1975-04-15<tspan x=\"0\" dy=\"1.1000em\">-8.8</tspan></text>\n",
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       "        <text text-anchor=\"middle\" dy=\"0.35em\" transform=\"rotate(-90,0, 2)\">Hc (K)</text>\n",
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       "<defs>\n",
       "  <clipPath id=\"img-466669ba-13\">\n",
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       "</defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "\"<Cropbox.Plot{Gadfly.Plot}>\""
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Low Elevation Seed Source Model Fit\n",
    "plot!(p74L, Hc_Obs_Low, :date, :Hc, kind=:scatter)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69acf326",
   "metadata": {},
   "source": [
    "# Evaluation\n",
    "Model fit is evaluated below. The statistic used is RMSE, which allow error to be in demonstrated in the same unit as the model. So RMSE can be considered as an average of how much error there is between preidcitons and observations. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "994463db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.313728944813495 K"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evaluate(ColdHardinessEstimator,  LowTest;\n",
    "    config= @config(calib_config_Low, D6_1974_config), \n",
    "    index = :date,\n",
    "    target = :Hc,\n",
    "    stop = :stop,\n",
    "    metric = :rmse,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "25e9ea1d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7921563820280066 K"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evaluate(ColdHardinessEstimator,  HighTest;\n",
    "    config= @config(calib_config_High, D6_1974_config), \n",
    "    index = :date,\n",
    "    target = :Hc,\n",
    "    stop = :stop,\n",
    "    metric = :rmse,\n",
    ")"
   ]
  }
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